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2022-05-23
|
Global existence, uniqueness and $L^{\infty}$-bound of weak solutions of fractional time-space Keller-Segel system
|
This paper studies the properties of weak solutions to a class of space-time
fractional parabolic-elliptic Keller-Segel equations with logistic source terms
in $\mathbb{R}^{n}$, $n\geq 2$. The global existence and $L^{\infty}$-bound of
weak solutions are established. We mainly divide the damping coefficient into
two cases: (i) $b>1-\frac{\alpha}{n}$, for any initial value and birth rate;
(ii) $0<b\leq 1-\frac{\alpha}{n}$, for small initial value and small birth
rate. The existence result is obtained by verifying the existence of a solution
to the constructed regularization equation and incorporate the generalized
compactness criterion of time fractional partial differential equation. At the
same time, we get the $L^{\infty}$-bound of weak solutions by establishing the
fractional differential inequality and using the Moser iterative method.
Furthermore, we prove the uniqueness of weak solutions by using the
hyper-contractive estimates when the damping coefficient is strong. Finally, we
also propose a blow-up criterion for weak solutions, that is, if a weak
solution blows up in finite time, then for all $h>q$, the $L^{h}$-norms of the
weak solution blow up at the same time.
|
2205.11041v1
|
2022-05-23
|
Schur complement dominant operator matrices
|
We propose a method for the spectral analysis of unbounded operator matrices
in a general setting which fully abstains from standard perturbative arguments.
Rather than requiring the matrix to act in a Hilbert space $\mathcal{H}$, we
extend its action to a suitable distributional triple $\mathcal{D} \subset
\mathcal{H} \subset \mathcal{D}_-$ and restrict it to its maximal domain in
$\mathcal{H}$. The crucial point in our approach is the choice of the spaces
$\mathcal{D}$ and $\mathcal{D}_-$ which are essentially determined by the Schur
complement of the matrix. We show spectral equivalence between the resulting
operator matrix in $\mathcal{H}$ and its Schur complement, which allows to pass
from a suitable representation of the Schur complement (e.g. by generalised
form methods) to a representation of the operator matrix. We thereby generalise
classical spectral equivalence results imposing standard dominance patterns.
The abstract results are applied to damped wave equations with possibly
unbounded and/or singular damping, to Dirac operators with Coulomb-type
potentials, as well as to generic second order matrix differential operators.
By means of our methods, previous regularity assumptions can be weakened
substantially.
|
2205.11653v1
|
2022-05-24
|
Extensions and Analysis of an Iterative Solution of the Helmholtz Equation via the Wave Equation
|
In this paper we extend analysis of the WaveHoltz iteration -- a time-domain
iterative method for the solution of the Helmholtz equation. We expand the
previous analysis of energy conserving problems and prove convergence of the
WaveHoltz iteration for problems with impedance boundary conditions in a single
spatial dimension. We then consider interior Dirichlet/Neumann problems with
damping in any spatial dimension, and show that for a sufficient level of
damping the WaveHoltz iteration converges in a number of iteration independent
of the frequency. Finally, we present a discrete analysis of the WaveHoltz
iteration for a family of higher order time-stepping schemes. We show that the
fixed-point of the discrete WaveHoltz iteration converges to the discrete
Helmholtz solution with the order of the time-stepper chosen. We present
numerical examples and demonstrate that it is possible to completely remove
time discretization error from the WaveHoltz solution through careful analysis
of the discrete iteration together with updated quadrature formulas.
|
2205.12349v1
|
2022-05-31
|
Phonon decay in 1D atomic Bose quasicondensates via Beliaev-Landau damping
|
In a 1D Bose gas, there is no non-trivial scattering channel involving three
Bogoliubov quasiparticles that conserves both energy and momentum.
Nevertheless, we show that such 3-wave mixing processes (Beliaev and Landau
damping) account for their decay via interactions with thermal fluctuations.
Within an appropriate time window where the Fermi Golden Rule is expected to
apply, the occupation number of the initially occupied mode decays
exponentially and the rate takes a simple analytic form. The result is shown to
compare favorably with simulations based on the Truncated Wigner Approximation.
It is also shown that the same processes slow down the exponential growth of
phonons induced by a parametric oscillation.
|
2205.15826v2
|
2022-06-02
|
Bistability in dissipatively coupled cavity magnonics
|
Dissipative coupling of resonators arising from their cooperative dampings to
a common reservoir induces intriguingly new physics such as energy level
attraction. In this study, we report the nonlinear properties in a
dissipatively coupled cavity magnonic system. A magnetic material YIG (yttrium
iron garnet) is placed at the magnetic field node of a Fabry-Perot-like
microwave cavity such that the magnons and cavity photons are dissipatively
coupled. Under high power excitation, a nonlinear effect is observed in the
transmission spectra, showing bistable behaviors. The observed bistabilities
are manifested as clockwise, counterclockwise, and butterfly-like hysteresis
loops with different frequency detuning. The experimental results are well
explained as a Duffing oscillator dissipatively coupled with a harmonic one and
the required trigger condition for bistability could be determined
quantitatively by the coupled oscillator model. Our results demonstrate that
the magnon damping has been suppressed by the dissipative interaction, which
thereby reduces the threshold for conventional magnon Kerr bistability. This
work sheds light upon potential applications in developing low power
nonlinearity devices, enhanced anharmonicity sensors and for exploring the
non-Hermitian physics of cavity magnonics in the nonlinear regime.
|
2206.01231v1
|
2022-06-02
|
Impact of Frequency Support by Wind Turbines on Small-Signal Stability of Power Systems
|
Rising wind energy integration, accompanied by a decreasing level of system
inertia, requires additional sources of ancillary services. Wind turbines based
on doubly fed induction generators (DFIG) can provide inertial and primary
frequency support, when equipped with specific controls. This paper
investigates the effect of frequency support provision by DFIGs on the
small-signal stability of power systems. To this end, a modified version of the
Kundur two-area test system is employed to analyze different scenarios. Wind
energy generation is either added to the existing system or displaces part of
the synchronous generation. Simulations show that primary frequency support
tends to improve the damping of electromechanical oscillations and deteriorate
it for converter control-based ones. On the other hand, inertial response may
be either beneficial, detrimental or negligible to damping, depending on the
tuning of control parameters.
|
2206.01237v1
|
2022-06-03
|
An Assessment Of Full-Wave Effects On Maxwellian Lower-Hybrid Wave Damping
|
Lower-hybrid current drive (LHCD) actuators are important components of
modern day fusion experiments as well as proposed fusion reactors. However,
simulations of LHCD often differ substantially from experimental results, and
from each other, especially in the inferred power deposition profile shape.
Here we investigate some possible causes of this discrepancy; "full-wave"
effects such as interference and diffraction, which are omitted from standard
raytracing simulations and the breakdown of the raytracing near reflections and
caustics. We compare raytracing simulations to state-of-the-art full-wave
simulations using matched hot-plasma dielectric tensors in realistic tokamak
scenarios for the first time. We show that differences between full-wave
simulations and raytracing in previous work were primarily due to numerical and
physical inconsistencies in the simulations, and we demonstrate that good
agreement between raytracing and converged full-wave simulations can be
obtained in reactor relevant-scenarios with large ray caustics and in
situations with weak damping.
|
2206.01773v2
|
2022-06-06
|
Fermi spin polaron and dissipative Fermi-polaron Rabi dynamics
|
We consider a spin impurity with multiple energy levels moving in a
non-interacting Fermi sea, and theoretically solve this Fermi spin polaron
problem at nonzero temperature by using a non-self-consistent many-body
$T$-matrix theory. We focus on the simplest case with spin half, where the two
energy states of the impurity are coupled by a Rabi flip term. At small Rabi
coupling, the impurity exhibits damped Rabi oscillations, where the decoherence
is caused by the interaction with the Fermi sea, as recently reported in Fermi
polaron experiments with ultracold atoms. We investigate the dependence of Rabi
oscillations on the Rabi coupling strength and examine the additional nonlinear
damping due to large Rabi coupling. At finite temperature and at nonzero
impurity concentration, the impurity can acquire a pronounced momentum
distribution. We show that the momentum/thermal average can sizably reduce the
visibility of Rabi oscillations. We compare our theoretical predictions to the
recent experimental data and find a good agreement without any adjustable
parameter.
|
2206.02317v4
|
2022-06-09
|
A deep learning method for the trajectory reconstruction of cosmic rays with the DAMPE mission
|
A deep learning method for the particle trajectory reconstruction with the
DAMPE experiment is presented. The developed algorithms constitute the first
fully machine-learned track reconstruction pipeline for space astroparticle
missions. Significant performance improvements over the standard
hand-engineered algorithms are demonstrated. Thanks to the better accuracy, the
developed algorithms facilitate the identification of the particle absolute
charge with the tracker in the entire energy range, opening a door to the
measurements of cosmic-ray proton and helium spectra at extreme energies,
towards the PeV scale, hardly achievable with the standard track reconstruction
methods. In addition, the developed approach demonstrates an unprecedented
accuracy in the particle direction reconstruction with the calorimeter at high
deposited energies, above several hundred GeV for hadronic showers and above a
few tens of GeV for electromagnetic showers.
|
2206.04532v2
|
2022-06-09
|
Excitation-damping quantum channels
|
We study a class of quantum channels describing a quantum system, split into
the direct sum of an excited and a ground sector, undergoing a one-way transfer
of population from the former to the latter; this construction, which provides
a generalization of the amplitude-damping qubit channel, can be regarded as a
way to upgrade a trace non-increasing quantum operation, defined on the excited
sector, to a possibly trace preserving operation on a larger Hilbert space. We
provide necessary and sufficient conditions for the complete positivity of such
channels, and we also show that complete positivity is equivalent to simple
positivity whenever the ground sector is one-dimensional. Finally, we examine
the time-dependent scenario and characterize all CP-divisible channels and
Markovian semigroups belonging to this class.
|
2206.04623v1
|
2022-06-16
|
Modeling, robust control synthesis and worst-case analysis for an on-orbit servicing mission with large flexible spacecraft
|
This paper outlines a complete methodology for modeling an on-orbit servicing
mission scenario and designing a feedback control system for the attitude
dynamics that is guaranteed to robustly meet pointing requirements, despite
model uncertainties as well as large inertia and flexibility changes throughout
the mission scenario. A model of the uncertain plant was derived, which fully
captures the dynamics and couplings between all subsystems as well as the
decoupled/coupled configurations of the chaser/target system in a single linear
fractional representation (LFR). In addition, a new approach is proposed to
model and analyze a closed-loop kinematic chain formed by the chaser and the
target spacecraft through the chaser's robotic arm, which uses two local
spring-damper systems with uncertain damping and stiffness. This approach
offers the possibility to model the dynamical behaviour of a docking mechanism
with dynamic stiffness and damping. The controller was designed by taking into
account all the interactions between subsystems and uncertainties as well as
the time-varying and coupled flexible dynamics. Lastly, the robust stability
and worst-case performances were assessed by means of a structured singular
value analysis.
|
2206.08324v1
|
2022-06-23
|
Anisotropic magnon damping by zero-temperature quantum fluctuations in ferromagnetic CrGeTe$_3$
|
Spin and lattice are two fundamental degrees of freedom in a solid, and their
fluctuations about the equilibrium values in a magnetic ordered crystalline
lattice form quasiparticles termed magnons (spin waves) and phonons (lattice
waves), respectively. In most materials with strong spin-lattice coupling
(SLC), the interaction of spin and lattice induces energy gaps in the spin wave
dispersion at the nominal intersections of magnon and phonon modes. Here we use
neutron scattering to show that in the two-dimensional (2D) van der Waals
honeycomb lattice ferromagnetic CrGeTe3, spin waves propagating within the 2D
plane exhibit an anomalous dispersion, damping, and break-down of quasiparticle
conservation, while magnons along the c axis behave as expected for a local
moment ferromagnet. These results indicate the presence of dynamical SLC
arising from the zero-temperature quantum fluctuations in CrGeTe3, suggesting
that the observed in-plane spin waves are mixed spin and lattice quasiparticles
fundamentally different from pure magnons and phonons.
|
2206.11962v1
|
2022-06-28
|
Strongly damped wave equations with mass-like terms of the logarithmic-Laplacian
|
We consider strongly damped wave equations with logarithmic mass-like terms
with a parameter $\theta \in (0; 1]$. This research is a part of a series of
wave equations that was initiated by Char\~ao-Ikehata [6],
Char\~ao-D'Abbicco-Ikehata considered in [5] depending on a parameter $\theta
\in (1/2,1)$ and Piske- Char\~ao-Ikehata [26] for small parameter $\theta \in
(0,1/2)$. We derive a leading term (as time goes to infinity) of the solution,
and by using it, a growth and a decay property of the solution itself can be
precisely studied in terms of L^2-norm. An interesting aspect appears in the
case of n = 1, roughly speaking, a small $\theta$ produces a diffusive
property, and a large $\theta$ gives a kind of singularity, expressed by growth
rates.
|
2206.13713v1
|
2022-08-10
|
Phonon renormalization effects accompanying the 6 K anomaly in the Quantum Spin Liquid Candidate $κ$-(BEDT-TTF)$_{2}$Cu$_{2}$(CN)$_{3}$
|
The low-temperature state of the quantum spin liquid candidate
$\kappa$-(BEDT-TTF)$_{2}$Cu$_{2}$(CN)$_{3}$ emerges via an anomaly at
$T^{*}\sim6$ K. Although signatures of this anomaly have been revealed in
various quantities, its origin has remained unclear. Here we report inelastic
neutron scattering measurements on single crystals of
$\kappa$-(BEDT-TTF)$_{2}$Cu$_{2}$(CN)$_{3}$, aiming at studying phonon
renormalization effects at $T^{*}$. A drastic change was observed in the phonon
damping across $T^{*}$ for a breathing mode of BEDT-TTF dimers at $E=4.7$ meV.
The abrupt change in the phonon damping is attributed to a phase transition
into a valence bond solid state based on an effective model describing the
spin-charge coupling in this dimer-Mott system.
|
2208.05096v2
|
2022-08-16
|
Particle dynamics on torsional galilean spacetimes
|
We study free particle motion on homogeneous kinematical spacetimes of
galilean type. The three well-known cases of Galilei and (A)dS--Galilei
spacetimes are included in our analysis, but our focus will be on the
previously unexplored torsional galilean spacetimes. We show how in well-chosen
coordinates free particle motion becomes equivalent to the dynamics of a damped
harmonic oscillator, with the damping set by the torsion. The realization of
the kinematical symmetry algebra in terms of conserved charges is subtle and
comes with some interesting surprises, such as a homothetic version of
hamiltonian vector fields and a corresponding generalization of the Poisson
bracket. We show that the Bargmann extension is universal to all galilean
kinematical symmetries, but also that it is no longer central for nonzero
torsion. We also present a geometric interpretation of this fact through the
Eisenhart lift of the dynamics.
|
2208.07611v2
|
2022-08-27
|
Quantum Langevin Equation of a spin in a magnetic field : an analysis
|
We derive a quantum Langevin equation for a quantum spin in the presence of a
magnetic field and study its dynamics in the Markovian limit using the Ohmic
bath model. We extend our analysis to the Drude bath with a finite memory. We
study the time evolution of the expectation values of the magnetic moments. The
spin auto-correlation functions exhibit a damped oscillatory behaviour with the
randomization time being determined by the damping rate and also the memory
time for the Drude bath model. We also analyse the spin response function of
the system for the Ohmic bath model. Our results are consistent with findings
in cold atom experiments. In addition we make predictions which can be tested
in future ultra cold atom experiments.
|
2208.12989v1
|
2022-09-01
|
\textit{Ab initio} study on spin fluctuations of itinerant kagome magnet FeSn
|
Kagome antiferromagnetic metal FeSn has become an attracting platform for the
exploration of novel electronic states, such as topological Dirac states and
the formation of flat bands by localized electrons. Apart from the electronic
properties, Dirac magnons and flat magnon bands have also been proposed by
applying simplified Heisenberg models to kagome magnetic systems.Inelastic
neutron scattering studies on FeSn found well defined magnon dispersions at low
energies,but magnons at high energies are strongly dampled, which can not be
explained by localized spin models. In this paper, we utilize both linear spin
wave theory and time-dependent density functional perturbation theory to
investigate spin fluctuations of FeSn. Through the comparison of calculated
spin wave spectra and Stoner continuum, we explicitly show that the damping of
magnons at high energies are due to the Landau damping, and the appearance of
high energy optical-magnon like branches at the M and K point are resulted by
relatively low Stoner excitation intensity at those regions.
|
2209.00187v1
|
2022-09-01
|
Comment on "Damping of neutrino oscillations, decoherence and the lengths of neutrino wave packets''
|
We point out three apparent inconsistencies in the treatment of oscillation
coherence from reactor neutrino and source neutrino experiments in recent paper
"Damping of neutrino oscillations, decoherence and the lengths of neutrino wave
packets''. First, that the dependence of the oscillation probability upon the
subsequent interactions of entangled recoil particles implies causality
violations and in some situations superluminal signaling; second, that
integrating over a non-orthogonal basis for the entangled recoil leads to
unphysical effects; and third, that the question of what interactions serve to
measure the position of the initial state particle remains ambiguous. These
points taken together appear to undermine the claim made therein that the
effects of wave packet separation must be strictly unobservable in reactor and
radioactive source based neutrino experiments.
|
2209.00561v1
|
2022-09-02
|
The thermal-orbital evolution of the Earth-Moon system with a subsurface magma ocean and fossil figure
|
Various theories have been proposed to explain the Moon's current inclined
orbit. We test the viability of these theories by reconstructing the
thermal-orbital history of the Moon. We build on past thermal-orbital models
and incorporate the evolution of the lunar figure including a fossil figure
component. Obliquity tidal heating in the lunar magma ocean would have produced
rapid inclination damping, making it difficult for an early inclination to
survive to the present-day. An early inclination is preserved only if the
solid-body of the early Moon were less dissipative than at present. If
instabilities at the Laplace plane transition were the source of the
inclination, then the Moon had to recede slowly, which is consistent with
previous findings of a weakly dissipative early Earth. If collisionless
encounters with planetesimals up to 140 Myr after Moon formation excited the
inclination, then the Moon had to migrate quickly to pass through the Cassini
state transition at 33 Earth radii and reach a period of limited inclination
damping. The fossil figure was likely established before 16 Earth radii to
match the present-day degree-2 gravity field observations.
|
2209.00935v1
|
2022-09-05
|
A new T-compatibility condition and its application to the discretization of the damped time-harmonic Galbrun's equation
|
We consider the approximation of weakly T-coercive operators. The main
property to ensure the convergence thereof is the regularity of the
approximation (in the vocabulary of discrete approximation schemes). In a
previous work the existence of discrete operators $T_n$ which converge to $T$
in a discrete norm was shown to be sufficient to obtain regularity. Although
this framework proved usefull for many applications for some instances the
former assumption is too strong. Thus in the present article we report a weaker
criterium for which the discrete operators $T_n$ only have to converge
point-wise, but in addition a weak T-coercivity condition has to be satisfied
on the discrete level. We apply the new framework to prove the convergence of
certain $H^1$-conforming finite element discretizations of the damped
time-harmonic Galbrun's equation, which is used to model the oscillations of
stars. A main ingredient in the latter analysis is the uniformly stable
invertibility of the divergence operator on certain spaces, which is related to
the topic of divergence free elements for the Stokes equation.
|
2209.01878v2
|
2022-09-06
|
Suppressing Amplitude Damping in Trapped Ions: Discrete Weak Measurements for a Non-unitary Probabilistic Noise Filter
|
The idea of exploiting maximally-entangled states as a resource lies at the
core of several modalities of quantum information processing, including secure
quantum communication, quantum computation, and quantum sensing. However, due
to imperfections during or after the entangling gates used to prepare such
states, the amount of entanglement decreases and their quality as a resource
gets degraded. We introduce a low-overhead protocol to reverse this degradation
by partially filtering out a specific type of noise relevant to many quantum
technologies. We present two trapped-ion schemes for the implementation of a
non-unitary probabilistic filter against amplitude damping noise, which can
protect any maximally-entangled pair from spontaneous photon scattering during
or after the two-qubit trapped-ion entangling gates. This filter can be
understood as a protocol for single-copy quasi-distillation, as it uses only
local operations to realise a reversal operation that can be understood in
terms of weak measurements.
|
2209.02753v1
|
2022-09-10
|
Bulk Viscosity of Relativistic $npeμ$ Matter in Neutron-Star Mergers
|
We discuss the bulk viscosity of hot and dense $npe\mu$ matter arising from
weak-interaction direct Urca processes. We consider two regimes of interest:
(a) the neutrino-transparent regime with $T\leq T_{\rm tr}$ ($T_{\rm tr}\simeq
5\div 10$ MeV is the neutrino-trapping temperature); and (b) the
neutrino-trapped regime with $T\geq T_{\rm tr}$. Nuclear matter is modeled in
relativistic density functional approach with density-dependent parametrization
DDME2. The maximum of the bulk viscosity is achieved at temperatures $T \simeq
5\div 6$ MeV in the neutrino-transparent regime, then it drops rapidly at
higher temperatures where neutrino-trapping occurs. As an astrophysical
application, we estimate the damping timescales of density oscillations by the
bulk viscosity in neutron star mergers and find that, e.g., at the oscillation
frequency $f=10$ kHz, the damping will be very efficient at temperatures $4\leq
T\leq 7$ MeV where the bulk viscosity might affect the evolution of the
post-merger object.
|
2209.04717v1
|
2022-09-11
|
Approximation of Algebraic Riccati Equations with Generators of Noncompact Semigroups
|
In this work, we demonstrate that the Bochner integral representation of the
Algebraic Riccati Equations (ARE) are well-posed without any compactness
assumptions on the coefficient and semigroup operators. From this result, we
then are able to determine that, under some assumptions, the solution to the
Galerkin approximations to these equations are convergent to the infinite
dimensional solution. Going further, we apply this general result to
demonstrate that the finite element approximation to the ARE are optimal for
weakly damped wave semigroup processes in the $H^1(\Omega) \times L^2(\Omega)$
norm. Optimal convergence rates of the functional gain for a weakly damped wave
optimal control system in both the $H^1(\Omega) \times L^2(\Omega)$ and
$L^2(\Omega)\times L^2(\Omega)$ norms are demonstrated in the numerical
examples.
|
2209.04769v5
|
2022-09-11
|
Toward a Framework for Adaptive Impedance Control of an Upper-limb Prosthesis
|
Adapting upper-limb impedance (i.e., stiffness, damping, inertia) is
essential for humans interacting with dynamic environments for executing
grasping or manipulation tasks. On the other hand, control methods designed for
state-of-the-art upper-limb prostheses infer motor intent from surface
electromyography (sEMG) signals in terms of joint kinematics, but they fail to
infer and use the underlying impedance properties of the limb. We present a
framework that allows a human user to simultaneously control the kinematics,
stiffness, and damping of a simulated robot through wrist's flexion-extension.
The framework includes muscle-tendon units and a forward dynamics block to
estimate the motor intent from sEMG signals, and a variable impedance
controller that implements the estimated intent on the robot, allowing the user
to adapt the robot's kinematics and dynamics online. We evaluate our framework
with 8 able-bodied subjects and an amputee during reaching tasks performed in
free space, and in the presence of unexpected external perturbations that
require adaptation of the wrist impedance to ensure stable interaction with the
environment. We experimentally demonstrate that our approach outperforms a
data-driven baseline in terms of its ability to adapt to external
perturbations, overall controllability, and feedback from participants.
|
2209.04937v2
|
2022-09-14
|
Time rescaling of a primal-dual dynamical system with asymptotically vanishing damping
|
In this work, we approach the minimization of a continuously differentiable
convex function under linear equality constraints by a second-order dynamical
system with an asymptotically vanishing damping term. The system under
consideration is a time rescaled version of another system previously found in
the literature. We show fast convergence of the primal-dual gap, the
feasibility measure, and the objective function value along the generated
trajectories. These convergence rates now depend on the rescaling parameter,
and thus can be improved by choosing said parameter appropriately. When the
objective function has a Lipschitz continuous gradient, we show that the
primal-dual trajectory asymptotically converges weakly to a primal-dual optimal
solution to the underlying minimization problem. We also exhibit improved rates
of convergence of the gradient along the primal trajectories and of the adjoint
of the corresponding linear operator along the dual trajectories. Even in the
unconstrained case, some trajectory convergence result seems to be new. We
illustrate the theoretical outcomes through numerical experiments.
|
2209.06438v1
|
2022-09-18
|
Numerical Approximations for the Null Controllers of Structurally Damped Plate Dynamics
|
In this paper, we consider a structurally damped elastic equation under
hinged boundary conditions. Fully-discrete numerical approximation schemes are
generated for the null controllability of these parabolic-like PDEs. We mainly
use finite element method (FEM) and finite difference method (FDM)
approximations to show that the null controllers being approximated via FEM and
FDM exhibit exactly the same asymptotics of the associated minimal energy
function. For this, we appeal to the theory originally given by R. Triggiani
[20] for construction of null controllers of ODE systems. These null
controllers are also amenable to our numerical implementation in which we
discuss the aspects of FEM and FDM numerical approximations and compare both
methodologies. We justify our theoretical results with the numerical
experiments given for both approximation schemes.
|
2209.08486v1
|
2022-09-19
|
Calculating quasinormal modes of Schwarzschild anti-de Sitter black holes using the continued fraction method
|
We investigate the scalar, gravitational, and electromagnetic quasinormal
mode spectra of Schwarzschild anti-de Sitter black holes using the numerical
continued fraction method. The spectra have similar, almost linear structures.
With a few exceptions, the low overtone quasinormal modes are consistent with
previously obtained results in the literature that use other numerical
techniques. The intermediate and high overtone quasinormal modes, in comparison
to the Schwarzschild case, converge very quickly to the asymptotic formulas
previously obtained by analytic monodromy techniques. In addition, we find a
connection between the analytic asymptotic formulas and the purely imaginary
modes. In particular, these formulas can be used to predict the bifurcation of
the lowest damped electromagnetic modes. Finally, we find no high overtone
quasinormal modes with high oscillation frequency and low damping, which had
been previously predicted.
|
2209.09324v3
|
2022-09-20
|
Study of the Global Alignment for the DAMPE Detector
|
The Dark Matter Particle Explorer (DAMPE) is designed as a high energy
particle detector for probing cosmic-rays and $\gamma-$rays in a wide energy
range. The trajectory of the incident particle is mainly measured by the
Silicon-Tungsten tracKer-converter (STK) sub-detector, which heavily depends on
the precise internal alignment correction as well as the accuracy of the global
coordinate system. In this work, we carried out a global alignment method to
validate the potential displacement of these sub-detectors, and particularly
demonstrated that the track reconstruction of STK can well satisfy the required
objectives by means of comparing flight data and simulations.
|
2209.09440v1
|
2022-09-22
|
Open quantum system dynamics of $X$-states: Entanglement sudden death and sudden birth
|
The origin of disentanglement for two specific sub-classes of $X$-states
namely maximally nonlocal mixed states (MNMSs) and maximally entangled mixed
states (MEMSs) is investigated analytically for a physical system consisting of
two spatially separated qubits interacting with a common vacuum bath. The
phenomena of entanglement sudden death (ESD) and the entanglement sudden birth
(ESB) are observed, but the characteristics of ESD and ESB are found to be
different for the case of two photon coherence and single photon coherence
states. The role played by initial coherence for the underlying entanglement
dynamics is investigated. Further, the entanglement dynamics of MNMSs and MEMSs
under different environmental noises namely phase damping, amplitude damping
and RTN noise with respect to the decay and revival of entanglement is
analyzed. It's observed that the single photon coherence states are more robust
against the sudden death of entanglement indicating the usability of such
states in the development of technologies for the practical implementation of
quantum information processing tasks.
|
2209.11190v1
|
2022-09-23
|
Kernel-based quantum regressor models learn non-Markovianity
|
Quantum machine learning is a growing research field that aims to perform
machine learning tasks assisted by a quantum computer. Kernel-based quantum
machine learning models are paradigmatic examples where the kernel involves
quantum states, and the Gram matrix is calculated from the overlap between
these states. With the kernel at hand, a regular machine learning model is used
for the learning process. In this paper we investigate the quantum support
vector machine and quantum kernel ridge models to predict the degree of
non-Markovianity of a quantum system. We perform digital quantum simulation of
amplitude damping and phase damping channels to create our quantum dataset. We
elaborate on different kernel functions to map the data and kernel circuits to
compute the overlap between quantum states. We show that our models deliver
accurate predictions that are comparable with the fully classical models.
|
2209.11655v1
|
2022-09-24
|
Reflectionless Programmable Signal Routers
|
We demonstrate experimentally that reflectionless scattering modes (RSMs), a
generalized version of coherent perfect absorption, can be functionalized to
perform reflectionless programmable signal routing. We achieve versatile
programmability both in terms of operating frequencies and routing
functionality with negligible reflection upon in-coupling, which avoids
unwanted signal-power echoes in radio-frequency or photonic networks. We report
in-situ observations of routing functionalities like wavelength demultiplexing,
including cases where multi-channel excitation requires adapted coherent input
wavefronts. All experiments are performed in the microwave domain based on the
same irregularly shaped cavity with strong modal overlap that is massively
parametrized by a 304-element programmable metasurface. RSMs in our highly
overdamped multi-resonance transport problem are fundamentally intriguing
because the simple critical-coupling picture for reflectionless excitation of
isolated resonances fails spectacularly. We show in simulation that the
distribution of damping rates of scattering singularities broadens under strong
absorption so that weakly damped zeros can be tuned toward functionalized RSMs.
|
2209.11991v1
|
2022-09-30
|
A simple analytical expression of quantum Fisher and Skew information and their dynamics under decoherence channels
|
In statistical estimation theory, it has been shown previously that the
Wigner-Yanase skew information is bounded by the quantum Fisher information
associated with the phase parameter. Besides, the quantum Cram\'er-Rao
inequality is expressed in terms of skew information. Since these two
fundamental quantities are based on the concept of quantum uncertainty, we
derive here their analytical formulas for arbitrary two qubit $X$-states using
the same analytical procedures. A comparison of these two informational
quantifiers for two quasi-Werner states composed of two bipartite superposed
coherent states is examined. Moreover, we investigated the decoherence effects
on such quantities generated by the phase damping, depolarization and amplitude
damping channels. We showed that decoherence strongly influences the quantum
criteria during the evolution and these quantities exhibit similar dynamic
behaviors. This current work is characterized by the fact that these two
concepts play the same role and capture similar properties in quantum
estimation protocols.
|
2209.15593v2
|
2022-10-01
|
Nonlinear features of the superconductor--ferromagnet--superconductor $\varphi_0$ Josephson junction in ferromagnetic resonance region
|
We demonstrate the manifestations of the nonlinear features in magnetic
dynamics and IV-characteristics of the $\varphi_0$ Josephson junction in the
ferromagnetic resonance region. We show that at small values of system
parameters, namely, damping, spin-orbit interaction, and Josephson to magnetic
energy ratio, the magnetic dynamics is reduced to the dynamics of the scalar
Duffing oscillator, driven by the Josephson oscillations. The role of
increasing superconducting current in the resonance region is clarified.
Shifting of the ferromagnetic resonant frequency and the reversal of its
damping dependence due to nonlinearity are demonstrated by the full
Landau-Lifshitz-Gilbert-Josephson system of equations, and in its different
approximations. Finally, we demonstrate the negative differential resistance in
the IV--characteristics, and its correlation with the foldover effect.
|
2210.00366v1
|
2022-10-03
|
Voltage control of frequency, effective damping and threshold current in nano-constriction-based spin Hall nano-oscillators
|
Using micromagnetic simulations, we study the interplay between strongly
voltage-controlled magnetic anisotropy (VCMA), $\Delta K = \pm$200 kJ/m$^3$,
and gate width, $w=$ 10--400 nm, in voltage-gated W/CoFeB/MgO based
nano-constriction spin Hall nano-oscillators. The VCMA modifies the local
magnetic properties such that the magnetodynamics transitions between regimes
of \emph{i}) confinement, \emph{ii}) tuning, and \emph{iii}) separation, with
qualitatively different behavior. We find that the strongest tuning is achieved
for gate widths of the same size as the the constriction width, for which the
effective damping can be increased an order of magnitude compared to its
intrinsic value. As a consequence, voltage control remains efficient over a
very large frequency range, and subsequent manufacturing advances could allow
SHNOs to be easily integrated into next-generation electronics for further
fundamental studies and industrial applications.
|
2210.01042v1
|
2022-10-18
|
Evidence of fresh cosmic ray in galactic plane based on DAMPE measurement of B/C and B/O ratios
|
More and more experiments have identified that the energy spectra of both
primary and secondary cosmic-rays exhibit a hardening above $\sim 200$ GV. Most
recently, the DAMPE experiment has reported a hardening of boron-to-carbon
ratio at $200$ GV. These signs call for modifications of the conventional
cosmic-ray (CR) picture. In this work, we propose that the plethoric secondary
cosmic rays, for example, boron, antiprotons, originate from the hadronic
interactions of freshly accelerated cosmic rays with the interstellar gas near
the sources. We find that secondary-to-primary ratios, for example,
boron-to-carbon, boron-to-oxygen and antiproton-to-proton ratios, could be well
described. The measurements of electrons and positrons could also be accounted
for.
|
2210.09591v2
|
2022-10-19
|
Design and Modeling of a PVDF-TrFe Flexible Wind Energy Harvester
|
This study presents the simulation, experimentation, and design
considerations of a Poly(vinylidene fluoride co-trifluoroethylene)/
Polyethylene Terephthalate (PVDF-TrFe / PET), laser-cut, flexible piezoelectric
energy harvester. It is possible to obtain energy from the environment around
autonomous sensor systems, which can then be used to power various equipment.
This article investigates the actuation means of ambient vibration, which is a
good candidate for using piezoelectric energy harvester (PEH) devices. The
output voltage characteristics were analyzed in a wind test apparatus. Finite
element modeling (FEM) was done for von Mises stress and modal analysis.
Resonance frequency sweeps, quality factors, and damping ratios of the circular
plate were given numerically. For a PVDF-TrFe piezoelectric layer thickness of
18 $\mu$m and 1.5 mm radius, a damping ratio of 0.117 and a quality factor of
4.284 was calculated. $V_{max}$ was calculated as 984 mV from the wind setup
and compared with the FEM outputs.
|
2210.10540v1
|
2022-10-20
|
Parameter analysis in continuous data assimilation for three-dimensional Brinkman-Forchheimer-extended Darcy
|
In this paper, we study analytically the long-time behavior of
three-dimensional Brinkman-Forchheimer-extended Darcy model, in the context
that the parameters related to the damping nonlinear term are unknown. This
work is inspired by the approach firstly introduced for two-dimensional
Navier-Stokes equations by Carlson, Hudson and Larios. We show estimates in L2
and H1 for large-time error between the true solution and the assimilated
solution, which is constructed with the unknown damping parameters and
observational measurements obtained continuously in time from a continuous data
assimilation technique proposed by Azouani, Olson and Titi.
|
2210.11432v1
|
2022-10-21
|
Breathers in lattices with alternating strain-hardening and strain-softening interactions
|
This work focuses on the study of time-periodic solutions, including
breathers, in a nonlinear lattice consisting of elements whose contacts
alternate between strain-hardening and strain-softening. The existence,
stability, and bifurcation structure of such solutions, as well as the system
dynamics in the presence of damping and driving are studied systematically. It
is found that the linear resonant peaks in the system bend toward the frequency
gap in the presence of nonlinearity. The time-periodic solutions that lie
within the frequency gap compare well to Hamiltonian breathers if the damping
and driving are small. In the Hamiltonian limit of the problem, we use a
multiple scale analysis to derive a Nonlinear Schr\"odinger (NLS) equation to
construct both acoustic and optical breathers. The latter compare very well
with the numerically obtained breathers in the Hamiltonian limit.
|
2210.11690v1
|
2022-10-28
|
Two novel families of multiscale staggered patch schemes efficiently simulate large-scale, weakly damped, linear waves
|
Many multiscale wave systems exhibit macroscale emergent behaviour, for
example, the fluid dynamics of floods and tsunamis. Resolving a large range of
spatial scales typically requires a prohibitively high computational cost. The
small dissipation in wave systems poses a significant challenge to further
developing multiscale modelling methods in multiple dimensions. This article
develops and evaluates two families of equation-free multiscale methods on
novel 2D staggered patch schemes, and demonstrates the power and utility of
these multiscale schemes for weakly damped linear waves. A detailed study of
sensitivity to numerical roundoff errors establishes the robustness of
developed staggered patch schemes. Comprehensive eigenvalue analysis over a
wide range of parameters establishes the stability, accuracy, and consistency
of the multiscale schemes. Analysis of the computational complexity shows that
the measured compute times of the multiscale schemes may be 10^5 times smaller
than the compute time for the corresponding full-domain computation. This work
provides the essential foundation for efficient large-scale simulation of
challenging nonlinear multiscale waves.
|
2210.15823v1
|
2022-11-07
|
A role of potential on L^{2}-estimates for some evolution equations
|
In this papwe we consider an effective role of the potential of the wave
equations with/without damping on the L^{2}-estimate of the solution itself. In
the free wave equation case it is known that the L^{2}-norm of the solution
itself generally grows to infinity (as time goes to infinity) in the one and
two dimensional cases, however, by adding the potential with quite generous
conditions one can controle the growth property to get the L^{2}-bounds. This
idea can be also applied to the damped wave equations with potential in order
to get fast energy and L^{2} decay results in the low dimensional case, which
are open for a long period. Applications to heat and plate equations with a
potential can be also studied. In this paper the low dimensional case is a main
target.
|
2211.03389v1
|
2022-11-08
|
Cost-optimal adaptive iterative linearized FEM for semilinear elliptic PDEs
|
We consider scalar semilinear elliptic PDEs where the nonlinearity is
strongly monotone, but only locally Lipschitz continuous. We formulate an
adaptive iterative linearized finite element method (AILFEM) which steers the
local mesh refinement as well as the iterative linearization of the arising
nonlinear discrete equations. To this end, we employ a damped Zarantonello
iteration so that, in each step of the algorithm, only a linear Poisson-type
equation has to be solved. We prove that the proposed AILFEM strategy
guarantees convergence with optimal rates, where rates are understood with
respect to the overall computational complexity (i.e., the computational time).
Moreover, we formulate and test an adaptive algorithm where also the damping
parameter of the Zarantonello iteration is adaptively adjusted. Numerical
experiments underline the theoretical findings.
|
2211.04123v2
|
2022-11-11
|
Radiation reaction effects in relativistic plasmas -- the electrostatic limit
|
We study the evolution of electrostatic plasma waves, using the relativistic
Vlasov equation extended by the Landau-Lifshitz radiation reaction, accounting
for the back-reaction due to the emission of single particle Larmor radiation.
In particular, the Langmuir wave damping is calculated as a function of
wavenumber, initial temperature, and initial electric field amplitude.
Moreover, the background distribution function loses energy in the process, and
we calculate the cooling rate as a function of initial temperature and initial
wave amplitude. Finally, we investigate how the relative magnitude of wave
damping and background cooling varies with the initial parameters. In
particular, it is found that the relative contribution to the energy loss
associated with background cooling decreases slowly with the initial wave
amplitude.
|
2211.06240v1
|
2022-11-14
|
Magnetization Dynamics in Synthetic Antiferromagnets with Perpendicular Magnetic Anisotropy
|
Understanding the rich physics of magnetization dynamics in perpendicular
synthetic antiferromagnets (p-SAFs) is crucial for developing next-generation
spintronic devices. In this work, we systematically investigate the
magnetization dynamics in p-SAFs combining time-resolved magneto-optical Kerr
effect (TR-MOKE) measurements with theoretical modeling. These model analyses,
based on a Landau-Lifshitz-Gilbert approach incorporating exchange coupling,
provide details about the magnetization dynamic characteristics including the
amplitudes, directions, and phases of the precession of p-SAFs under varying
magnetic fields. These model-predicted characteristics are in excellent
quantitative agreement with TR-MOKE measurements on an asymmetric p-SAF. We
further reveal the damping mechanisms of two procession modes co-existing in
the p-SAF and successfully identify individual contributions from different
sources, including Gilbert damping of each ferromagnetic layer, spin pumping,
and inhomogeneous broadening. Such a comprehensive understanding of
magnetization dynamics in p-SAFs, obtained by integrating high-fidelity TR-MOKE
measurements and theoretical modeling, can guide the design of p-SAF-based
architectures for spintronic applications.
|
2211.07744v2
|
2022-11-15
|
Limits of the phonon quasi-particle picture at the cubic-to-tetragonal phase transition in halide perovskites
|
The soft modes associated with continuous-order phase transitions are
associated with strong anharmonicity. This leads to the overdamped limit where
the phonon quasi-particle picture can breakdown. However, this limit is
commonly restricted to a narrow temperature range, making it difficult to
observe its signature feature, namely the breakdown of the inverse relationship
between the relaxation time and damping. Here we present a physically intuitive
picture based on the relaxation times of the mode coordinate and its conjugate
momentum, which at the instability approach infinity and the inverse damping
factor, respectively. We demonstrate this behavior for the cubic-to-tetragonal
phase transition of the inorganic halide perovskite CsPbBr$_3$ via molecular
dynamics, and show that the overdamped region extends almost 200 K above the
transition temperature. Further, we investigate how the dynamics of these soft
phonon modes change when crossing the phase transition.
|
2211.08197v2
|
2022-11-18
|
Accelerated gradient methods with strong convergence to the minimum norm minimizer: a dynamic approach combining time scaling, averaging, and Tikhonov regularization
|
In a Hilbert framework, for convex differentiable optimization, we consider
accelerated gradient methods obtained by combining temporal scaling and
averaging techniques with Tikhonov regularization. We start from the continuous
steepest descent dynamic with an additional Tikhonov regularization term whose
coefficient vanishes asymptotically. We provide an extensive Lyapunov analysis
of this first-order evolution equation. Then we apply to this dynamic the
method of time scaling and averaging recently introduced by Attouch, Bot and
Nguyen. We thus obtain an inertial dynamic which involves viscous damping
associated with Nesterov's method, implicit Hessian damping and Tikhonov
regularization. Under an appropriate setting of the parameters, just using
Jensen's inequality, without the need for another Lyapunov analysis, we show
that the trajectories have at the same time several remarkable properties: they
provide a rapid convergence of values, fast convergence of the gradients to
zero, and strong convergence to the minimum norm minimizer. These results
complete and improve the previous results obtained by the authors.
|
2211.10140v1
|
2022-12-15
|
DAMP: Doubly Aligned Multilingual Parser for Task-Oriented Dialogue
|
Modern virtual assistants use internal semantic parsing engines to convert
user utterances to actionable commands. However, prior work has demonstrated
that semantic parsing is a difficult multilingual transfer task with low
transfer efficiency compared to other tasks. In global markets such as India
and Latin America, this is a critical issue as switching between languages is
prevalent for bilingual users. In this work we dramatically improve the
zero-shot performance of a multilingual and codeswitched semantic parsing
system using two stages of multilingual alignment. First, we show that
constrastive alignment pretraining improves both English performance and
transfer efficiency. We then introduce a constrained optimization approach for
hyperparameter-free adversarial alignment during finetuning. Our Doubly Aligned
Multilingual Parser (DAMP) improves mBERT transfer performance by 3x, 6x, and
81x on the Spanglish, Hinglish and Multilingual Task Oriented Parsing
benchmarks respectively and outperforms XLM-R and mT5-Large using 3.2x fewer
parameters.
|
2212.08054v2
|
2022-12-22
|
Bayesian Physics-Informed Neural Networks for Robust System Identification of Power Systems
|
This paper introduces for the first time, to the best of our knowledge, the
Bayesian Physics-Informed Neural Networks for applications in power systems.
Bayesian Physics-Informed Neural Networks (BPINNs) combine the advantages of
Physics-Informed Neural Networks (PINNs), being robust to noise and missing
data, with Bayesian modeling, delivering a confidence measure for their output.
Such a confidence measure can be very valuable for the operation of safety
critical systems, such as power systems, as it offers a degree of
trustworthiness for the neural network output. This paper applies the BPINNs
for robust identification of the system inertia and damping, using a single
machine infinite bus system as the guiding example. The goal of this paper is
to introduce the concept and explore the strengths and weaknesses of BPINNs
compared to existing methods. We compare BPINNs with the PINNs and the recently
popular method for system identification, SINDy. We find that BPINNs and PINNs
are robust against all noise levels, delivering estimates of the system inertia
and damping with significantly lower error compared to SINDy, especially as the
noise levels increases.
|
2212.11911v1
|
2022-12-29
|
Scheduling of Software-Defined Microgrids for Optimal Frequency Regulation
|
Integrated with a high share of Inverter-Based Resources (IBRs), microgrids
face increasing complexity of frequency dynamics, especially after
unintentional islanding from the maingrid. These IBRs, on the other hand,
provide more control flexibility to shape the frequency dynamics of microgrid
and together with advanced communication infrastructure offer new opportunities
in the future software-defined microgrids. To enhance the frequency stability
of microgrids with high IBR penetration, this paper proposes an optimal
scheduling framework for software-defined microgrids to maintain frequency
stability by utilizing the non-essential load shedding and dynamical
optimization of the virtual inertia and virtual damping from IBRs. Moreover,
side effects of these services, namely, the time delay associated with
non-essential load shedding and potential IBR control parameter update failure
are explicitly modeled to avoid underestimations of frequency deviation and
over-optimistic results. The effectiveness and significant economic value of
the proposed simultaneous and dynamic virtual inertia and damping provision
strategy are demonstrated based on case studies in the modified IEEE 33-bus
system.
|
2212.14250v3
|
2023-01-01
|
Blow-up of a structural acoustics model
|
This article studies the finite time blow-up of weak solutions to a
structural acoustics model consisting of a semilinear wave equation defined on
a bounded domain $\Omega\subset\mathbb{R}^3$ which is strongly coupled with a
Berger plate equation acting on the elastic wall, namely, a flat portion of the
boundary. The system is influenced by several competing forces, including
boundary and interior source and damping terms. We stress that the power-type
source term acting on the wave equation is allowed to have a supercritical
exponent, in the sense that its associated Nemytskii operators is not locally
Lipschitz from $H^1$ into $L^2$. In this paper, we prove the blow-up results
for weak solutions when the source terms are stronger than damping terms, by
considering two scenarios of the initial data: (i) the initial total energy is
negative; (ii) the initial total energy is positive but small, while the
initial quadratic energy is sufficiently large. The most significant challenge
in this work arises from the coupling of the wave and plate equations on the
elastic wall.
|
2301.00485v1
|
2023-01-03
|
Spin-orbit torque for field-free switching in C_{3v} crystals
|
Spin-orbit torques in noncentrosymmetric polycrystalline magnetic
heterostructures are usually described in terms of field-like and damping-like
torques. However, materials with a lower symmetry point group can exhibit
torques whose behavior substantially deviates from the conventional ones. In
particular, based on symmetry arguments it was recently proposed that systems
belonging to the C_{3v} point group display spin-orbit torques that can promote
field-free switching [Liu et al. Nature Nanotechnology 16, 277 (2021)]. In the
present work, we analyze the general form of the torques expected in C3v
crystals using the Invariant Theory. We uncover several new components that
arise from the coexistence of the three-fold rotation and mirror symmetries.
Using both tight binding model and first principles simulations, we show that
these unconventional torque components arise from the onset of trigonal warping
of the Fermi surface and can be as large as the damping-like torque. In other
words, the Fermi surface warping is a key indicator to the onset of field-free
switching in low symmetry crystals.
|
2301.01133v2
|
2023-01-06
|
A Deep Reinforcement Learning-Based Controller for Magnetorheological-Damped Vehicle Suspension
|
This paper proposes a novel approach to controller design for MR-damped
vehicle suspension system. This approach is predicated on the premise that the
optimal control strategy can be learned through real-world or simulated
experiments utilizing a reinforcement learning algorithm with continuous
states/actions. The sensor data is fed into a Twin Delayed Deep Deterministic
Policy Gradient (TD3) algorithm, which generates the actuation voltage required
for the MR damper. The resulting suspension space (displacement), sprung mass
acceleration, and dynamic tire load are calculated using a quarter vehicle
model incorporating the modified Bouc-Wen MR damper model. Deep RL's reward
function is based on sprung mass acceleration. The proposed approach
outperforms traditional suspension control strategies regarding ride comfort
and stability, as demonstrated by multiple simulated experiments
|
2301.02714v2
|
2023-01-07
|
Quantization of the Bateman damping system with conformable derivative
|
In this work, the conformable Bateman Lagrangian for the damped harmonic
oscillator system is proposed using the conformable derivative concept. In
other words, the integer derivatives are replaced by conformable derivatives of
order $\alpha$ with $0<\alpha\leq 1$. The corresponding conformable
Euler-Lagrange equations of motion and fractional Hamiltonian are then
obtained. The system is then canonically quantized and the conformable
Schrodinger equation is constructed. The fractional-order dependence of the
energy eigenvalues $E_n ^\alpha$ and eigenfunctions $\psi_n ^\alpha$ are
obtained using using suitable transformations and the extended fractional
Nikiforov-Uvarov method. The corresponding conformable continuity equation is
also derived and the probability density and probability current are thus
suitably defined. The probability density evolution as well as its dependence
on $\alpha$ is plotted and analyzed for various situations. It is found that
the energy eigenvalues are real and there are sort of gradual ordering in the
behavior of the probability densities.
|
2301.02769v1
|
2023-01-17
|
Taking advantage of noise in quantum reservoir computing
|
The biggest challenge that quantum computing and quantum machine learning are
currently facing is the presence of noise in quantum devices. As a result, big
efforts have been put into correcting or mitigating the induced errors. But,
can these two fields benefit from noise? Surprisingly, we demonstrate that
under some circumstances, quantum noise can be used to improve the performance
of quantum reservoir computing, a prominent and recent quantum machine learning
algorithm. Our results show that the amplitude damping noise can be beneficial
to machine learning, while the depolarizing and phase damping noises should be
prioritized for correction. This critical result sheds new light into the
physical mechanisms underlying quantum devices, providing solid practical
prescriptions for a successful implementation of quantum information processing
in nowadays hardware.
|
2301.06814v3
|
2023-01-18
|
Damping versus oscillations for a gravitational Vlasov-Poisson system
|
We consider a family of isolated inhomogeneous steady states to the
gravitational Vlasov-Poisson system with a point mass at the centre. They are
parametrised by the polytropic index $k>1/2$, so that the phase space density
of the steady state is $C^1$ at the vacuum boundary if and only if $k>1$. We
prove the following sharp dichotomy result: if $k>1$ the linear perturbations
Landau damp and if $1/2< k\le1$ they do not.
The above dichotomy is a new phenomenon and highlights the importance of
steady state regularity at the vacuum boundary in the discussion of long-time
behaviour of the perturbations. Our proof of (nonquantitative) gravitational
relaxation around steady states with $k>1$ is the first such result for the
gravitational Vlasov-Poisson system. The key step in the proof is to show that
no embedded eigenvalues exist in the essential spectrum of the linearised
system.
|
2301.07662v1
|
2023-01-22
|
Magnon bundle in a strongly dissipative magnet
|
Hybrid quantum systems based on magnetic platforms have witnessed the birth
and fast development of quantum spintronics. Until now, most of the studies
rely on magnetic excitations in low-damping magnetic insulators, particularly
yttrium iron garnet, while a large class of magnetic systems is ruled out in
this interdisciplinary field. Here we propose the generation of a magnon bundle
in a hybrid magnet-qubit system, where two or more magnons are emitted
simultaneously. By tuning the driving frequency of qubit to match the detuning
between magnon and qubit mode, one can effectively generate a magnon bundle via
super-Rabi oscillations. In contrast with general wisdom, magnetic dissipation
plays an enabling role in generating the magnon bundle, where the relaxation
time of magnons determines the typical time delay between two successive
magnons. The maximal damping that allows an antibunched magnon bundle can reach
the order of 0.1, which may break the monopoly of low-dissipation magnetic
insulators in quantum spintronics and enables a large class of magnetic
materials for quantum manipulation. Further, our finding may provide a scalable
and generic platform to study multi-magnon physics and benefit the design of
magnonic networks for quantum information processing.
|
2301.09095v1
|
2023-01-24
|
Effect of mesonic off-shell correlations in the PNJL equation of state
|
We study the meson contribution to the equation of state of the 2-flavor PNJL
model, including the full momentum dependence of the meson polarization loops.
Within the Beth-Uhlenbeck approach, we demonstrate that the contribution from
the quark-antiquark continuum excitations in the spacelike region $\omega^2 -
q^2 < 0$, i.e. the Landau damping, leads to an increase of the pressure for
temperatures $\gtrsim 0.8\,T_c^\chi$ and a significant meson momentum cut-off
dependence in the mesonic pressure and the QCD trace anomaly. We investigate
the dependence of the results on the choice of the Polyakov-loop potential
parameter $T_0$. From the dependence of the mesonic pressure on the current
quark mass, by means of the Feynman-Hellmann theorem, we evaluate the
contribution of the pion quasiparticle gas and Landau damping to the chiral
condensate.
|
2301.09882v1
|
2023-01-28
|
A speed restart scheme for a dynamics with Hessian driven damping
|
In this paper, we analyze a speed restarting scheme for the dynamical system
given by $$ \ddot{x}(t) + \dfrac{\alpha}{t}\dot{x}(t) + \nabla \phi(x(t)) +
\beta \nabla^2 \phi(x(t))\dot{x}(t)=0, $$ where $\alpha$ and $\beta$ are
positive parameters, and $\phi:\mathbb{R}^n \to \mathbb{R}$ is a smooth convex
function. If $\phi$ has quadratic growth, we establish a linear convergence
rate for the function values along the restarted trajectories. As a byproduct,
we improve the results obtained by Su, Boyd and Cand\`es
\cite{JMLR:v17:15-084}, obtained in the strongly convex case for $\alpha=3$ and
$\beta=0$. Preliminary numerical experiments suggest that both adding a
positive Hessian driven damping parameter $\beta$, and implementing the restart
scheme help improve the performance of the dynamics and corresponding iterative
algorithms as means to approximate minimizers of $\phi$.
|
2301.12240v1
|
2023-01-31
|
Force moment partitioning and scaling analysis of vortices shed by a 2D pitching wing in quiescent fluid
|
We experimentally study the dynamics and strength of vortices shed from a
NACA 0012 wing undergoing sinusoidal pitching in quiescent water. We
characterize the temporal evolution of the vortex trajectory and circulation
over a range of pitching frequencies, amplitudes and pivot locations. By
employing a physics-based force and moment partitioning method (FMPM), we
estimate the vortex-induced aerodynamic moment from the velocity fields
measured using particle image velocimetry. The vortex circulation, formation
time and vorticity-induced moment are shown to follow scaling laws based on the
feeding shear-layer velocity. The vortex dynamics, together with the spatial
distribution of the vorticity-induced moment, provide quantitative explanations
for the nonlinear behaviors observed in the fluid damping (Zhu et al., J. Fluid
Mech., vol. 923, 2021, R2). The FMPM-estimated moment and damping are shown to
match well in trend with direct force measurements, despite a discrepancy in
magnitude. Our results demonstrate the powerful capability of the FMPM in
dissecting experimental flow field data and providing valuable insights into
the underlying flow physics.
|
2301.13373v2
|
2023-02-16
|
Energy decay for wave equations with a potential and a localized damping
|
We consider the total energy decay together with L^2-bound of the solution
itself of the Cauchy problem for wave equations with a localized damping and a
short-range potential. We treat it in the one dimensional Euclidean space R. We
adopt a simple multiplier method to study them. In this case, it is essential
that the compactness of the support of the initial data is not assumed. Since
this problem is treated in the whole space, the Poincare and Hardy inequalities
are not available as is developed in the exterior domain case. For compensating
such a lack of useful tools, the potential plays an effective role. As an
application, the global existence of small data solution for a semilinear
problem is provided.
|
2302.08114v1
|
2023-02-24
|
An Oscillation-free Spectral Volume Method for Hyperbolic Conservation Laws
|
In this paper, an oscillation-free spectral volume (OFSV) method is proposed
and studied for the hyperbolic conservation laws. The numerical scheme is
designed by introducing a damping term in the standard spectral volume method
for the purpose of controlling spurious oscillations near discontinuities.
Based on the construction of control volumes (CVs), two classes of OFSV schemes
are presented. A mathematical proof is provided to show that the proposed OFSV
is stable and has optimal convergence rate and some desired superconvergence
properties when applied to the linear scalar equations. Both analysis and
numerical experiments indicate that the damping term would not destroy the
order of accuracy of the original SV scheme and can control the oscillations
discontinuities effectively. Numerical experiments are presented to demonstrate
the accuracy and robustness of our scheme.
|
2302.12412v1
|
2023-03-01
|
Event-triggered boundary damping of a linear wave equation
|
This article presents an analysis of the stabilization of a multidimensional
partial differential wave equation under a well designed event-triggering
mechanism that samples the boundary control input. The wave equation is set in
a bounded domain and the control is performed through a boundary classical
damping term, where the Neumann boundary condition is made proportional to the
velocity. First of all, existence and regularity of the solution to the
closed-loop system under the event-triggering mechanism of the control are
proven. Then, sufficient conditions based on the use of a specific Lyapunov
functional are proposed in order to ensure that the solutions converge into a
compact set containing the origin, that can be tuned by the designer.
Furthermore, as expected, any Zeno behavior of the closed-loop system is
avoided.
|
2303.00381v1
|
2023-03-05
|
Coupling of magnetism and Dirac fermions in YbMnSb2
|
We report inelastic neutron scattering measurements of magnetic excitations
in YbMnSb2, a low-carrier-density Dirac semimetal in which the
antiferromagnetic Mn layers are interleaved with Sb layers that host Dirac
fermions. We observe a considerable broadening of spin waves, which is
consistent with substantial spin fermion coupling. The spin wave damping,
$\gamma$, in YbMnSb2 is roughly twice larger compared to that in a sister
material, YbMnBi2, where an indication of a small damping consistent with
theoretical analysis of the spin-fermion coupling was reported. The inter-plane
interaction between the Mn layers in YbMnSb2 is also much stronger, suggesting
that the interaction mechanism is rooted in the same spin-fermion coupling. Our
results establish the systematics of spin-fermion interactions in layered
magnetic Dirac materials.
|
2303.02587v2
|
2023-03-08
|
Initial value formulation of a quantum damped harmonic oscillator
|
The in-in formalism and its influence functional generalization are widely
used to describe the out-of-equilibrium dynamics of unitary and open quantum
systems, respectively. In this paper, we build on these techniques to develop
an effective theory of a quantum damped harmonic oscillator and use it to study
initial state-dependence, decoherence, and thermalization. We first consider a
Gaussian initial state and quadratic influence functional and obtain general
equations for the Green's functions of the oscillator. We solve the equations
in the specific case of time-local dissipation and use the resulting Green's
functions to obtain the purity and unequal-time two-point correlations of the
oscillator. In particular, we find that the dynamics must include a
non-vanishing noise term to yield physical results. We show that the oscillator
decoheres in time such that the late-time density operator is thermal, and find
the parameter regime for which the fluctuation-dissipation relation is
satisfied. We next develop a double in-out path integral approach to go beyond
Gaussian initial states and show that our equal-time results are in fact
non-perturbative in the initial state.
|
2303.04829v1
|
2023-03-17
|
Stochastic wave equations with constraints: well-posedness and Smoluchowski-Kramers diffusion approximation
|
We investigate the well-posedness of a class of stochastic second-order in
time damped evolution equations in Hilbert spaces, subject to the constraint
that the solution lie within the unitary sphere. Then, we focus on a specific
example, the stochastic damped wave equation in a bounded domain of a
$d$-dimensional Euclidean space, endowed with the Dirichlet boundary condition,
with the added constraint that the $L^2$-norm of the solution is equal to one.
We introduce a small mass $\mu>0$ in front of the second-order derivative in
time and examine the validity of a Smoluchowski-Kramers diffusion
approximation. We demonstrate that, in the small mass limit, the solution
converges to the solution of a stochastic parabolic equation subject to the
same constraint. We further show that an extra noise-induced drift emerges,
which in fact does not account for the Stratonovich-to-It\^{o} correction term.
|
2303.09717v2
|
2023-03-21
|
Entropically damped artificial compressibility for the discretization corrected particle strength exchange method in incompressible fluid mechanics
|
We present a consistent mesh-free numerical scheme for solving the
incompressible Navier-Stokes equations. Our method is based on entropically
damped artificial compressibility for imposing the incompressibility constraint
explicitly, and the Discretization-Corrected Particle Strength Exchange
(DC-PSE) method to consistently discretize the differential operators on
mesh-free particles. We further couple our scheme with Brinkman penalization to
solve the Navier-Stokes equations in complex geometries. The method is
validated using the 3D Taylor-Green vortex flow and the lid-driven cavity flow
problem in 2D and 3D, where we also compare our method with hr-SPH and report
better accuracy for DC-PSE. In order to validate DC-PSE Brinkman penalization,
we study flow past obstacles, such as a cylinder, and report excellent
agreement with previous studies.
|
2303.11983v2
|
2023-03-30
|
Superfluid $^3$He-B Surface States in a Confined Geometry Probed by a Microelectromechanical Oscillator
|
A microelectromechanical oscillator with a 0.73 $\mu$m gap structure is
employed to probe the surface Andreev bound states in superfluid $^3$He-B. The
surface specularity of the oscillator is increased by preplating it with 1.6
monolayers of $^4$He. In the linear regime, the temperature dependence of the
damping coefficient is measured at various pressures, and the normalized energy
gap is extracted. The damping coefficient increases after preplating at lower
pressures, which is attributed to the decreased energy minigap of the surface
bound states. The device is also driven into the nonlinear regime, where the
temperature independent critical velocity at each pressure is measured. The
critical velocity is observed to increase after preplating at all pressures,
which might be related to the increased average energy gap. The observed
behavior warrants a microscopic theory beyond a single parameter
characterization of the surface.
|
2303.17073v1
|
2023-04-04
|
A damped Kačanov scheme for the numerical solution of a relaxed p(x)-Poisson equation
|
The focus of the present work is the (theoretical) approximation of a
solution of the p(x)-Poisson equation. To devise an iterative solver with
guaranteed convergence, we will consider a relaxation of the original problem
in terms of a truncation of the nonlinearity from below and from above by using
a pair of positive cut-off parameters. We will then verify that, for any such
pair, a damped Ka\v{c}anov scheme generates a sequence converging to a solution
of the relaxed equation. Subsequently, it will be shown that the solutions of
the relaxed problems converge to the solution of the original problem in the
discrete setting. Finally, the discrete solutions of the unrelaxed problem
converge to the continuous solution. Our work will finally be rounded up with
some numerical experiments that underline the analytical findings.
|
2304.01566v1
|
2023-04-05
|
Optomechanical coupling and damping of a carbon nanotube quantum dot
|
Carbon nanotubes are excellent nano-electromechanical systems, combining high
resonance frequency, low mass, and large zero-point motion. At cryogenic
temperatures they display high mechanical quality factors. Equally they are
outstanding single electron devices with well-known quantum levels and have
been proposed for the implementation of charge or spin qubits. The integration
of these devices into microwave optomechanical circuits is however hindered by
a mismatch of scales, between typical microwave wavelengths, nanotube segment
lengths, and nanotube deflections. As experimentally demonstrated recently in
[Blien et al., Nat. Comm. 11, 1363 (2020)], coupling enhancement via the
quantum capacitance allows to circumvent this restriction. Here we extend the
discussion of this experiment. We present the subsystems of the device and
their interactions in detail. An alternative approach to the optomechanical
coupling is presented, allowing to estimate the mechanical zero point motion
scale. Further, the mechanical damping is discussed, hinting at hitherto
unknown interaction mechanisms.
|
2304.02748v3
|
2023-04-12
|
Micromagnetics simulations and phase transitions of ferromagnetics with Dzyaloshinskii-Moriya interaction
|
Magnetic skyrmions widely exist in a diverse range of magnetic systems,
including chiral magnets with a non-centrosymmetric structure characterized by
Dzyaloshinkii-Moriya interaction~(DMI). In this study, we propose a generalized
semi-implicit backward differentiation formula projection method, enabling the
simulations of the Landau-Lifshitz~(LL) equation in chiral magnets in a typical
time step-size of $1$ ps, markedly exceeding the limit subjected by existing
numerical methods of typically $0.1$ ps. Using micromagnetics simulations, we
show that the LL equation with DMI reveals an intriguing dynamic instability in
magnetization configurations as the damping varies. Both the isolated
skyrmionium and skyrmionium clusters can be consequently produced using a
simple initialization strategy and a specific damping parameter. Assisted by
the string method, the transition path between skyrmion and skyrmionium, along
with the escape of a skyrmion from the skyrmion clusters, are then thoroughly
examined. The numerical methods developed in this work not only provide a
reliable paradigm to investigate the skyrmion-based textures and their
transition paths, but also facilitate the understandings for magnetization
dynamics in complex magnetic systems.
|
2304.05789v1
|
2023-04-12
|
Abstract damped wave equations: The optimal decay rate
|
The exponential decay rate of the semigroup $S(t)=e^{t\mathbb{A}}$ generated
by the abstract damped wave equation $$\ddot u + 2f(A) \dot u +A u=0 $$ is here
addressed, where $A$ is a strictly positive operator. The continuous function
$f$, defined on the spectrum of $A$, is subject to the constraints $$\inf
f(s)>0\qquad\text{and}\qquad \sup f(s)/s <\infty$$ which are known to be
necessary and sufficient for exponential stability to occur. We prove that the
operator norm of the semigroup fulfills the estimate $$\|S(t)\|\leq
Ce^{\sigma_*t}$$ being $\sigma_*<0$ the supremum of the real part of the
spectrum of $\mathbb{A}$. This estimate always holds except in the resonant
cases, where the negative exponential $e^{\sigma_*t}$ turns out to be penalized
by a factor $(1+t)$. The decay rate is the best possible allowed by the theory.
|
2304.05816v1
|
2023-04-28
|
Primal-Dual Damping algorithms for optimization
|
We propose an unconstrained optimization method based on the well-known
primal-dual hybrid gradient (PDHG) algorithm. We first formulate the optimality
condition of the unconstrained optimization problem as a saddle point problem.
We then compute the minimizer by applying generalized primal-dual hybrid
gradient algorithms. Theoretically, we demonstrate the continuous-time limit of
the proposed algorithm forms a class of second-order differential equations,
which contains and extends the heavy ball ODEs and Hessian-driven damping
dynamics. Following the Lyapunov analysis of the ODE system, we prove the
linear convergence of the algorithm for strongly convex functions.
Experimentally, we showcase the advantage of algorithms on several convex and
non-convex optimization problems by comparing the performance with other
well-known algorithms, such as Nesterov's accelerated gradient methods. In
particular, we demonstrate that our algorithm is efficient in training
two-layer and convolution neural networks in supervised learning problems.
|
2304.14574v2
|
2023-05-01
|
Global existence and optimal decay of solutions to the incompressible Oldroyd-B model with only stress tensor dissipation and without damping mechanism
|
We study the $d$-dimensional ($d\geq2$) incompressible Oldroyd-B model with
only stress tensor diffusion and without velocity dissipation as well as the
damping mechanism on the stress tensor. Firstly, based upon some new
observations on the model, we develope the pure energy argument (independent of
spectral analysis) in general $L^p$ framework, and present a small initial data
global existence and uniqueness of solutions to the model. Our results yield
that the coupling and interaction of the velocity and the non-Newtonian stress
actually enhances the regularity of the system. Later, by adding some
additional $L^2$ type conditions on the low frequencies of the initial data
$(u_0,\tau_0)$, %but without any more smallness restrictions, we obtain the
optimal time-decay rates of the global solution $(u,\tau)$. Our result solves
the problem proposed in Wang, Wu, Xu and Zhong \cite{Wang-Wu-Xu-Zhong} ({\it J.
Funct. Anal.}, 282 (2022), 109332.).
|
2305.00839v3
|
2023-05-02
|
Non-Markovian quantum interconnect formed by a surface plasmon polariton waveguide
|
Allowing the generation of effective interactions between distant quantum
emitters (QEs) via flying photons, quantum interconnect (QI) is essentially a
light-matter interface and acts as a building block in quantum technologies. A
surface plasmon polariton (SPP) supported by a metallic waveguide provides an
ideal interface to explore strong light-matter couplings and to realize QI.
However, the loss of SPP in metal makes the mediated entanglement of the QEs
damp with the increase of the distance and time, which hinders its
applications. We propose a scheme of non-Markovian QI formed by the SPP of a
metallic nanowire. A mechanism to make the generated entanglement of the QEs
persistent is discovered. We find that, as long as bound states are formed in
the energy spectrum of total QE-SPP system, the damping of the SPP-mediated
entanglement is overcome even in the presence of the metal absorption to the
SPP. Our finding enriches our understanding of light-matter couplings in
absorptive medium and paves the way for using the SPP in designing QI.
|
2305.01156v2
|
2023-05-17
|
Stationary solutions for the nonlinear Schrödinger equation
|
We construct stationary statistical solutions of a deterministic unforced
nonlinear Schr\"odinger equation, by perturbing it by a linear damping $\gamma
u$ and a stochastic force whose intensity is proportional to $\sqrt \gamma$,
and then letting $\gamma\to 0^+$. We prove indeed that the family of stationary
solutions $\{U_\gamma\}_{\gamma>0}$ of the perturbed equation possesses an
accumulation point for any vanishing sequence $\gamma_j\to 0^+$ and this
stationary limit solves the deterministic unforced nonlinear Schr\"odinger
equation and is not the trivial zero solution. This technique has been
introduced in [KS04], using a different dissipation. However considering a
linear damping of zero order and weaker solutions we can deal with larger
ranges of the nonlinearity and of the spatial dimension; moreover we consider
the focusing equation and the defocusing equation as well.
|
2305.10393v1
|
2023-05-22
|
Sketch-and-Project Meets Newton Method: Global $\mathcal O(k^{-2})$ Convergence with Low-Rank Updates
|
In this paper, we propose the first sketch-and-project Newton method with
fast $\mathcal O(k^{-2})$ global convergence rate for self-concordant
functions. Our method, SGN, can be viewed in three ways: i) as a
sketch-and-project algorithm projecting updates of Newton method, ii) as a
cubically regularized Newton ethod in sketched subspaces, and iii) as a damped
Newton method in sketched subspaces. SGN inherits best of all three worlds:
cheap iteration costs of sketch-and-project methods, state-of-the-art $\mathcal
O(k^{-2})$ global convergence rate of full-rank Newton-like methods and the
algorithm simplicity of damped Newton methods. Finally, we demonstrate its
comparable empirical performance to baseline algorithms.
|
2305.13082v2
|
2023-05-23
|
Current-driven motion of magnetic topological defects in ferromagnetic superconductors
|
Recent years have seen a number of instances where magnetism and
superconductivity intrinsically coexist. Our focus is on the case where
spin-triplet superconductivity arises out of ferromagnetism, and we make a
hydrodynamic analysis of the effect of a charge supercurrent on magnetic
topological defects like domain walls and merons. We find that the emergent
electromagnetic field that arises out of the superconducting order parameter
provides a description for not only the physical quantities such as the local
energy flux density and the interaction between current and defects but also
the energy dissipation through magnetic dynamics of the Gilbert damping, which
becomes more prominent compared to the normal state as superconductivity
attenuates the energy dissipation through the charge sector. In particular, we
reveal that the current-induced dynamics of domain walls and merons in the
presence of the Gilbert damping give rise to the nonsingular $4\pi$ and $2\pi$
phase slips, respectively, revealing the intertwined dynamics of spin and
charge degrees of freedom in ferromagnetic superconductors.
|
2305.13564v1
|
2023-05-26
|
Energetic cost for speedy synchronization in non-Hermitian quantum dynamics
|
Quantum synchronization is crucial for understanding complex dynamics and
holds potential applications in quantum computing and communication. Therefore,
assessing the thermodynamic resources required for finite-time synchronization
in continuous-variable systems is a critical challenge. In the present work, we
find these resources to be extensive for large systems. We also bound the speed
of quantum and classical synchronization in coupled damped oscillators with
non-Hermitian anti-PT-symmetric interactions, and show that the speed of
synchronization is limited by the interaction strength relative to the damping.
Compared to the classical limit, we find that quantum synchronization is slowed
by the non-commutativity of the Hermitian and anti-Hermitian terms. Our general
results could be tested experimentally and we suggest an implementation in
photonic systems.
|
2305.16560v1
|
2023-05-31
|
Viscous damping in weltering motion of trapped hydrodynamic dipolar Fermi gases
|
We consider collective motion and damping of dipolar Fermi gases in the
hydrodynamic regime. We investigate the trajectories of collective oscillations
-- here dubbed ``weltering'' motions -- in cross-dimensional rethermalization
experiments via Monte Carlo simulations, where we find stark differences from
the dilute regime. These observations are interpreted within a semi-empirical
theory of viscous hydrodynamics for gases confined to anisotropic harmonic
potentials. The derived equations of motion provide a simple effective theory
that show favorable agreement with full numerical solutions. To do so, the
theory must carefully account for the size and shape of the effective volume
within which the gas' behavior is hydrodynamic. Although formulated for dipolar
molecules, our theoretical framework retains a flexibility to accommodate
arbitrary elastic cross sections.
|
2306.00250v1
|
2023-06-01
|
Interferometry of Efimov states in thermal gases by modulated magnetic fields
|
We demonstrate that an interferometer based on modulated magnetic field
pulses enables precise characterization of the energies and lifetimes of Efimov
trimers irrespective of the magnitude and sign of the interactions in 85Rb
thermal gases. Despite thermal effects, interference fringes develop when the
dark time between the pulses is varied. This enables the selective excitation
of coherent superpositions of trimer, dimer and free atom states. The
interference patterns possess two distinct damping timescales at short and long
dark times that are either equal to or twice as long as the lifetime of Efimov
trimers, respectively. Specifically, this behavior at long dark times provides
an interpretation of the unusually large damping timescales reported in a
recent experiment with 7Li thermal gases [Phys. Rev. Lett. 122, 200402 (2019)].
Apart from that, our results constitute a stepping stone towards a high
precision few-body state interferometry for dense quantum gases.
|
2306.01199v3
|
2023-06-06
|
Convergence analysis of nonconform $H(\operatorname{div})$-finite elements for the damped time-harmonic Galbrun's equation
|
We consider the damped time-harmonic Galbrun's equation, which is used to
model stellar oscillations. We introduce a discontinuous Galerkin finite
element method (DGFEM) with $H(\operatorname{div})$-elements, which is
nonconform with respect to the convection operator. We report a convergence
analysis, which is based on the frameworks of discrete approximation schemes
and T-compatibility. A novelty is that we show how to interprete a DGFEM as a
discrete approximation scheme and this approach enables us to apply compact
perturbation arguments in a DG-setting, and to circumvent any extra regularity
assumptions on the solution. The advantage of the proposed
$H(\operatorname{div})$-DGFEM compared to $H^1$-conforming methods is that we
do not require a minimal polynomial order or any special assumptions on the
mesh structure. The considered DGFEM is constructed without a stabilization
term, which considerably improves the assumption on the smallness of the Mach
number compared to other DG methods and $H^1$-conforming methods, and the
obtained bound is fairly explicit. In addition, the method is robust with
respect to the drastic changes of magnitude of the density and sound speed,
which occur in stars. The convergence of the method is obtained without
additional regularity assumptions on the solution, and for smooth solutions and
parameters convergence rates are derived.
|
2306.03496v1
|
2023-06-06
|
Plasmons for the Hartree equations with Coulomb interaction
|
In this work, we establish the existence and decay of {\em plasmons}, the
quantum of Langmuir's oscillatory waves found in plasma physics, for the
linearized Hartree equations describing an interacting gas of infinitely many
fermions near general translation-invariant steady states, including compactly
supported Fermi gases at zero temperature, in the whole space $\RR^d$ for $d\ge
2$. Notably, these plasmons exist precisely due to the long-range pair
interaction between the particles. Next, we provide a survival threshold of
spatial frequencies, below which the plasmons purely oscillate and disperse
like a Klein-Gordon's wave, while at the threshold they are damped by {\em
Landau damping}, the classical decaying mechanism due to their resonant
interaction with the background fermions. The explicit rate of Landau damping
is provided for general radial homogenous equilibria. Above the threshold, the
density of the excited fermions is well approximated by that of the free gas
dynamics and thus decays rapidly fast for each Fourier mode via {\em phase
mixing}. Finally, pointwise bounds on the Green function and dispersive
estimates on the density are established.
|
2306.03800v1
|
2023-06-07
|
Helicity-dependent optical control of the magnetization state emerging from the Landau-Lifshitz-Gilbert equation
|
It is well known that the Gilbert relaxation time of a magnetic moment scales
inversely with the magnitude of the externally applied field, H, and the
Gilbert damping, {\alpha}. Therefore, in ultrashort optical pulses, where H can
temporarily be extremely large, the Gilbert relaxation time can momentarily be
extremely short, reaching even picosecond timescales. Here we show that for
typical ultrashort pulses, the optical control of the magnetization emerges by
merely considering the optical magnetic field in the Landau-Lifshitz-Gilbert
(LLG) equation. Surprisingly, when circularly polarized optical pulses are
introduced to the LLG equation, an optically induced helicity-dependent torque
results. We find that the strength of the interaction is determined by
{\eta}={\alpha}{\gamma}H/f_opt, where f_opt and {\gamma} are the optical
frequency and gyromagnetic ratio. Our results illustrate the generality of the
LLG equation to the optical limit and the pivotal role of the Gilbert damping
in the general interaction between optical magnetic fields and spins in solids.
|
2306.04617v2
|
2023-06-10
|
Discrepant Approaches to Modeling Stellar Tides, and the Blurring of Pseudosynchronization
|
We examine the reasons for discrepancies between two alternative approaches
to modeling small-amplitude tides in binary systems. The 'direct solution' (DS)
approach solves the governing differential equations and boundary conditions
directly, while the 'modal decomposition' (MD) approach relies on a normal-mode
expansion. Applied to a model for the primary star in the heartbeat system
KOI-54, the two approaches predict quite different behavior of the secular
tidal torque. The MD approach exhibits the pseudosynchronization phenomenon,
where the torque due to the equilibrium tide changes sign at a single,
well-defined and theoretically predicted stellar rotation rate. The DS approach
instead shows 'blurred' pseudosynchronization, where positive and negative
torques intermingle over a range of rotation rates.
We trace a major source of these differences to an incorrect damping
coefficient in the profile functions describing the frequency dependence of the
MD expansion coefficients. With this error corrected some differences between
the approaches remain; however, both are in agreement that
pseudosynchronization is blurred in the KOI-54 system. Our findings generalize
to any type of star for which the tidal damping depends explicitly or
implicitly on the forcing frequency.
|
2306.06429v1
|
2023-06-19
|
Spin transport and magnetic proximity effect in CoFeB/normal metal/Pt trilayers
|
We present a study of the damping and spin pumping properties of CoFeB/X/Pt
systems with $\rm X=Al,Cr$ and $\rm Ta$. We show that the total damping of the
CoFeB/Pt systems is strongly reduced when an interlayer is introduced
independently of the material. Using a model that considers spin relaxation, we
identify the origin of this contribution in the magnetically polarized Pt
formed by the magnetic proximity effect (MPE), which is suppressed by the
introduction of the interlayer. The induced ferromagnetic order in the Pt layer
is confirmed by transverse magneto-optical Kerr spectroscopy at the M$_{2,3}$
and N$_7$ absorption edges as an element-sensitive probe. We discuss the impact
of the MPE on parameter extraction in the spin transport model.
|
2306.11009v2
|
2023-06-23
|
Energy-optimal control of adaptive structures
|
Adaptive structures are equipped with sensors and actuators to actively
counteract external loads such as wind. This can significantly reduce resource
consumption and emissions during the life cycle compared to conventional
structures. A common approach for active damping is to derive a
port-Hamiltonian model and to employ linear-quadratic control. However, the
quadratic control penalization lacks physical interpretation and merely serves
as a regularization term. Rather, we propose a controller, which achieves the
goal of vibration damping while acting energy-optimal. Leveraging the
port-Hamiltonian structure, we show that the optimal control is uniquely
determined, even on singular arcs. Further, we prove a stable long-time
behavior of optimal trajectories by means of a turnpike property. Last, the
proposed controller's efficiency is evaluated in a numerical study.
|
2306.13331v2
|
2023-06-23
|
Low-Lying Collective Excitations of Superconductors and Charged Superfluids
|
We investigate theoretically the momentum-dependent frequency and damping of
low-lying collective excitations of superconductors and charged superfluids in
the BCS-BEC crossover regime. The study is based on the Gaussian
pair-and-density fluctuation method for the propagator of Gaussian fluctuations
of the pair and density fields. Eigenfrequencies and damping rates are
determined in a mutually consistent nonperturbative way as complex poles of the
fluctuation propagator. Particular attention is paid to new features with
respect to preceding theoretical studies, which were devoted to collective
excitations of superconductors in the far BCS regime. We find that at a
sufficiently strong coupling, new branches of collective excitations appear,
which manifest different behavior as functions of the momentum and the
temperature.
|
2306.13393v1
|
2023-06-27
|
On Nonlinear Scattering of Drift Wave by Toroidal Alfven Eigenmode in Tokamak Plasmas
|
Using electron drift wave (eDW) as a paradigm model, we have investigated
analytically direct wave-wave interactions between a test DW and ambient
toroidal Alfv\'en eigenmodes (TAE) in toroidal plasmas, and their effects on
the stability of the eDW. The nonlinear effects enter via scatterings to
short-wavelength electron Landau damped kinetic Alfv\'en waves (KAWs).
Specifically, it is found that scatterings to upper-sideband KAW lead to
stimulated absorption of eDW. Scatterings to the lower-sideband KAW, on the
contrary, lead to its spontaneous emission. As a consequence, for typical
parameters and fluctuation intensity, nonlinear scatterings by TAE have
negligible net effects on the eDW stability; in contrast to the ``reverse"
process investigated in Ref. [Nuclear Fusion {\bf 62}, 094001 (2022)], where it
is shown that nonlinear scattering by ambient eDW may lead to significant
damping of TAE.
|
2306.15238v1
|
2023-06-27
|
Ground-state cooling of a mechanical oscillator by heating
|
Dissipation and the accompanying fluctuations are often seen as detrimental
for quantum systems, since they are associated with fast relaxation and loss of
phase coherence. However, it has been proposed that a pure state can be
prepared if external noise induces suitable downwards transitions, while
exciting transitions are blocked. We demonstrate such a refrigeration mechanism
in a cavity optomechanical system, where we prepare a mechanical oscillator in
its ground state by injecting strong electromagnetic noise at frequencies
around the red mechanical sideband of the cavity. The optimum cooling is
reached with a noise bandwidth smaller than, but on the order of the cavity
decay rate. At higher bandwidths, cooling is less efficient. In the opposite
regime where the noise bandwidth becomes comparable to the mechanical damping
rate, damping follows the noise amplitude adiabatically, and the cooling is
also suppressed.
|
2306.15746v1
|
2023-07-03
|
Magnetic lump motion in saturated ferromagnetic films
|
In this paper, we study in detail the nonlinear propagation of magnetic
soliton in a ferromagnetic film. The sample is magnetized to saturation by an
external field perpendicular to film plane. A new generalized (2+1)-dimensional
short-wave asymptotic model is derived. The bilinear-like forms of this
equation are constructed, and exact magnetic line soliton solutions are
exhibited. It is observed that a series of stable lumps can be generated by an
unstable magnetic soliton under Gaussian disturbance. Such magnetic lumps are
highly stable and can maintain their shapes and velocities during evolution or
collision. The interaction between lump and magnetic soliton, as well as
interaction between two lumps, are numerically investigated. We further discuss
the nonlinear motion of lumps in ferrites with Gilbert-damping and
inhomogeneous exchange effects. The results show that the Gilbert-damping
effects make the amplitude and velocity of the magnetic lump decay
exponentially during propagation. And the shock waves are generated from a lump
when quenching the strength of inhomogeneous exchange.
|
2307.00903v1
|
2023-07-07
|
Tikhonov regularized second-order plus first-order primal-dual dynamical systems with asymptotically vanishing damping for linear equality constrained convex optimization problems
|
In this paper, in the setting of Hilbert spaces, we consider a Tikhonov
regularized second-order plus first-order primal-dual dynamical system with
asymptotically vanishing damping for a linear equality constrained convex
optimization problem. The convergence properties of the proposed dynamical
system depend heavily upon the choice of the Tikhonov regularization parameter.
When the Tikhonov regularization parameter decreases rapidly to zero, we
establish the fast convergence rates of the primal-dual gap, the objective
function error, the feasibility measure, and the gradient norm of the objective
function along the trajectory generated by the system. When the Tikhonov
regularization parameter tends slowly to zero, we prove that the primal
trajectory of the Tikhonov regularized dynamical system converges strongly to
the minimal norm solution of the linear equality constrained convex
optimization problem. Numerical experiments are performed to illustrate the
efficiency of our approach.
|
2307.03612v1
|
2023-07-14
|
The Effects of Viscosity on the Linear Stability of Damped Stokes Waves, Downshifting, and Rogue Wave Generation
|
We investigate a higher order nonlinear Schr\"odinger equation with linear
damping and weak viscosity, recently proposed as a model for deep water waves
exhibiting frequency downshifting. Through analysis and numerical simulations,
we discuss how the viscosity affects the linear stability of the Stokes wave
solution, enhances rogue wave formation, and leads to permanent downshift in
the spectral peak. The novel results in this work include the analysis of the
transition from the initial Benjamin-Feir instability to a predominantly
oscillatory behavior, which takes place in a time interval when most rogue wave
activity occurs. In addition, we propose new criteria for downshifting in the
spectral peak and determine the relation between the time of permanent
downshift and the location of the global minimum of the momentum and the
magnitude of its second derivative.
|
2307.07156v2
|
2023-07-17
|
Tidal excitation of the obliquity of Earth-like planets in the habitable zone of M-dwarf stars
|
Close-in planets undergo strong tidal interactions with the parent star that
modify their spins and orbits. In the two-body problem, the final stage for
tidal evolution is the synchronisation of the rotation and orbital periods, and
the alignment of the planet spin axis with the normal to the orbit (zero planet
obliquity). The orbital eccentricity is also damped to zero, but over a much
longer timescale, that may exceed the lifetime of the system. For non-zero
eccentricities, the rotation rate can be trapped in spin-orbit resonances that
delay the evolution towards the synchronous state. Here we show that capture in
some spin-orbit resonances may also excite the obliquity to high values rather
than damp it to zero. Depending on the system parameters, obliquities of 60 to
80 degrees can be maintained throughout the entire lifetime of the planet. This
unexpected behaviour is particularly important for Earth-like planets in the
habitable zone of M-dwarf stars, as it may help to sustain temperate
environments and thus more favourable conditions for life.
|
2307.08770v1
|
2023-07-20
|
Interaction-mitigated Landau damping
|
Bosonic collective modes are ubiquitous in metals, but over a wide range of
energy and momenta suffer from Landau damping, decaying into the continuum of
particle-hole excitations. Here we point out that interactions can suppress
this decay, protecting a finite fraction of the total spectral weight
associated with the collective mode, e.g. a plasmon. The underlying mechanism
is level repulsion between a discrete mode and the continuum. We demonstrate
the effect using a number of simplified models of strongly correlated
Fermi-liquid metals, including a ``solvable" random flavor model in the
large$-N$ limit. We discuss in detail the possibility of observing such an
avoided decay for plasmons in (moir\'e) graphene-like systems.
|
2307.11169v2
|
2023-07-20
|
Electron-positron plasma in BBN: damped-dynamic screening
|
We characterize in detail the very dense $e^- e^+ \gamma$ plasma present
during the Big-Bang Nucleosynthesis (BBN) and explore how it is perturbed
electromagnetically by \lq\lq impurities, {\it i.e.\/}, spatially dispersed
protons and light nuclei undergoing thermal motion. The internuclear
electromagnetic screened potential is obtained (analytically) using the linear
response approach, allowing for the dynamic motion of the electromagnetic field
sources and the damping effects due to plasma component scattering. We discuss
the limits of the linear response method and suggest additional work needed to
improve BBN reaction rates in the primordial Universe. Our theoretical methods
to describe the potential between charged dust particles align with previous
studies on planetary and space dusty plasma and could have significant impact
on interpretation of standard cosmological model results.
|
2307.11264v2
|
2023-07-22
|
Damping of strong GHz waves near magnetars and the origin of fast radio bursts
|
We investigate how a GHz radio burst emitted near a magnetar propagates
through its magnetosphere at radii $r=10^7$-$10^9$ cm. Bursts propagating near
the magnetic equator behave as magnetohydrodynamic (MHD) waves if they have
luminosity $L\gg 10^{40}$ erg/s. The waves develop plasma shocks in each
oscillation and dissipate at $r\sim 3 \times 10^8 L_{42}^{-1/4}$ cm. GHz waves
with lower $L$ or propagation directions closer to the magnetic axis do not
obey MHD. Instead, they interact with individual particles, which requires a
kinetic description. The kinetic interaction quickly accelerates particles to
Lorentz factors $10^4$-$10^5$ at the expense of the wave energy, which again
results in strong damping of the wave. In either regime of wave propagation,
MHD or kinetic, the magnetosphere acts as a pillow absorbing the GHz burst and
re-radiating the absorbed energy in X-rays. We conclude that a GHz source
confined in the inner magnetosphere would be blocked by the outer magnetosphere
at practically all relevant luminosities and viewing angles. This result
constrains the origin of observed fast radio bursts (FRBs). We argue that
observed FRBs come from magnetospheric explosions ejecting powerful outflows.
|
2307.12182v1
|
2023-07-25
|
Computational Guarantees for Doubly Entropic Wasserstein Barycenters via Damped Sinkhorn Iterations
|
We study the computation of doubly regularized Wasserstein barycenters, a
recently introduced family of entropic barycenters governed by inner and outer
regularization strengths. Previous research has demonstrated that various
regularization parameter choices unify several notions of entropy-penalized
barycenters while also revealing new ones, including a special case of debiased
barycenters. In this paper, we propose and analyze an algorithm for computing
doubly regularized Wasserstein barycenters. Our procedure builds on damped
Sinkhorn iterations followed by exact maximization/minimization steps and
guarantees convergence for any choice of regularization parameters. An inexact
variant of our algorithm, implementable using approximate Monte Carlo sampling,
offers the first non-asymptotic convergence guarantees for approximating
Wasserstein barycenters between discrete point clouds in the
free-support/grid-free setting.
|
2307.13370v1
|
2023-07-30
|
Energy transfer and radiation in Hamiltonian nonlinear Klein-Gordon equations: general case
|
In this paper, we consider Klein-Gordon equations with cubic nonlinearity in
three spatial dimensions, which are Hamiltonian perturbations of the linear one
with potential. It is assumed that the corresponding Klein-Gordon operator $B =
\sqrt{-\Delta + V(x) + m^2} $ admits an arbitrary number of possibly degenerate
eigenvalues in $(0, m)$, and hence the unperturbed linear equation has multiple
time-periodic solutions known as bound states. In \cite{SW1999}, Soffer and
Weinstein discovered a mechanism called Fermi's Golden Rule for this nonlinear
system in the case of one simple but relatively large eigenvalue $\Omega\in
(\frac{m}{3}, m)$, by which energy is transferred from discrete to continuum
modes and the solution still decays in time. In particular, the exact energy
transfer rate is given. In \cite{LLY22}, we solved the general one simple
eigenvalue case. In this paper, we solve this problem in full generality:
multiple and simple or degenerate eigenvalues in $(0, m)$. The proof is based
on a kind of pseudo-one-dimensional cancellation structure in each eigenspace,
a renormalized damping mechanism, and an enhanced damping effect. It also
relies on a refined Birkhoff normal form transformation and an accurate
generalized Fermi's Golden Rule over those of Bambusi--Cuccagna \cite{BC}.
|
2307.16191v1
|
2023-08-01
|
On damping a control system with global aftereffect on quantum graphs
|
The paper naturally connects theory of quantum graphs, optimal control theory
and theory of functional-differential equations, and gives a new look at
quantum graphs as temporal networks. This means that the variable
parameterizing the edges is associated with time, while each internal vertex
opens several scenarios for the process flow. Under such settings, we extend
the problem of damping a first-order control system of the retarded type, which
was studied before only on an interval, to an arbitrary tree graph by employing
the recently suggested concept of the global delay. The latter means that the
delay imposed starting from the initial moment of time, associated with the
root of the tree, propagates through all its internal vertices. By minimizing
the energy functional, we arrive at the corresponding variational problem and
then prove its equivalence to a self-adjoint boundary value problem on the tree
for some second-order equations involving both the global delay and the global
advance, whose unique solvability is also established. Noteworthy is that at
the internal vertices, the optimal trajectory obeys Kirchhoff-type conditions,
which are common also for various models dealing with spacial networks.
|
2308.00496v2
|
2023-08-03
|
Part II On strong and non uniform stability of locally damped Timoshenko beam: Mathematical corrections to the proof of Theorem 2.2 in the publication referenced as [1] in the bibliography
|
In part I of the rebuttal (see [2] to the article [1] entitled "Uniform
stabilization for the Timoshenko beam by a locally distributed damping"
published in 2003, in the journal Electronic Journal of Differential Equations,
we prove that Lemma 3.6 and Theorem 3.1 are unproved due to major flaws
(contradictory assumptions). We also show that Theorem 2.2 and its proofs of
strong stability, and non uniform stability in the case of different speeds of
propagation, contain several incorrect arguments and several gaps (including
missing functional frames). In this part II, we give the precise missing
functional frames, fill the gaps and correct several parts contained in the
proof of Theorem 2.2 in [1]. We also complete a missing argument (see Remark
4.23 and Remark 3.2) in the proof of Theorem A in [5] used by [1]. For this we
state and prove Proposition 4.4 (see also Proposition 4.6 for a general
formulation in Banach spaces). We also give the correct formulations, and
proofs of strong stability and non uniform stability (in case of different
speeds of propagation) for Timoshenko beams.
|
2308.01625v1
|
2023-08-05
|
The isometric immersion of surfaces with finite total curvature
|
In this paper, we study the smooth isometric immersion of a complete simply
connected surface with a negative Gauss curvature in the three-dimensional
Euclidean space. For a surface with a finite total Gauss curvature and
appropriate oscillations of the Gauss curvature, we prove the global existence
of a smooth solution to the Gauss-Codazzi system and thus establish a global
smooth isometric immersion of the surface into the three-dimensional Euclidean
space. Based on a crucial observation that some linear combinations of the
Riemann invariants decay faster than others, we reformulate the Gauss-Codazzi
system as a symmetric hyperbolic system with a partial damping. Such a damping
effect and an energy approach permit us to derive global decay estimates and
meanwhile control the non-integrable coefficients of nonlinear terms.
|
2308.02832v2
|
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