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2021-01-26 | Generalized Damped Newton Algorithms in Nonsmooth Optimization via Second-Order Subdifferentials | The paper proposes and develops new globally convergent algorithms of the
generalized damped Newton type for solving important classes of nonsmooth
optimization problems. These algorithms are based on the theory and
calculations of second-order subdifferentials of nonsmooth functions with
employing the machinery of second-order variational analysis and generalized
differentiation. First we develop a globally superlinearly convergent damped
Newton-type algorithm for the class of continuously differentiable functions
with Lipschitzian gradients, which are nonsmooth of second order. Then we
design such a globally convergent algorithm to solve a structured class of
nonsmooth quadratic composite problems with extended-real-valued cost
functions, which typically arise in machine learning and statistics. Finally,
we present the results of numerical experiments and compare the performance of
our main algorithm applied to an important class of Lasso problems with those
achieved by other first-order and second-order optimization algorithms. | 2101.10555v3 |
2021-01-26 | Damped and Driven Breathers and Metastability | In this article we prove the existence of a new family of periodic solutions
for discrete, nonlinear Schrodinger equations subject to spatially localized
driving and damping. They provide an alternate description of the metastable
behavior in such lattice systems which agrees with previous predictions for the
evolution of metastable states while providing more accurate approximations to
these states. We analyze the stability of these breathers, finding a very small
positive eigenvalue whose eigenvector lies almost tangent to the surface of the
cylinder formed by the family of breathers. This causes solutions to slide
along the cylinder without leaving its neighborhood for very long times. | 2101.10999v2 |
2021-02-05 | A simple artificial damping method for total Lagrangian smoothed particle hydrodynamics | In this paper, we present a simple artificial damping method to enhance the
robustness of total Lagrangian smoothed particle hydrodynamics (TL-SPH).
Specifically, an artificial damping stress based on the Kelvin-Voigt type
damper with a scaling factor imitating a von Neumann-Richtmyer type artificial
viscosity is introduced in the constitutive equation to alleviate the spurious
oscillation in the vicinity of the sharp spatial gradients. After validating
the robustness and accuracy of the present method with a set of benchmark tests
with very challenging cases, we demonstrate its potentials in the field of
bio-mechanics by simulating the deformation of complex stent structures. | 2102.04898v1 |
2021-02-18 | Probing black hole microstructure with the kinetic turnover of phase transition | By treating black hole as the macroscopic stable state on the free energy
landscape, we propose that the stochastic dynamics of the black hole phase
transition can be effectively described by the Langevin equation or
equivalently by the Fokker-Planck equation in phase space. We demonstrate the
turnover of the kinetics for the charged anti-de Sitter black hole phase
transition, which shows that the mean first passage time is linear with the
friction in the high damping regime and inversely proportional to the friction
in the low damping regime. The fluctuations in the kinetics are shown to be
large/small in the high/low damping regime and the switching behavior from the
small fluctuations to the large fluctuations takes place at the kinetic
turnover point. Because the friction is a reflection of the microscopic degrees
of freedom acting on the order parameter of the black hole, the turnover and
the corresponding fluctuations of the phase transition kinetics can be used to
probe the black hole microstructure. | 2102.09439v1 |
2021-02-25 | Energy Decay of some boundary coupled systems involving wave$\backslash$ Euler-Bernoulli beam with one locally singular fractional Kelvin-Voigt damping | In this paper, we investigate the energy decay of hyperbolic systems of
wave-wave, wave-Euler- Bernoulli beam and beam-beam types. The two equations
are coupled through boundary connection with only one localized non-smooth
fractional Kelvin-Voigt damping. First, we reformulate each system into an
augmented model and using a general criteria of Arendt-Batty, we prove that our
models are strongly stable. Next, by using frequency domain approach, combined
with multiplier technique and some interpolation inequalities, we establish
different types of polynomial energy decay rate which depends on the order of
the fractional derivative and the type of the damped equation in the system. | 2102.12732v2 |
2021-03-01 | Fluid-plate interaction under periodic forcing | The motion of a thin elastic plate interacting with a viscous fluid is
investigated. A periodic force acting on the plate is considered, which in a
setting without damping could lead to a resonant response. The interaction with
the viscous fluid provides a damping mechanism due to the energy dissipation in
the fluid. Moreover, an internal damping mechanism in the plate is introduced.
In this setting, we show that the periodic forcing leads to a time-periodic
(non-resonant) solution. We employ the Navier-Stokes and the Kirchhoff-Love
plate equation in a periodic cell structure to model the motion of the viscous
fluid and the elastic plate, respectively. Maximal Lp regularity for the
linearized system is established in a framework of time-periodic function
spaces. Existence of a solution to the fully nonlinear system is subsequently
shown with a fixed-point argument. | 2103.00795v1 |
2021-03-25 | Nonlinear inviscid damping and shear-buoyancy instability in the two-dimensional Boussinesq equations | We investigate the long-time properties of the two-dimensional inviscid
Boussinesq equations near a stably stratified Couette flow, for an initial
Gevrey perturbation of size $\varepsilon$. Under the classical Miles-Howard
stability condition on the Richardson number, we prove that the system
experiences a shear-buoyancy instability: the density variation and velocity
undergo an $O(t^{-1/2})$ inviscid damping while the vorticity and density
gradient grow as $O(t^{1/2})$. The result holds at least until the natural,
nonlinear timescale $t \approx \varepsilon^{-2}$. Notice that the density
behaves very differently from a passive scalar, as can be seen from the
inviscid damping and slower gradient growth. The proof relies on several
ingredients: (A) a suitable symmetrization that makes the linear terms amenable
to energy methods and takes into account the classical Miles-Howard spectral
stability condition; (B) a variation of the Fourier time-dependent energy
method introduced for the inviscid, homogeneous Couette flow problem developed
on a toy model adapted to the Boussinesq equations, i.e. tracking the potential
nonlinear echo chains in the symmetrized variables despite the vorticity
growth. | 2103.13713v1 |
2021-03-31 | Research of Damped Newton Stochastic Gradient Descent Method for Neural Network Training | First-order methods like stochastic gradient descent(SGD) are recently the
popular optimization method to train deep neural networks (DNNs), but
second-order methods are scarcely used because of the overpriced computing cost
in getting the high-order information. In this paper, we propose the Damped
Newton Stochastic Gradient Descent(DN-SGD) method and Stochastic Gradient
Descent Damped Newton(SGD-DN) method to train DNNs for regression problems with
Mean Square Error(MSE) and classification problems with Cross-Entropy
Loss(CEL), which is inspired by a proved fact that the hessian matrix of last
layer of DNNs is always semi-definite. Different from other second-order
methods to estimate the hessian matrix of all parameters, our methods just
accurately compute a small part of the parameters, which greatly reduces the
computational cost and makes convergence of the learning process much faster
and more accurate than SGD. Several numerical experiments on real datesets are
performed to verify the effectiveness of our methods for regression and
classification problems. | 2103.16764v1 |
2021-04-08 | Landau Damping in the Transverse Modulational Dynamics of Co-Propagating Light and Matter Beams | The optomechanical coupling and transverse stability of a co-propagating
monochromatic electromagnetic wave and mono-energetic beam of two-level atoms
is investigated in the collisionless regime. The coupled dynamics are studied
through a Landau stability analysis of the coupled gas- kinetic and paraxial
wave equations, including the effect of the electronic nonlinearity. The
resulting dispersion relation captures the interaction of kinetic and
saturation effects and shows that for blue detuning the combined nonlinear
interaction is unstable below a critical wavenumber which reduces to the result
of Bespalov and Talanov in the limit of a negligible kinetic nonlinearity. For
red detuning we find that under a saturation parameter threshold exists whereby
the system stabilizes unconditionally. With negligible saturation, an
optomechanical form of Landau damping stabilizes all wavenumbers above a
critical wavenumber determined by the combined strength of the kinetic and
refractive optomechanical feedback. The damping is mediated primarily by atoms
traveling along the primary diagonals of the Talbot carpet. | 2104.04100v1 |
2021-04-15 | Simulating cosmological supercooling with a cold atom system II | We perform an analysis of the supercooled state in an analogue of an early
universe phase transition based on a one dimensional, two-component Bose gas
with time-dependent interactions. We demonstrate that the system behaves in the
same way as a thermal, relativistic Bose gas undergoing a first order phase
transition. We propose a way to prepare the state of the system in the
metastable phase as an analogue to supercooling in the early universe. While we
show that parametric resonances in the system can be suppressed by thermal
damping, we find that the theoretically estimated thermal damping in our model
is too weak to suppress the resonances for realistic experimental parameters.
However, we propose that experiments to investigate the effective damping rate
in experiments would be worthwhile. | 2104.07428v1 |
2021-05-04 | Linear response theory and damped modes of stellar clusters | Because all stars contribute to its gravitational potential, stellar clusters
amplify perturbations collectively. In the limit of small fluctuations, this is
described through linear response theory, via the so-called response matrix.
While the evaluation of this matrix is somewhat straightforward for unstable
modes (i.e. with a positive growth rate), it requires a careful analytic
continuation for damped modes (i.e. with a negative growth rate). We present a
generic method to perform such a calculation in spherically symmetric stellar
clusters. When applied to an isotropic isochrone cluster, we recover the
presence of a low-frequency weakly damped $\ell = 1$ mode. We finally use a set
of direct $N$-body simulations to test explicitly this prediction through the
statistics of the correlated random walk undergone by a cluster's density
centre. | 2105.01371v1 |
2021-05-10 | Passivity-based control of mechanical systems with linear damping identification | We propose a control approach for a class of nonlinear mechanical systems to
stabilize the system under study while ensuring that the oscillations of the
transient response are reduced. The approach is twofold: (i) we apply our
technique for linear viscous damping identification of the system to improve
the accuracy of the selected control technique, and (ii) we implement a
passivity-based controller to stabilize and reduce the oscillations by
selecting the control parameters properly in accordance with the identified
damping. Moreover, we provide an analysis for a particular passivity-based
control approach that has been shown successfully for reducing such
oscillations. Also, we validate the methodology by implementing it
experimentally in a planar manipulator. | 2105.04324v4 |
2021-05-26 | Decay dynamics of Localised Surface Plasmons: damping of coherences and populations of the oscillatory plasmon modes | Properties of plasmonic materials are associated with surface plasmons - the
electromagnetic excitations coupled to coherent electron charge density
oscillations on a metal/dielectric interface. Although decay of such
oscillations cannot be avoided, there are prospects for controlling plasmon
damping dynamics. In spherical metal nanoparticles (MNPs) the basic properties
of Localized Surface Plasmons (LSPs) can be controlled with their radius. The
present paper handles the link between the size-dependent description of LSP
properties derived from the dispersion relation based on Maxwell's equations
and the quantum picture in which MNPs are treated as "quasi-particles". Such
picture, based on the reduced density-matrix of quantum open systems ruled by
the master equation in the Lindblad form, enables to distinguish between
damping processes of populations and coherences of multipolar plasmon
oscillatory states and to establish the intrinsic relations between the rates
of these processes, independently of the size of MNP. The impact of the
radiative and the nonradiative energy dissipation channels is discussed. | 2105.12463v1 |
2021-06-05 | The electron acoustic waves in plasmas with two kappa-distributed electrons at the same temperatures and immobile ions | The linear electron acoustic waves propagating in plasmas with two
kappa-distributed electrons and stationary ions are investigated. The
temperatures of the two electrons are assumed to be the same, but the kappa
indices are not. It shows that if one kappa index is small enough and the other
one is large enough, a weak damping regime of the electron acoustic waves
exists. The dispersions and damping rates are numerically studied. The
parameter spaces for the weakly damped electron acoustic waves are analyzed.
Moreover, the electron acoustic waves in the present model are compared with
those in other models, especially the plasmas with two-temperature electrons.
At last, we perform Vlasov-Poisson simulations to verify the theory. | 2106.02910v2 |
2021-06-18 | Global existence and asymptotic behavior for semilinear damped wave equations on measure spaces | This paper is concerned with the semilinear damped wave equation on a measure
space with a self-adjoint operator, instead of the standard Laplace operator.
Under a certain decay estimate on the corresponding heat semigroup, we
establish the linear estimates which generalize the so-called Matsumura
estimates, and prove the small data global existence of solutions to the damped
wave equation based on the linear estimates. Our approach is based on a direct
spectral analysis analogous to the Fourier analysis. The self-adjoint operators
treated in this paper include some important examples such as the Laplace
operators on Euclidean spaces, the Dirichlet Laplacian on an arbitrary open
set, the Robin Laplacian on an exterior domain, the Schr\"odinger operator, the
elliptic operator, the Laplacian on Sierpinski gasket, and the fractional
Laplacian. | 2106.10322v3 |
2021-06-21 | On the small time asymptotics of stochastic Ladyzhenskaya-Smagorinsky equations with damping perturbed by multiplicative noise | The Ladyzhenskaya-Smagorinsky equations model turbulence phenomena, and are
given by $$\frac{\partial \boldsymbol{u}}{\partial t}-\mu
\mathrm{div}\left(\left(1+|\nabla\boldsymbol{u}|^2\right)^{\frac{p-2}{2}}\nabla\boldsymbol{u}\right)+(\boldsymbol{u}\cdot\nabla)\boldsymbol{u}+\nabla
p=\boldsymbol{f}, \ \nabla\cdot\boldsymbol{u}=0,$$ for $p\geq 2,$ in a bounded
domain $\mathcal{O}\subset\mathbb{R}^d$ ($2\leq d\leq 4$). In this work, we
consider the stochastic Ladyzhenskaya-Smagorinsky equations with the damping
$\alpha\boldsymbol{u}+\beta|\boldsymbol{u}|^{r-2}\boldsymbol{u},$ for $r\geq 2$
($\alpha,\beta\geq 0$), subjected to multiplicative Gaussian noise. We show the
local monotoincity ($p\geq \frac{d}{2}+1,\ r\geq 2$) as well as global
monotonicity ($p\geq 2,\ r\geq 4$) properties of the linear and nonlinear
operators, which along with an application of stochastic version of
Minty-Browder technique imply the existence of a unique pathwise strong
solution. Then, we discuss the small time asymptotics by studying the effect of
small, highly nonlinear, unbounded drifts (small time large deviation
principle) for the stochastic Ladyzhenskaya-Smagorinsky equations with damping. | 2106.10861v1 |
2021-06-23 | Improved convergence rates and trajectory convergence for primal-dual dynamical systems with 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 asymptotically vanishing damping term. The system is formulated in
terms of the augmented Lagrangian associated to the minimization problem. We
show fast convergence of the primal-dual gap, the feasibility measure, and the
objective function value along the generated trajectories. In case the
objective function has Lipschitz continuous gradient, we show that the
primal-dual trajectory asymptotically weakly converges to a primal-dual optimal
solution of the underlying minimization problem. To the best of our knowledge,
this is the first result which guarantees the convergence of the trajectory
generated by a primal-dual dynamical system with asymptotic vanishing damping.
Moreover, we will rediscover in case of the unconstrained minimization of a
convex differentiable function with Lipschitz continuous gradient all
convergence statements obtained in the literature for Nesterov's accelerated
gradient method. | 2106.12294v1 |
2021-07-01 | On behavior of solutions to a Petrovsky equation with damping and variable-exponent source | This paper deals with the following Petrovsky equation with damping and
nonlinear source \[u_{tt}+\Delta^2 u-M(\|\nabla u\|_2^2)\Delta u-\Delta
u_t+|u_t|^{m(x)-2}u_t=|u|^{p(x)-2}u\] under initial-boundary value conditions,
where $M(s)=a+ bs^\gamma$ is a positive $C^1$ function with parameters
$a>0,~b>0,~\gamma\geq 1$, and $m(x),~p(x)$ are given measurable functions. The
upper bound of the blow-up time is derived for low initial energy using the
differential inequality technique. For $m(x)\equiv2$, in particular, the upper
bound of the blow-up time is obtained by the combination of Levine's concavity
method and some differential inequalities under high initial energy. In
addition, by making full use of the strong damping, the lower bound of the
blow-up time is discussed. Moreover, the global existence of solutions and an
energy decay estimate are presented by establishing some energy estimates and
by exploiting a key integral inequality. | 2107.00273v2 |
2021-07-21 | A combined volume penalization / selective frequency damping approach for immersed boundary methods applied to high-order schemes | There has been an increasing interest in developing efficient immersed
boundary method (IBM) based on Cartesian grids, recently in the context of
high-order methods. IBM based on volume penalization is a robust and easy to
implement method to avoid body-fitted meshes and has been recently adapted to
high order discretisations (Kou et al., 2021). This work proposes an
improvement over the classic penalty formulation for flux reconstruction high
order solvers. We include a selective frequency damping (SFD) approach
(Aakervik et al., 2006) acting only inside solid body defined through the
immersed boundary masking, to damp spurious oscillations. An encapsulated
formulation for the SFD method is implemented, which can be used as a wrapper
around an existing time-stepping code. The numerical properties have been
studied through eigensolution analysis based on the advection equation. These
studies not only show the advantages of using the SFD method as an alternative
of the traditional volume penalization, but also show the favorable properties
of combining both approaches. This new approach is then applied to the
Navier-Stokes equation to simulate steady flow past an airfoil and unsteady
flow past a circular cylinder. The advantages of the SFD method in providing
improved accuracy are reported. | 2107.10177v1 |
2021-07-25 | Dispatch of Virtual Inertia and Damping: Numerical Method with SDP and ADMM | Power grids are evolving toward 100% renewable energy interfaced by
inverters. Virtual inertia and damping provided by inverters are essential to
synchronism and frequency stability of future power grids. This paper
numerically addresses the problem of dispatch of virtual inertia and damping
(DID) among inverters in the transmission network. The DID problem is first
formulated as a nonlinear program (NLP) by the Radua collocation method which
is flexible to handle various types of disturbances and bounds constraints.
Since the NLP of DID is highly non-convex, semi-definite programming (SDP)
relaxation for the NLP is further derived to tackle the non-convexity, followed
by its sparsity being exploited hierarchically based on chordality of graphs to
seek enhancement of computational efficiency. Considering high dimension and
inexactness of the SDP relaxation, a feasibility-embedded distributed approach
is finally proposed under the framework of alternating direction method of
multipliers (ADMM), which achieves parallel computing and solution feasibility
regarding the original NLP. Numerical simulations carried out for five test
power systems demonstrate the proposed method and necessity of DID. | 2107.11764v1 |
2021-08-09 | Damping perturbation based time integration asymptotic method for structural dynamics | The light damping hypothesis is usually assumed in structural dynamics since
dissipative forces are in general weak with respect to inertial and elastic
forces. In this paper a novel numerical method of time integration based on the
artificial perturbation of damping is proposed. The asymptotic expansion of the
transient response results in an infinite series which can be summed, leading
to a well-defined explicit iterative step-by-step scheme. Conditions for
convergence are rigorously analyzed, enabling the determination of the
methodology boundaries in form of maximum time step. The numerical properties
of the iterative scheme, i.e. stability, accuracy and computational effort are
also studied in detail. The approach is validated with two numerical examples,
showing a high accuracy and computational efficiency relative to other methods. | 2108.03813v1 |
2021-09-22 | Antibunching via cooling by heating | We investigate statistics of the photon (phonon) field undergoing linear and
nonlinear damping processes. An effective two-photon (phonon) nonlinear
"cooling by heating" process is realized from linear damping by spectral
filtering of the heat baths present in the system. This cooling process driven
by incoherent quantum thermal noise can create quantum states of the photon
field. In fact, for high temperatures of the spectrally filtered heat baths,
sub-Poissonian statistics with strong antibunching in the photon (phonon) field
are reported. This notion of the emergence and control of quantumness by
incoherent thermal quantum noise is applied to a quantum system comprising of a
two-level system and a harmonic oscillator or analogous optomechanical setting.
Our analysis may provide a promising direction for the preparation and
protection of quantum features via nonlinear damping that can be controlled
with incoherent thermal quantum noise. | 2109.10516v2 |
2021-10-13 | Tutorial on stochastic systems | In this tutorial, three examples of stochastic systems are considered: A
strongly-damped oscillator, a weakly-damped oscillator and an undamped
oscillator (integrator) driven by noise. The evolution of these systems is
characterized by the temporal correlation functions and spectral densities of
their displacements, which are determined and discussed. Damped oscillators
reach steady stochastic states. Their correlations are decreasing functions of
the difference between the sample times and their spectra have peaks near their
resonance frequencies. An undamped oscillator never reaches a steady state. Its
energy increases with time and its spectrum is sharply peaked at low
frequencies. The required mathematical methods and physical concepts are
explained on a just-in-time basis, and some theoretical pitfalls are mentioned.
The insights one gains from studies of oscillators can be applied to a wide
variety of physical systems, such as atom and semiconductor lasers, which will
be discussed in a subsequent tutorial. | 2110.06966v1 |
2021-10-18 | Structured vector fitting framework for mechanical systems | In this paper, we develop a structure-preserving formulation of the
data-driven vector fitting algorithm for the case of modally damped mechanical
systems. Using the structured pole-residue form of the transfer function of
modally damped second-order systems, we propose two possible structured
extensions of the barycentric formula of system transfer functions. Integrating
these new forms within the classical vector fitting algorithm leads to the
formulation of two new algorithms that allow the computation of modally damped
mechanical systems from data in a least squares fashion. Thus, the learned
model is guaranteed to have the desired structure. We test the proposed
algorithms on two benchmark models. | 2110.09220v1 |
2021-10-27 | Integrability and solvability of polynomial Liénard differential systems | We provide the necessary and sufficient conditions of Liouvillian
integrability for Li\'{e}nard differential systems describing nonlinear
oscillators with a polynomial damping and a polynomial restoring force. We
prove that Li\'{e}nard differential systems are not Darboux integrable
excluding subfamilies with certain restrictions on the degrees of the
polynomials arising in the systems. We demonstrate that if the degree of a
polynomial responsible for the restoring force is greater than the degree of a
polynomial producing the damping, then a generic Li\'{e}nard differential
system is not Liouvillian integrable with the exception of linear Li\'{e}nard
systems. However, for any fixed degrees of the polynomials describing the
damping and the restoring force we present subfamilies possessing Liouvillian
first integrals. As a by-product of our results, we find a number of novel
Liouvillian integrable subfamilies. In addition, we study the existence of
non-autonomous Darboux first integrals and non-autonomous Jacobi last
multipliers with a time-dependent exponential factor. | 2110.14306v2 |
2021-10-28 | Global Solution to the Vacuum Free Boundary Problem with Physical Singularity of Compressible Euler Equations with Damping and Gravity | The global existence of smooth solutions to the vacuum free boundary problem
with physical singularity of compressible Euler equations with damping and
gravity is proved in space dimensions $n=1, 2, 3$, for the initial data being
small perturbations of the stationary solution. Moreover, the exponential decay
of the velocity is obtained for $n=1, 2, 3$. The exponentially fast convergence
of the density and vacuum boundary to those of the stationary solution is shown
for $n=1$, and it is proved for $n=2, 3$ that they stay close to those of the
stationary solution if they do so initially. The proof is based on the weighted
estimates of both hyperbolic and parabolic types with weights capturing the
singular behavior of higher-order normal derivatives near vacuum states,
exploring the balance between the physical singularity which pushes the vacuum
boundary outwards and the effect of gravity which pulls it inwards, and the
dissipation of the frictional damping. The results obtained in this paper are
the first ones on the global existence of solutions to the vacuum free boundary
problems of inviscid compressible fluids with the non-expanding background
solutions. Exponentially fast convergence when the vacuum state is involved
discovered in this paper is a new feature of the problem studied. | 2110.14909v1 |
2021-10-29 | Spinons and damped phonons in spin-1/2 quantum-liquid Ba$_{4}$Ir${}_3$O${}_{10}$ observed by Raman scattering | In spin-1/2 Mott insulators, non-magnetic quantum liquid phases are often
argued to arise when the system shows no magnetic ordering, but identifying
positive signatures of these phases or related spinon quasiparticles can be
elusive. Here we use Raman scattering to provide three signatures for spinons
in a possible spin-orbit quantum liquid material Ba${}_4$Ir${}_3$O${}_{10}$:
(1) A broad hump, which we show can arise from Luttinger Liquid spinons in
Raman with parallel photon polarizations normal to 1D chains; (2) Strong phonon
damping from phonon-spin coupling via the spin-orbit interaction; and (3) the
absence of (1) and (2) in the magnetically ordered phase that is produced when
2% of Ba is substituted by Sr
((Ba${}_{0.98}$Sr${}_{0.02}$)${}_4$Ir${}_3$O${}_{10}$). The phonon damping via
itinerant spinons seen in this quantum-liquid insulator suggests a new
mechanism for enhancing thermoelectricity in strongly correlated conductors,
through a neutral quantum liquid that need not affect electronic transport. | 2110.15916v1 |
2021-11-03 | Pointwise space-time estimates of two-phase fluid model in dimension three | In this paper, we investigate the pointwise space-time behavior of two-phase
fluid model derived by Choi \cite{Choi} [SIAM J. Math. Anal., 48(2016), pp.
3090-3122], which is the compressible damped Euler equations coupled with
compressible Naiver-Stokes equations. Based on Green's function method together
with frequency analysis and nonlinear coupling of different wave patterns, it
shows that both of two densities and momentums obey the generalized Huygens'
principle as the compressible Navier-Stokes equations \cite{LW}, however, it is
different from the compressible damped Euler equations \cite{Wang2}. The main
contributions include seeking suitable combinations to avoid the singularity
from the Hodge decomposition in the low frequency part of the Green's function,
overcoming the difficulty of the non-conservation arising from the damped
mechanism of the system, and developing the detailed description of the
singularities in the high frequency part of the Green's function. Finally, as a
byproduct, we extend $L^2$-estimate in \cite{Wugc} [SIAM J. Math. Anal.,
52(2020), pp. 5748-5774] to $L^p$-estimate with $p>1$. | 2111.01987v1 |
2021-11-09 | Turbulent cascades for a family of damped Szegö equations | In this paper, we study the transfer of energy from low to high frequencies
for a family of damped Szeg\"o equations. The cubic Szeg\"o equation has been
introduced as a toy model for a totally non-dispersive degenerate Hamiltonian
equation. It is a completely integrable system which develops growth of high
Sobolev norms, detecting transfer of energy and hence cascades phenomena.
Here, we consider a two-parameter family of variants of the cubic Szeg\"o
equation and prove that adding a damping term unexpectedly promotes the
existence of turbulent cascades. Furthermore, we give a panorama of the
dynamics for such equations on a six-dimensional submanifold. | 2111.05247v1 |
2021-11-22 | Global well-posedness for a generalized Keller-Segel system with degenerate dissipation and mixing | We study the mixing effect for a generalized Keller-Segel system with
degenerate dissipation and advection by a weakly mixing. Here the attractive
operator has weak singularity, namely, the negative derivative appears in the
nonlinear term by singular integral. Without advection, the solution of
equation blows up in finite time. We show that the global well-posedness of
solution with large advection. Since dissipation term degenerate into the
damping, the enhanced dissipation effect of mixing no longer occurs, we prove
that the mixing effect can weak the influence of nonlinear term. In this case,
the mixing effect is similar with inviscid damping of shear flow. Combining to
the mixing effect and damping effect of degenerate dissipation, the global
$L^\infty$ estimate of solution is established. | 2111.11083v1 |
2021-11-26 | Transition from order to chaos in reduced quantum dynamics | We study a damped kicked top dynamics of a large number of qubits ($N
\rightarrow \infty$) and focus on an evolution of a reduced single-qubit
subsystem. Each subsystem is subjected to the amplitude damping channel
controlled by the damping constant $r\in [0,1]$, which plays the role of the
single control parameter. In the parameter range for which the classical
dynamics is chaotic, while varying $r$ we find the universal period-doubling
behavior characteristic to one-dimensional maps: period-two dynamics starts at
$r_1 \approx 0.3181$, while the next bifurcation occurs at $ r_2 \approx
0.5387$. In parallel with period-four oscillations observed for $r \leq r_3
\approx 0.5672$, we identify a secondary bifurcation diagram around $r\approx
0.544$, responsible for a small-scale chaotic dynamics inside the attractor.
The doubling of the principal bifurcation tree continues until $r \leq
r_{\infty} \sim 0.578$, which marks the onset of the full scale chaos
interrupted by the windows of the oscillatory dynamics corresponding to the
Sharkovsky order. | 2111.13477v1 |
2021-12-06 | Damped physical oscillators, temperature and chemical clocks | The metaphor of a clock in physics describes near-equilibrium reversible
phenomena such as an oscillating spring. It is surprising that for chemical and
biological clocks the focus has been exclusively on the far-from-equilibrium
dissipative processes. We show here that one can represent chemical
oscillations (the Lotka-Volterra system and the Brusselator) by equations
analogous to Onsager's phenomenological equations when the condition of the
reciprocal relations, i.e. the symmetry in the coupling of thermodynamic forces
to fluxes is relaxed and antisymmetric contributions are permitted. We compare
these oscillations to damped oscillators in physics (e.g., springs, coupled
springs and electrical circuits) which are represented by similar equations.
Onsager's equations and harmonic Hamiltonian systems are shown to be limiting
cases of a more general formalism.
The central element of un-damped physical oscillations is the conservation of
entropy which unavoidably results in reversible temperature oscillations. Such
temperature oscillations exist in springs and electrical LC-circuits, but have
among others also been found in the oscillating Belousov-Zhabotinsky reaction,
in oscillations of yeast cells, and during the nervous impulse. This suggests
that such oscillations contain reversible entropy-conserving elements, and that
physical and chemical clocks may be more similar than expected. | 2112.03083v1 |
2021-12-10 | Existence of Zero-damped Quasinormal Frequencies for Nearly Extremal Black Holes | It has been observed that many spacetimes which feature a near-extremal
horizon exhibit the phenomenon of zero-damped modes. This is characterised by
the existence of a sequence of quasinormal frequencies which all converge to
some purely imaginary number $i\alpha$ in the extremal limit and cluster in a
neighbourhood of the line $\Im s=\alpha$. In this paper, we establish that this
property is present for the conformal Klein-Gordon equation on a
Reissner-Nordstr\"om-de Sitter background. This follows from a similar result
that we prove for a class of spherically symmetric black hole spacetimes with a
cosmological horizon. We also show that the phenomenon of zero-damped modes is
stable to perturbations that arise through adding a potential. | 2112.05669v3 |
2021-12-22 | Quantifying Spin-Orbit Torques in Antiferromagnet/Heavy Metal Heterostructures | The effect of spin currents on the magnetic order of insulating
antiferromagnets (AFMs) is of fundamental interest and can enable new
applications. Toward this goal, characterizing the spin-orbit torques (SOT)
associated with AFM/heavy metal (HM) interfaces is important. Here we report
the full angular dependence of the harmonic Hall voltages in a predominantly
easy-plane AFM, epitaxial c-axis oriented $\alpha$-Fe$_2$O$_3$ films, with an
interface to Pt. By modeling the harmonic Hall signals together with the
$\alpha$-Fe$_2$O$_3$ magnetic parameters, we determine the amplitudes of
field-like and damping-like SOT. Out-of-plane field scans are shown to be
essential to determining the damping-like component of the torques. In contrast
to ferromagnetic/heavy metal heterostructures, our results demonstrate that the
field-like torques are significantly larger than the damping-like torques,
which we correlate with the presence of a large imaginary component of the
interface spin-mixing conductance. Our work demonstrates a direct way of
characterizing SOT in AFM/HM heterostructures. | 2112.12238v1 |
2022-01-04 | Focusing of nonlinear eccentric waves in astrophysical discs. II. Excitation and damping of tightly-wound waves | In this paper I develop a nonlinear theory of tightly-wound (highly twisted)
eccentric waves in astrophysical discs, based on the averaged Lagrangian method
of Whitham. Viscous dissipation is included in the theory by use of a
pseudo-Lagrangian. This work is an extension of the theory developed by Lee \&
Goodman to 3D discs, with the addition of viscosity. I confirm that linear
tightly-wound eccentric waves are overstable and are excited by the presence of
a shear viscosity and show this persists for weakly nonlinear waves. I find the
waves are damped by shear viscosity when the wave become sufficiently
nonlinear, a result previously found in particulate discs. Additionally I
compare the results of this model to recent simulations of eccentric waves
propagating in the inner regions of black hole discs and show that an ingoing
eccentric wave can be strongly damped near the marginally stable orbit,
resulting in a nearly circular disc with a strong azimuthal variation in the
disc density. | 2201.01156v1 |
2022-01-12 | Local Well-Posedness of the Gravity-Capillary Water Waves System in the Presence of Geometry and Damping | We consider the gravity-capillary water waves problem in a domain $\Omega_t
\subset \mathbb{T} \times \mathbb{R}$ with substantial geometric features.
Namely, we consider a variable bottom, smooth obstacles in the flow and a
constant background current. We utilize a vortex sheet model introduced by
Ambrose, et. al. in arXiv:2108.01786. We show that the water waves problem is
locally-in-time well-posed in this geometric setting and study the lifespan of
solutions. We then add a damping term and derive evolution equations that
account for the damper. Ultimately, we show that the same well-posedness and
lifespan results apply to the damped system. We primarily utilize energy
methods. | 2201.04713v2 |
2022-02-04 | Finite-temperature plasmons, damping and collective behavior for $α-\mathcal{T}_3$ model | We have conducted a thorough theoretical and numerical investigation of the
electronic susceptibility, polarizability, plasmons, their damping rates, as
well as the static screening in pseudospin-1 Dirac cone materials with a flat
band, or for a general $\alpha - \mathcal{T}_3$ model, at finite temperatures.
This includes calculating the polarization function, plasmon dispersions and
their damping rates at arbitrary temperatures and obtaining analytical
approximations the long wavelength limit, low and high temperatures. We
demonstrate that the integral transformation of the polarization function
cannot be used directly for a dice lattice revealing some fundamental
properties and important applicability limits of the flat band dispersions
model. At $k_B T \ll E_F$, the largest temperature-induced change of the
polarization function and plasmons comes from the mismatch between the chemical
potential and the Fermi energy. We have also obtained a series of closed-form
semi-analytical expressions for the static limit of the polarization function
of an arbitrary $\alpha - \mathcal{T}_3$ material at any temperature with exact
analytical formulas for the high, low and zero temperature limits which is of
tremendous importance for all types of transport and screening calculations for
the flat band Dirac materials. | 2202.01945v1 |
2022-02-04 | Enhancing the Formation of Wigner Negativity in a Kerr Oscillator via Quadrature Squeezing | Motivated by quantum experiments with nanomechanical systems, the evolution
of a Kerr oscillator with focus on creation of states with a negative Wigner
function is investigated. Using the phase space formalism, results are
presented that demonstrate an asymptotic behavior in the large squeezing regime
for the negativity of a squeezed vacuum state under unitary evolution. The
analysis and model are extended to squeezed vacuum states of open systems,
adding the decoherence effects of damping and dephasing. To increase
experimental relevance, the regime of strong damping is considered. These
effects are investigated, yielding similar asymptotic results for the behavior
of these effects in the large squeezing regime. Combining these results, it is
shown that a weak nonlinearity as compared to damping may be improved by
increasing the squeezing of the initial state. It is also shown that this may
be done without exacerbating the effects of dephasing. | 2202.02285v1 |
2022-02-11 | Spin stiffness, spectral weight, and Landau damping of magnons in metallic spiral magnets | We analyze the properties of magnons in metallic electron systems with spiral
magnetic order. Our analysis is based on the random phase approximation for the
susceptibilities of tight binding electrons with a local Hubbard interaction in
two or three dimensions. We identify three magnon branches from poles in the
susceptibilities, one associated with in-plane, the other two associated with
out-of-plane fluctuations of the spiral order parameter. We derive general
expressions for the spin stiffnesses and the spectral weights of the magnon
modes, from which also the magnon velocities can be obtained. Moreover, we
determine the size of the decay rates of the magnons due to Landau damping.
While the decay rate of the in-plane mode is of the order of its excitation
energy, the decay rate of the out-of-plane mode is smaller so that these modes
are asymptotically stable excitations even in the presence of Landau damping. | 2202.05660v1 |
2022-04-01 | Effect of interfacial spin mixing conductance on gyromagnetic ratio of Gd substituted Y$_{3}$Fe$_{5}$O$_{12}$ | Due to its low intrinsic damping, Y$_3$Fe$_5$O$_{12}$ and its substituted
variations are often used for ferromagnetic layer at spin pumping experiment.
Spin pumping is an interfacial spin current generation in the interface of
ferromagnet and non-magnetic metal, governed by spin mixing conductance
parameter $G^{\uparrow\downarrow}$. $G^{\uparrow\downarrow}$ has been shown to
enhance the damping of the ferromagnetic layer. The theory suggested that the
effect of $G^{\uparrow\downarrow}$ on gyromagnetic ratio only come from its
negligible imaginary part. In this article, we show that the different damping
of ferrimagnetic lattices induced by $G^{\uparrow\downarrow}$ can affect the
gyromagnetic ratio of Gd-substituted Y$_3$Fe$_5$O$_{12}$. | 2204.00310v1 |
2022-04-04 | A Vanka-based parameter-robust multigrid relaxation for the Stokes-Darcy Brinkman problems | We propose a block-structured multigrid relaxation scheme for solving the
Stokes-Darcy Brinkman equations discretized by the marker and cell scheme. An
element-based additive Vanka smoother is used to solve the corresponding
shifted Laplacian operator. Using local Fourier analysis, we present the
stencil for the additive Vanka smoother and derive an optimal smoothing factor
for Vanka-based Braess-Sarazin relaxation for the Stokes-Darcy Brinkman
equations. Although the optimal damping parameter is dependent on meshsize and
physical parameter, it is very close to one. Numerical results of two-grid and
V(1,1)-cycle are presented, which show high efficiency of the proposed
relaxation scheme and its robustness to physical parameters and the meshsize.
Using a damping parameter equal to one gives almost the same results as these
for the optimal damping parameter at a lower computational overhead. | 2204.01237v1 |
2022-04-19 | Blow-up and lifespan estimate for wave equations with critical damping term of space-dependent type related to Glassey conjecture | The main purpose of the present paper is to study the blow-up problem of the
wave equation with space-dependent damping in the \textit{scale-invariant case}
and time derivative nonlinearity with small initial data. Under appropriate
initial data which are compactly supported, by using a test function method and
taking into account the effect of the damping term
($\frac{\mu}{\sqrt{1+|x|^2}}u_t$), we provide that in higher dimensions the
blow-up region is given by $p \in (1, p_G(N+\mu)]$ where $p_G(N)$ is the
Glassey exponent. Furthermore, we shall establish a blow-up region, independent
of $\mu$ given by $p\in (1, 1+\frac{2}{N}),$ for appropriate initial data in
the energy space with noncompact support. | 2204.09156v1 |
2022-04-28 | Strong coupling of quantum emitters and the exciton polariton in MoS$_2$ nanodisks | As a quasiparticle formed by light and excitons in semiconductors, the
exciton-polariton (EP) as a quantum bus is promising for the development of
quantum interconnect devices at room temperature. However, the significant
damping of EPs in the material generally causes a loss of quantum information.
We propose a mechanism to overcome the destructive effect of a damping EP on
its mediated correlation dynamics of quantum emitters (QEs). Via an
investigation of the near-field coupling between two QEs and the EP in a
monolayer MoS$_{2}$ nanodisk, we find that, with the complete dissipation of
the QEs efficiently avoided, a persistent quantum correlation between the QEs
can be generated and stabilized even to their steady state. This is due to the
fact that, with upon decreasing the QE-MoS$_2$ distance, the QEs become so
hybridized with the EP that one or two bound states are formed between them.
Our result supplies a useful way to avoid the destructive impact of EP damping,
and it refreshes our understanding of the light-matter interaction in absorbing
medium. | 2204.13383v2 |
2022-05-09 | Scalable all-optical cold damping of levitated nanoparticles | The field of levitodynamics has made significant progress towards controlling
and studying the motion of a levitated nanoparticle. Motional control relies on
either autonomous feedback via a cavity or measurement-based feedback via
external forces. Recent demonstrations of measurement-based ground-state
cooling of a single nanoparticle employ linear velocity feedback, also called
cold damping, and require the use of electrostatic forces on charged particles
via external electrodes. Here we introduce a novel all-optical cold damping
scheme based on spatial modulation of the trap position that is scalable to
multiple particles. The scheme relies on using programmable optical tweezers to
provide full independent control over trap frequency and position of each
tweezer. We show that the technique cools the center-of-mass motion of
particles down to $17\,$mK at a pressure of $2 \times 10^{-6}\,$mbar and
demonstrate its scalability by simultaneously cooling the motion of two
particles. Our work paves the way towards studying quantum interactions between
particles, achieving 3D quantum control of particle motion without cavity-based
cooling, electrodes or charged particles, and probing multipartite entanglement
in levitated optomechanical systems. | 2205.04455v1 |
2022-06-08 | Thermal ion kinetic effects and Landau damping in fishbone modes | The kinetic-MHD hybrid simulation approach for macroscopic instabilities in
plasmas can be extended to include the kinetic effects of both thermal ions and
energetic ions. The new coupling scheme includes synchronization of density and
parallel velocity between thermal ions and MHD, in addition to pressure
coupling, to ensure the quasineutrality condition and avoid numerical errors.
The new approach has been implemented in the kinetic-MHD code M3D-C1-K, and was
used to study the thermal ion kinetic effects and Landau damping in fishbone
modes in both DIII-D and NSTX. It is found that the thermal ion kinetic effects
can cause an increase of the frequencies of the non-resonant $n=1$ fishbone
modes driven by energetic particles for $q_\mathrm{min}>1$, and Landau damping
can provide additional stabilization effects. A nonlinear simulation for $n=1$
fishbone mode in NSTX is also performed, and the perturbation on magnetic flux
surfaces and the transport of energetic particles are calculated. | 2206.03648v1 |
2022-07-12 | Resonant Multilevel Amplitude Damping Channels | We introduce a new set of quantum channels: resonant multilevel amplitude
damping (ReMAD) channels. Among other instances, they can describe energy
dissipation effects in multilevel atomic systems induced by the interaction
with a zero-temperature bosonic environment. At variance with the already known
class of multilevel amplitude damping (MAD) channels, this new class of maps
allows the presence of an environment unable to discriminate transitions with
identical energy gaps. After characterizing the algebra of their composition
rules, by analyzing the qutrit case, we show that this new set of channels can
exhibit degradability and antidegradability in vast regions of the allowed
parameter space. There we compute their quantum capacity and private classical
capacity. We show that these capacities can be computed exactly also in regions
of the parameter space where the channels aren't degradable nor antidegradable. | 2207.05646v2 |
2022-07-14 | Estimates for the nonlinear viscoelastic damped wave equation on compact Lie groups | Let $G$ be a compact Lie group. In this article, we investigate the Cauchy
problem for a nonlinear wave equation with the viscoelastic damping on $G$.
More preciously, we investigate some $L^2$-estimates for the solution to the
homogeneous nonlinear viscoelastic damped wave equation on $G$ utilizing the
group Fourier transform on $G$. We also prove that there is no improvement of
any decay rate for the norm $\|u(t,\cdot)\|_{L^2(G)}$ by further assuming the
$L^1(G)$-regularity of initial data. Finally, using the noncommutative Fourier
analysis on compact Lie groups, we prove a local in time existence result in
the energy space $\mathcal{C}^1([0,T],H^1_{\mathcal L}(G)).$ | 2207.06645v3 |
2022-08-04 | Normal and Quasinormal Modes of Holographic Multiquark Star | The quadrupole normal-mode oscillation frequency $f_{n}$ of multiquark star
are computed for $n=1-5$. At the transition from low to high density multiquark
in the core region, the first 2 modes jump to larger values, a distinctive
signature of the presence of the high-density core. When the star oscillation
couples with spacetime, gravitational waves~(GW) will be generated and the star
will undergo damped oscillation. The quasinormal modes~(QNMs) of the
oscillation are computed using two methods, direct scan and WKB, for QNMs with
small and large imaginary parts respectively. The small imaginary QNMs have
frequencies $1.5-2.6$ kHz and damping times $0.19-1.7$ secs for multiquark star
with mass $M=0.6-2.1 M_{\odot}$~(solar mass). The WKB QNMs with large imaginary
parts have frequencies $5.98-9.81$ kHz and damping times $0.13-0.46$ ms for
$M\simeq 0.3-2.1 M_{\odot}$. They are found to be the fluid $f-$modes and
spacetime curvature $w-$modes respectively. | 2208.02761v2 |
2022-08-10 | Erasure qubits: Overcoming the $T_1$ limit in superconducting circuits | The amplitude damping time, $T_1$, has long stood as the major factor
limiting quantum fidelity in superconducting circuits, prompting concerted
efforts in the material science and design of qubits aimed at increasing $T_1$.
In contrast, the dephasing time, $T_{\phi}$, can usually be extended above
$T_1$ (via, e.g., dynamical decoupling), to the point where it does not limit
fidelity. In this article we propose a scheme for overcoming the conventional
$T_1$ limit on fidelity by designing qubits in a way that amplitude damping
errors can be detected and converted into erasure errors. Compared to standard
qubit implementations our scheme improves the performance of fault-tolerant
protocols, as numerically demonstrated by the circuit-noise simulations of the
surface code. We describe two simple qubit implementations with superconducting
circuits and discuss procedures for detecting amplitude damping errors,
performing entangling gates, and extending $T_\phi$. Our results suggest that
engineering efforts should focus on improving $T_\phi$ and the quality of
quantum coherent control, as they effectively become the limiting factor on the
performance of fault-tolerant protocols. | 2208.05461v1 |
2022-08-12 | Critical exponent for nonlinear wave equations with damping and potential terms | The aim of this paper is to determine the critical exponent for the nonlinear
wave equations with damping and potential terms of the scale invariant order,
by assuming that these terms satisfy a special relation. We underline that our
critical exponent is different from the one for related equations such as the
nonlinear wave equation without lower order terms, only with a damping term,
and only with a potential term. Moreover, we study the effect of the decaying
order of initial data at spatial infinity. In fact, we prove that not only the
lower order terms but also the order of the initial data affects the critical
exponent, as well as the sharp upper and lower bounds of the maximal existence
time of the solution. | 2208.06106v3 |
2022-08-17 | Conservation laws and variational structure of damped nonlinear wave equations | All low-order conservation laws are found for a general class of nonlinear
wave equations in one dimension with linear damping which is allowed to be
time-dependent. Such equations arise in numerous physical applications and have
attracted much attention in analysis. The conservation laws describe
generalized momentum and boost momentum, conformal momentum, generalized
energy, dilational energy, and light-cone energies. Both the conformal momentum
and dilational energy have no counterparts for nonlinear undamped wave
equations in one dimension. All of the conservation laws are obtainable through
Noether's theorem, which is applicable because the damping term can be
transformed into a time-dependent self-interaction term by a change of
dependent variable. For several of the conservation laws, the corresponding
variational symmetries have a novel form which is different than any of the
well known variation symmetries admitted by nonlinear undamped wave equations
in one dimension. | 2208.08026v2 |
2022-08-27 | Impact of the free-streaming neutrinos to the second order induced gravitational waves | The damping effect of the free-streaming neutrinos on the second order
gravitational waves is investigated in detail. We solve the Boltzmann equation
and give the anisotropic stress induced by neutrinos to second order. The first
order tensor and its coupling with scalar perturbations induced gravitational
waves are considered. We give the analytic equations of the damping kernel
functions and finally obtain the energy density spectrum. The results show that
the free-streaming neutrinos suppress the density spectrum significantly for
low frequency gravitational waves and enlarge the logarithmic slope $n$ in the
infrared region ($k \ll k_*$) of the spectrum. For the spectrum of $k_*\sim
10^{-7}$Hz, the damping effect in the range of $k<k_*$ is significant. The
combined effect of the first and second order could reduce the amplitude by
$30\%$ and make $n$ jump from $1.54$ to $1.63$ at $k\sim 10^{-9}$Hz, which may
be probed by the pulsar timing arrays (PTA) in the future. | 2208.12948v1 |
2022-08-28 | The small mass limit for long time statistics of a stochastic nonlinear damped wave equation | We study the long time statistics of a class of semi--linear damped wave
equations with polynomial nonlinearities and perturbed by additive Gaussian
noise in dimensions 2 and 3. We find that if sufficiently many directions in
the phase space are stochastically forced, the system is exponentially
attractive toward its unique invariant measure with a convergent rate that is
uniform with respect to the mass. Then, in the small mass limit, we prove the
convergence of the first marginal of the invariant measures in a suitable
Wasserstein distance toward the unique invariant measure of a stochastic
reaction--diffusion equation. This together with uniform geometric ergodcity
implies the validity of the small mass limit for the solutions on the infinite
time horizon $[0,\infty)$, thereby extending previously known results
established for the damped wave equations under Lipschitz nonlinearities. | 2208.13287v2 |
2022-08-30 | Results on high energy galactic cosmic rays from the DAMPE space mission | DAMPE (Dark Matter Particle Explorer) is a satellite-born experiment launched
in 2015 in a sun-synchronous orbit at 500 km altitude, and it has been taking
data in stable conditions ever since. Its main goals include the spectral
measurements up to very high energies, cosmic electrons/positrons and gamma
rays up to tens of TeV, and protons and nuclei up to hundreds of TeV. The
detector's main features include the 32 radiation lengths deep calorimeter and
large geometric acceptance, making DAMPE one of the most powerful space
instruments in operation, covering with high statistics and small systematics
the high energy frontier up to several hundreds TeV. The results of spectral
measurements of different species are shown and discussed. | 2208.14300v2 |
2022-09-05 | Generation and routing of nanoscale droplet solitons without compensation of magnetic damping | Magnetic droplet soliton is a localized dynamic spin state which can serve as
a nanoscale information carrier and nonlinear oscillator. The present opinion
is that the formation of droplet solitons requires the compensation of magnetic
damping by a torque created by a spin-polarized electric current or pure spin
current. Here we demonstrate theoretically that nanoscale droplet solitons can
be generated and routed in ferromagnetic nanostructures with voltage-controlled
magnetic anisotropy in the presence of uncompensated magnetic damping.
Performing micromagnetic simulations for the MgO/Fe/MgO trilayer with almost
perpendicular-to-plane magnetization, we reveal the formation of the droplet
soliton under a nanoscale gate electrode subjected to a sub-nanosecond voltage
pulse. The soliton lives up to 50 ns at room temperature and can propagate over
micrometer distances in a ferromagnetic waveguide due to nonzero gradient of
the demagnetizing field. Furthermore, we show that an electrical routing of the
soliton to different outputs of a spintronic device can be realized with the
aid of an additional semiconducting nanostripe electrode creating controllable
gradient of the perpendicular magnetic anisotropy. | 2209.01893v1 |
2022-09-06 | Emergence of damped-localized excitations of the Mott state due to disorder | A key aspect of ultracold bosonic quantum gases in deep optical lattice
potential wells is the realization of the strongly interacting Mott insulating
phase. Many characteristics of this phase are well understood, however little
is known about the effects of a random external potential on its gapped
quasiparticle and quasihole low-energy excitations. In the present study we
investigate the effect of disorder upon the excitations of the Mott insulating
state at zero temperature described by the Bose-Hubbard model. Using a
field-theoretical approach we obtain a resummed expression for the disorder
ensemble average of the spectral function. Its analysis shows that disorder
leads to an increase of the effective mass of both quasiparticle and quasihole
excitations. Furthermore, it yields the emergence of damped states, which
exponentially decay during propagation in space and dominate the whole band
when disorder becomes comparable to interactions. We argue that such
damped-localized states correspond to single-particle excitations of the
Bose-glass phase. | 2209.02435v2 |
2022-09-21 | Asymptotic profile of L^2-norm of solutions for wave equations with critical log-damping | We consider wave equations with a special type of log-fractional damping. We
study the Cauchy problem for this model in the whole space, and we obtain an
asymptotic profile and optimal estimates of solutions as time goes to infinity
in L^2-sense. A maximal discovery of this note is that under the effective
damping, in case of n = 1 L^2-norm of the solution blows up in infinite time,
and in case of n = 2 L^2-norm of the solution never decays and never blows up
in infinite time. The latter phenomenon seems to be a rare case. | 2209.10154v2 |
2022-09-25 | Origin of Immediate Damping of Coherent Oscillations in Photoinduced Charge Density Wave Transition | In stark contrast to the conventional charge density wave (CDW) materials,
the one-dimensional CDW on the In/Si(111) surface exhibits immediate damping of
the CDW oscillation during the photoinduced phase transition. Here, by
successfully reproducing the experimentally observed photoinduced CDW
transition on the In/Si(111) surface by performing real-time time-dependent
density functional theory (rt-TDDFT) simulations, we demonstrate that
photoexcitation promotes valence electrons from Si substrate to empty surface
bands composed primarily of the covalent p-p bonding states of the long In-In
bonds, generating interatomic forces to shorten the long bonds and in turn
drives coherently the structural transition. We illustrate that after the
structural transition, the component of these surface bands occurs a switch
among different covalent In bonds, causing a rotation of the interatomic forces
by about {\pi}/6 and thus quickly damping the oscillations in feature CDW
modes. These findings provide a deeper understanding of photoinduced phase
transitions. | 2209.12135v1 |
2022-10-11 | QKD in the NISQ era: enhancing secure key rates via quantum error correction | Error mitigation is one of the key challenges in realising the full potential
of quantum cryptographic protocols. Consequently, there is a lot of interest in
adapting techniques from quantum error correction (QEC) to improve the
robustness of quantum cryptographic protocols. In this work, we benchmark the
performance of different QKD protocols on noisy quantum devices, with and
without error correction. We obtain the secure key rates of BB84, B92 and BBM92
QKD protocols over a quantum channel that is subject to amplitude-damping
noise. We demonstrate, theoretically and via implementations on the IBM quantum
processors, that B92 is the optimal protocol under amplitude-damping and
generalized amplitude-damping noise. We then show that the security of the
noisy BBM92 protocol crucially depends on the type and the mode of distribution
of an entangled pair. Finally, we implement an error-corrected BB84 protocol
using dual-rail encoding on a noisy quantum processor, and show that the
dual-rail BB84 implementation outperforms the conventional BB84 in the presence
of noise. Our secure key rate calculation also takes into account the effects
of CNOT imperfections on the error rates of the protocols. | 2210.05297v1 |
2022-10-17 | Engineering imaginary stark ladder in a dissipative lattice: passive $\mathcal{PT}$ symmetry, K symmetry and localized damping | We study an imaginary stark ladder model and propose a realization of the
model in a dissipative chain with linearly increasing site-dependent
dissipation strength. Due to the existence of a $K$-symmetry and passive
$\mathcal{PT}$ symmetry, the model exhibits quite different feature from its
Hermitian counterpart. With the increase of dissipation strength, the system
first undergoes a passive $\mathcal{PT}$-symmetry breaking transition, with the
shifted eigenvalues changing from real to complex, and then a $K$-symmetry
restoring transition, characterized by the emergence of pure imaginary spectrum
with equal spacing. Accordingly, the eigenstates change from
$\mathcal{PT}$-unbroken extended states to the $\mathcal{PT}$-broken states,
and finally to stark localized states. In the framework of the quantum open
system governed by Lindblad equation with linearly increasing site-dependent
dissipation, we unveil that the dynamical evolution of single particle
correlation function is governed by the Hamiltonian of the imaginary stark
ladder model. By studying the dynamical evolution of the density distribution
under various initial states, we demonstrate that the damping dynamics displays
distinct behaviors in different regions. A localized damping is observed in the
strong dissipation limit. | 2210.08725v3 |
2022-10-18 | A quasi-local inhomogeneous dielectric tensor for arbitrary distribution functions | Treatments of plasma waves usually assume homogeneity, but the parallel
gradients ubiquitous in plasmas can modify wave propagation and absorption. We
derive a quasilocal inhomogeneous correction to the plasma dielectric for
arbitrary distributions by expanding the phase correlation integral and develop
a novel integration technique that allows our correction to be applied in many
situations and has greater accuracy than other inhomogeneous dielectric
formulas found in the literature. We apply this dielectric tensor to the
lower-hybrid current drive problem and demonstrate that inhomogeneous wave
damping does not affect the lower-hybrid wave's linear damping condition, and
in the non-Maxwellian problem damping and propagation should remain unchanged
except in the case of waves with very large phase velocities. | 2210.10214v1 |
2022-11-04 | On the collisional damping of plasma velocity space instabilities | For plasma velocity space instabilities driven by particle distributions
significantly deviated from a Maxwellian, weak collisions can damp the
instabilities by an amount that is significantly beyond the collisional rate
itself. This is attributed to the dual role of collisions that tend to relax
the plasma distribution toward a Maxwellian and to suppress the linearly
perturbed distribution function. The former effect can dominate in cases where
the unstable non-Maxwellian distribution is driven by collisionless transport
on a time scale much shorter than that of collisions, and the growth rate of
the ideal instability has a sensitive dependence on the distribution function.
The whistler instability driven by electrostatically trapped electrons is used
as an example to elucidate such a strong collisional damping effect of plasma
velocity space instabilities, which is confirmed by first-principles kinetic
simulations. | 2211.02723v3 |
2022-11-12 | Exponential Stability and exact controllability of a system of coupled wave equations by second order terms (via Laplacian) with only one non-smooth local damping | The purpose of this work is to investigate the exponential stability of a
second order coupled wave equations by laplacian with one locally internal
viscous damping. Firstly, using a unique continuation theorem combined with a
Carleman estimate, we prove that our system is strongly stable without any
geometric condition. Secondly, using a combination of the multiplier techniques
and the frequency domain approach, we show that our system is exponentially
stable under \textbf{(PMGC)} condition on the damping region without any
restriction on wave propagation speed (i.e whether the two wave equations
propagate at the same speed or not) | 2211.06706v2 |
2022-11-10 | Generalized Bagley-Torvik Equation and Fractional Oscillators | In this paper the Bagley-Torvik Equation is considered with the order of the
damping term allowed to range between one and two. The solution is found to be
representable as a convolution of trigonometric and exponential functions with
the driving force. The properties of the effective decay rate and the
oscillation frequency with respect to the order of the fractional damping are
also studied. It is found that the effective decay rate and oscillation
frequency have a complex dependency on the order of the derivative of the
damping term and exhibit properties one might expect of a thermodynamic
Equation of state: critical point, phase change, and lambda transition. | 2211.07575v1 |
2022-11-21 | Lifespan estimates for the compressible Euler equations with damping via Orlicz spaces techniques | In this paper we are interested in the upper bound of the lifespan estimate
for the compressible Euler system with time dependent damping and small initial
perturbations. We employ some techniques from the blow-up study of nonlinear
wave equations. The novelty consists in the introduction of tools from the
Orlicz spaces theory to handle the nonlinear term emerging from the pressure $p
\equiv p(\rho)$, which admits different asymptotic behavior for large and small
values of $\rho-1$, being $\rho$ the density. Hence we can establish, in high
dimensions $n\in\{2,3\}$, unified upper bounds of the lifespan estimate
depending only on the dimension $n$ and on the damping strength, and
independent of the adiabatic index $\gamma>1$. We conjecture our results to be
optimal. The method employed here not only improves the known upper bounds of
the lifespan for $n\in\{2,3\}$, but has potential application in the study of
related problems. | 2211.11377v1 |
2022-11-24 | A brief introduction to the mathematics of Landau damping | In these short, rather informal, expository notes I review the current state
of the field regarding the mathematics of Landau damping, based on lectures
given at the CIRM Research School on Kinetic Theory, November 14--18, 2022.
These notes are mainly on Vlasov-Poisson in $(x,v) \in \mathbb T^d \times
\mathbb R^d$ however a brief discussion of the important case of $(x,v) \in
\mathbb R^d \times \mathbb R^d$ is included at the end. The focus will be
nonlinear and these notes include a proof of Landau damping on $(x,v) \in
\mathbb T^d \times \mathbb R^d$ in the Vlasov--Poisson equations meant for
graduate students, post-docs, and others to learn the basic ideas of the
methods involved. The focus is also on the mathematical side, and so most
references are from the mathematical literature with only a small number of the
many important physics references included. A few open problems are included at
the end.
These notes are not currently meant for publication so they may not be
perfectly proof-read and the reference list might not be complete. If there is
an error or you have some references which you think should be included, feel
free to send me an email and I will correct it when I get a chance. | 2211.13707v1 |
2022-12-04 | Vibration suppression of a state-of-the-art wafer gripper | In this paper the implementation of piezoelectrics to a state-of-the-art
wafer gripper is investigated. The objective is to propose and validate a
solution method, which includes a mechanical design and control system, to
achieve at least 5% damping for two eigenmodes of a wafer gripper. This
objective serves as a 'proof of concept' to show the possibilities of
implementing a state-of-the-art damping method to an industrial application,
which in turn can be used to dampen different thin structures. The coupling
relation between the piezoelectrics and their host structure were used to
design the placement of the piezoelectric patches, together with modal analysis
data of the a state-of-the-art wafer gripper. This data had been measured
through an experimental setup. Active damping has been succesfully implemented
onto the wafer gripper where positive position feedback (PPF) is used as a
control algorithm to dampen two eigenmodes. | 2212.01854v1 |
2022-12-20 | Algebra of L-banded Matrices | Convergence is a crucial issue in iterative algorithms. Damping is commonly
employed to ensure the convergence of iterative algorithms. The conventional
ways of damping are scalar-wise, and either heuristic or empirical. Recently,
an analytically optimized vector damping was proposed for memory
message-passing (iterative) algorithms. As a result, it yields a special class
of covariance matrices called L-banded matrices. In this paper, we show these
matrices have broad algebraic properties arising from their L-banded structure.
In particular, compact analytic expressions for the LDL decomposition, the
Cholesky decomposition, the determinant after a column substitution, minors,
and cofactors are derived. Furthermore, necessary and sufficient conditions for
an L-banded matrix to be definite, a recurrence to obtain the characteristic
polynomial, and some other properties are given. In addition, we give new
derivations of the determinant and the inverse. (It's crucial to emphasize that
some works have independently studied matrices with this special structure,
named as L-matrices. Specifically, L-banded matrices are regarded as L-matrices
with real and finite entries.) | 2212.12431v3 |
2023-01-23 | Non-Markovianity in the time evolution of open quantum systems assessed by means of quantum state distance | We provide a quantitative evaluation of non-Markovianity (NM) for an XX chain
of interacting qubits with one end coupled to a reservoir. The NM of several
non-Markovian spectral densities is assessed in terms of various quantum state
distance (QSD) measures. Our approach is based on the construction of the
density matrix of the open chain, without the necessity of a master equation.
For the quantification of NM we calculate the dynamics of the QSD measures
between the Markovian-damped and various types of non-Markovian-damped cases.
Since in the literature several QSD measures, appear in forms that imply trace
preserving density matrices, we introduced appropriate modifications so as to
render them applicable to the case of decaying traces. The results produce
remarkable consistency between the various QSD measures. They also reveal a
subtle and potentially useful interplay between qubit-qubit interaction and
non-Markovian damping. Our calculations have also uncovered a surprisingly
dramatic slowing-down of dissipation by the squared Lorentzian reservoir. | 2301.09323v2 |
2023-01-26 | Optimisation of Power Grid Stability Under Uncertainty | The increased integration of intermittent and decentralised forms of power
production has eroded the stability margins of power grids and made it more
challenging to ensure reliable and secure power transmission. Reliable grid
operation requires system-scale stability in response to perturbations in
supply or load; previous studies have shown that this can be achieved by tuning
the effective damping parameters of the generators in the grid. In this paper,
we present and analyse the problem of tuning damping parameters when there is
some uncertainty in the underlying system. We show that sophisticated methods
that assume no uncertainty can yield results that are less robust than those
produced by simpler methods. We define a quantile-based metric of stability
that ensures that power grids remain stable even as worst-case scenarios are
approached, and we develop optimisation methods for tuning damping parameters
to achieve this stability. By comparing optimisation methods that rely on
different assumptions, we suggest efficient heuristics for finding parameters
that achieve highly stable and robust grids. | 2301.11215v1 |
2023-02-11 | Uniform stabilization for the semi-linear wave equation with nonlinear Kelvin-Voigt damping | This paper is concerned with the decay estimate of solutions to the
semilinear wave equation subject to two localized dampings in a bounded domain.
The first one is of the nonlinear Kelvin-Voigt type and is distributed around a
neighborhood of the boundary according to the Geometric Control Condition.
While the second one is a frictional damping and we consider it hurting the
geometric condition of control. We show uniform decay rate results of the
corresponding energy for all initial data taken in bounded sets of finite
energy phase-space. The proof is based on obtaining an observability inequality
which combines unique continuation properties and the tools of the Microlocal
Analysis Theory. | 2302.05667v1 |
2023-02-20 | Exponentially stable breather solutions in nonautonomous dissipative nonlinear Schrödinger lattices | We consider damped and forced discrete nonlinear Schr\"odinger equations on
the lattice $\mathbb{Z}$. First we establish the existence of periodic and
quasiperiodic breather solutions for periodic and quasiperiodic driving,
respectively. Notably, quasiperiodic breathers cannot exist in the system
without damping and driving. Afterwards the existence of a global uniform
attractor for the dissipative dynamics of the system is shown. For strong
dissipation we prove that the global uniform attractor has finite fractal
dimension and consists of a single trajectory that is confined to a finite
dimensional subspace of the infinite dimensional phase space, attracting any
bounded set in phase space exponentially fast. Conclusively, for strong damping
and periodic (quasiperiodic) forcing the single periodic (quasiperiodic)
breather solution possesses a finite number of modes and is exponentially
stable. | 2302.09869v2 |
2023-02-11 | Quasinormal modes, Hawking radiation and absorption of the massless scalar field for Bardeen black hole surrounded by perfect fluid dark matter | Bardeen black hole surrounded by perfect fluid dark matter for a massless
scalar field. Our result shows that the oscillation frequency of quasinormal
modes is enhanced as magnetic charge $g$ or the dark matter parameter $\alpha$
increases. For damping rate of quasinormal modes, the influence of them is
different. Specifically, the increase of dark matter parameter $\alpha$ makes
the damping rate increasing at first and then decreasing. While the damping
rate is continuously decreasing with the increase of the magnetic charge $g$.
Moreover, we find that the increase of the dark matter parameter $\alpha$
enhances the power emission spectrum whereas magnetic charge $g$ suppresses it.
This means that the lifespan of black holes increases for smaller value of
$\alpha$ and larger value of $g$ when other parameters are fixed. Finally, the
absorption cross section of the considered black hole is calculated with the
help of the partial wave approach. Our result suggests that the absorption
cross section decreases with the dark matter $\alpha$ or the magnetic charge
$g$ increasing. | 2302.10758v1 |
2023-02-24 | A Numerical Approach for Modeling the Shunt Damping of Thin Panels with Arrays of Separately Piezoelectric Patches | Two-dimensional thin plates are widely used in many aerospace and automotive
applications. Among many methods for the attenuation of vibration of these
mechanical structures, piezoelectric shunt damping is a promising way. It
enables a compact vibration damping method without adding significant mass and
volumetric occupancy. Analyzing the dynamics of these electromechanical systems
requires precise modeling tools that properly consider the coupling between the
piezoelectric elements and the host structure. This paper presents a
methodology for separately shunted piezoelectric patches for achieving higher
performance on vibration attenuation. The Rayleigh-Ritz method is used for
performing the modal analysis and obtaining the frequency response functions of
the electro-mechanical system. The effectiveness of the method is investigated
for a broader range of frequencies, and it was shown that separately shunted
piezoelectric patches are more effective. | 2302.12525v1 |
2023-02-27 | Enhancing quantum synchronization through homodyne measurement, noise and squeezing | Quantum synchronization has been a central topic in quantum nonlinear
dynamics. Despite rapid development in this field, very few have studied how to
efficiently boost synchronization. Homodyne measurement emerges as one of the
successful candidates for this task, but preferably in the semi-classical
regime. In our work, we focus on the phase synchronization of a harmonic-driven
quantum Stuart-Landau oscillator, and show that the enhancement induced by
homodyne measurement persists into the quantum regime. Interestingly, optimal
two-photon damping rates exist when the oscillator and driving are at resonance
and with a small single-photon damping rate. We also report noise-induced
enhancement in quantum synchronization when the single-photon damping rate is
sufficiently large. Apart from these results, we discover that adding a
squeezing Hamiltonian can further boost synchronization, especially in the
semi-classical regime. Furthermore, the addition of squeezing causes the
optimal two-photon pumping rates to shift and converge. | 2302.13465v2 |
2023-03-06 | Larmor precession in strongly correlated itinerant electron systems | Many-electron systems undergo a collective Larmor precession in the presence
of a magnetic field. In a paramagnetic metal, the resulting spin wave provides
insight into the correlation effects generated by the electron-electron
interaction. Here, we use dynamical mean-field theory to investigate the
collective Larmor precession in the strongly correlated regime, where dynamical
correlation effects such as quasiparticle lifetimes and non-quasiparticle
states are essential. We study the spin excitation spectrum, which includes a
dispersive Larmor mode as well as electron-hole excitations that lead to Stoner
damping. We also extract the momentum-resolved damping of slow spin waves. The
accurate theoretical description of these phenomena relies on the Ward
identity, which guarantees a precise cancellation of self-energy and vertex
corrections at long wavelengths. Our findings pave the way towards a better
understanding of spin wave damping in correlated materials. | 2303.03468v2 |
2023-03-19 | Asymptotic-preserving finite element analysis of Westervelt-type wave equations | Motivated by numerical modeling of ultrasound waves, we investigate robust
conforming finite element discretizations of quasilinear and possibly nonlocal
equations of Westervelt type. These wave equations involve either a strong
dissipation or damping of fractional-derivative type and we unify them into one
class by introducing a memory kernel that satisfies non-restrictive regularity
and positivity assumptions. As the involved damping parameter is relatively
small and can become negligible in certain (inviscid) media, it is important to
develop methods that remain stable as the said parameter vanishes. To this end,
the contributions of this work are twofold. First, we determine sufficient
conditions under which conforming finite element discretizations of (non)local
Westervelt equations can be made robust with respect to the dissipation
parameter. Secondly, we establish the rate of convergence of the semi-discrete
solutions in the singular vanishing dissipation limit. The analysis hinges upon
devising appropriate energy functionals for the semi-discrete solutions that
remain uniformly bounded with respect to the damping parameter. | 2303.10743v1 |
2023-03-31 | Measurement of the cosmic p+He energy spectrum from 46 GeV to 316 TeV with the DAMPE space mission | Recent observations of the light component of the cosmic-ray spectrum have
revealed unexpected features that motivate further and more precise
measurements up to the highest energies. The Dark Matter Particle Explorer
(DAMPE) is a satellite-based cosmic-ray experiment that is operational since
December 2015, continuously collecting data on high-energy cosmic particles
with very good statistics, energy resolution, and particle identification
capabilities. In this work, the latest measurements of the energy spectrum of
proton+helium in the energy range from 46 GeV to 316 TeV are presented. Among
the most distinctive features of the spectrum, a spectral hardening at
$\sim$600 GeV has been observed, along with a softening at $\sim$29 TeV
measured with a 6.6$\sigma$ significance. Moreover, by measuring the energy
spectrum up to 316 TeV, a strong link is established between space- and
ground-based experiments, also suggesting the presence of a second hardening at
$\sim$150 TeV. | 2304.00137v4 |
2023-04-18 | Edge-selective extremal damping from topological heritage of dissipative Chern insulators | One of the most important practical hallmarks of topological matter is the
presence of topologically protected, exponentially localised edge states at
interfaces of regions characterised by unequal topological invariants. Here, we
show that even when driven far from their equilibrium ground state, Chern
insulators can inherit topological edge features from their parent Hamiltonian.
In particular, we show that the asymptotic long-time approach of the
non-equilibrium steady state, governed by a Lindblad Master equation, can
exhibit edge-selective extremal damping. This phenomenon derives from edge
states of non-Hermitian extensions of the parent Chern insulator Hamiltonian.
The combination of (non-Hermitian) topology and dissipation hence allows to
design topologically robust, spatially localised damping patterns. | 2304.09040v3 |
2023-04-25 | Weakly damped bosons and precursor gap in the vicinity of an antiferromagnetic metallic transition | We study the electronic spectral function of a metal in the vicinity of an
antiferromagnetic (AFM) quantum critical point, focusing on a situation where
the bare bandwidth of the spin fluctuations is significantly smaller than the
Fermi energy. In this limit, we identify a range of energies where the
fermionic quasiparticles near the "hot spots'' on the Fermi surface are
strongly scattered by the quantum critical fluctuations, whereas the damping of
the AFM fluctuations by the electrons is negligible. Within a one-loop
approximation, there is a parameter range where the $T=0$ spectral function at
the hot spots has a "precursor gap'' feature, with a local maximum at a finite
frequency. However, the ratio of the bare spin wave velocity to the Fermi
velocity required to obtain a precursor gap is probably too small to explain
experiments in the electron-doped cuprate superconductors (He et al., Proc.
Natl. Acad. Sci 116, 3449 (2019)). At lower frequencies, the Landau damping of
the AFM fluctuations becomes important, and the electronic spectral function
has the familiar ${\omega}^{-1/2}$ singularity. Our one-loop perturbative
results are supported by a numerical Monte Carlo simulation of electrons
coupled to an undamped, nearly-critical AFM mode. | 2304.12697v1 |
2023-05-04 | Vibrational resonance in a damped and two-frequency driven system of particle on a rotating parabola | In the present work, we examine the role of nonlinearity in vibrational
resonance (VR) of a forced and damped form of a velocity-dependent potential
system. Many studies have focused on studying the vibrational resonance in
different potentials, like bistable potential, asymmetrically deformed
potential, and rough potential. In this connection, velocity-dependent
potential systems are very important from a physical point of view (Ex:
pion-pion interaction, cyclotrons and other electromagnetic devices influenced
by the Lorentz force, magnetrons, mass spectrometers). They also appear in
several mechanical contexts. In this paper, we consider a nonlinear dynamical
system with velocity-dependent potential along with additional damping and
driven forces, namely a particle moving on a rotating-parabola system, and
study the effect of two-frequency forcing with a wide difference in the
frequencies. We report that the system exhibits vibrational resonance in a
certain range of nonlinear strength. Using the method of separation of motions
(MSM), an analytical equation for the slow oscillations of the system is
obtained in terms of the parameters of the fast signal. The analytical
computations and the numerical studies concur well. | 2305.02674v1 |
2023-05-08 | Information capacity analysis of fully correlated multi-level amplitude damping channels | The primary objective of quantum Shannon theory is to evaluate the capacity
of quantum channels. In spite of the existence of rigorous coding theorems that
quantify the transmission of information through quantum channels,
superadditivity effects limit our understanding of the channel capacities. In
this paper, we mainly focus on a family of channels known as multi-level
amplitude damping channels. We investigate some of the information capacities
of the simplest member of multi-level Amplitude Damping Channel, a qutrit
channel, in the presence of correlations between successive applications of the
channel. We find the upper bounds of the single-shot classical capacities and
calculate the quantum capacities associated with a specific class of maps after
investigating the degradability property of the channels. Additionally, the
quantum and classical capacities of the channels have been computed in
entanglement-assisted scenarios. | 2305.04481v2 |
2023-05-09 | Lifespan estimates for semilinear damped wave equation in a two-dimensional exterior domain | Lifespan estimates for semilinear damped wave equations of the form
$\partial_t^2u-\Delta u+\partial_tu=|u|^p$ in a two dimensional exterior domain
endowed with the Dirichlet boundary condition are dealt with. For the critical
case of the semilinear heat equation $\partial_tv-\Delta v=v^2$ with the
Dirichlet boundary condition and the initial condition $v(0)=\varepsilon f$,
the corresponding lifespan can be estimated from below and above by
$\exp(\exp(C\varepsilon^{-1}))$ with different constants $C$. This paper
clarifies that the same estimates hold even for the critical semilinear damped
wave equation in the exterior of the unit ball under the restriction of radial
symmetry. To achieve this result, a new technique to control $L^1$-type norm
and a new Gagliardo--Nirenberg type estimate with logarithmic weight are
introduced. | 2305.05124v1 |
2023-05-19 | Cold damping of levitated optically coupled nanoparticles | Methods for controlling the motion of single particles, optically levitated
in vacuum, have developed rapidly in recent years. The technique of cold
damping makes use of feedback-controlled, electrostatic forces to increase
dissipation without introducing additional thermal fluctuations. This process
has been instrumental in the ground-state cooling of individual electrically
charged nanoparticles. Here we show that the same method can be applied to a
pair of nanoparticles, coupled by optical binding forces. These optical binding
forces are about three orders of magnitude stronger than typical Coulombic
inter-particle force and result in a coupled motion of both nanoparticles
characterized by a pair of normal modes. We demonstrate cold damping of these
normal modes, either independently or simultaneously, to sub-Kelvin
temperatures at pressures of 5x10^{-3} mbar. Experimental observations are
captured by a theoretical model which we use to survey the parameter space more
widely and to quantify the limits imposed by measurement noise and time delays.
Our work paves the way for the study of quantum interactions between meso-scale
particles and the exploration of multiparticle entanglement in levitated
optomechanical systems. | 2305.11809v1 |
2023-05-25 | Damping of three-dimensional waves on coating films dragged by moving substrates | Paints and coatings often feature interfacial defects due to disturbances
during the deposition process which, if they persist until solidification,
worsen the product quality. In this article, we investigate the stability of a
thin liquid film dragged by a vertical substrate moving against gravity, a flow
configuration found in a variety of coating processes. The receptivity of the
liquid film to three-dimensional disturbances is discussed with Direct
Numerical Simulations (DNS), an in-house non-linear Integral Boundary Layer
(IBL) film model, and Linear Stability Analysis (LSA). The thin film model,
successfully validated with the DNS computations, implements a pseudo-spectral
approach for the capillary terms that allows for investigating non-periodic
surface tension dominated flows. The combination of these numerical tools
allows for describing the mechanisms of capillary and non-linear damping, and
identifying the instability threshold of the coating processes. The results
show that transverse modulations can be beneficial for the damping of
two-dimensional waves within the range of operational conditions considered in
this study, typical of air-knife and slot-die coating. | 2305.16139v3 |
2023-06-12 | Realizable Eddy Damped Markovian Anisotropic Closure for Turbulence and Rossby Wave Interactions | A realizable Eddy Damped Markovian Anisotropic Closure (EDMAC) is presented
for the interaction of two dimensional turbulence and transient waves such as
Rossby waves. The structure of the EDMAC ensures that it is as computationally
efficient as the Eddy Damped Quasi Normal Markovian (EDQNM) closure but unlike
the EDQNM is guaranteed to be realizable in the presence of transient waves.
Jack Herring's important contributions to laying the foundations of statistical
dynamical closure theories of fluid turbulence are briefly reviewed. The topics
covered include equilibrium statistical mechanics, Eulerian and Lagrangian
statistical dynamical closure theories, and the statistical dynamics of the
interaction of turbulence with topography. The impact of Herring's work is
described and placed in the context of related developments. Some of the
further works that have built on Herring's foundations are discussed. The
relationships between theoretical approaches employed in statistical classical
and quantum field theories, and their overlap, are outlined. The seminal
advances made by the pioneers in strong interaction fluid turbulence are put
into perspective by comparing related developments in strong interaction
quantum filed theory. | 2306.06921v1 |
2023-06-26 | Revisiting the damped quantum harmonic oscillator | We reanalyse the quantum damped harmonic oscillator, introducing three less
than common features. These are (i) the use of a continuum model of the
reservoir rather than an ensemble of discrete oscillators, (ii) an exact
diagonalisation of the Hamiltonian by adapting a technique pioneered by Fano,
and (iii) the use of the thermofield technique for describing a finite
temperature reservoir. We recover in this way a number of well-known and some,
perhaps, less familiar results. An example of the latter is an ab initio proof
that the oscillator relaxes to the mean-force Gibbs state. We find that special
care is necessary when comparing the damped oscillator with its undamped
counterpart as the former has two distinct natural frequencies, one associated
with short time evolution and the other with longer times. | 2306.15013v1 |
2023-06-27 | SPDER: Semiperiodic Damping-Enabled Object Representation | We present a neural network architecture designed to naturally learn a
positional embedding and overcome the spectral bias towards lower frequencies
faced by conventional implicit neural representation networks. Our proposed
architecture, SPDER, is a simple MLP that uses an activation function composed
of a sinusoidal multiplied by a sublinear function, called the damping
function. The sinusoidal enables the network to automatically learn the
positional embedding of an input coordinate while the damping passes on the
actual coordinate value by preventing it from being projected down to within a
finite range of values. Our results indicate that SPDERs speed up training by
10x and converge to losses 1,500-50,000x lower than that of the
state-of-the-art for image representation. SPDER is also state-of-the-art in
audio representation. The superior representation capability allows SPDER to
also excel on multiple downstream tasks such as image super-resolution and
video frame interpolation. We provide intuition as to why SPDER significantly
improves fitting compared to that of other INR methods while requiring no
hyperparameter tuning or preprocessing. | 2306.15242v1 |
2023-07-03 | Fast Convergence of Inertial Multiobjective Gradient-like Systems with Asymptotic Vanishing Damping | We present a new gradient-like dynamical system related to unconstrained
convex smooth multiobjective optimization which involves inertial effects and
asymptotic vanishing damping. To the best of our knowledge, this system is the
first inertial gradient-like system for multiobjective optimization problems
including asymptotic vanishing damping, expanding the ideas laid out in [H.
Attouch and G. Garrigos, Multiobjective optimization: an inertial approach to
Pareto optima, preprint, arXiv:1506.02823, 201]. We prove existence of
solutions to this system in finite dimensions and further prove that its
bounded solutions converge weakly to weakly Pareto optimal points. In addition,
we obtain a convergence rate of order $O(t^{-2})$ for the function values
measured with a merit function. This approach presents a good basis for the
development of fast gradient methods for multiobjective optimization. | 2307.00975v3 |
2023-07-05 | Strong convergence rates for a full discretization of stochastic wave equation with nonlinear damping | The paper establishes the strong convergence rates of a spatio-temporal full
discretization of the stochastic wave equation with nonlinear damping in
dimension one and two. We discretize the SPDE by applying a spectral Galerkin
method in space and a modified implicit exponential Euler scheme in time. The
presence of the super-linearly growing damping in the underlying model brings
challenges into the error analysis. To address these difficulties, we first
achieve upper mean-square error bounds, and then obtain mean-square convergence
rates of the considered numerical solution. This is done without requiring the
moment bounds of the full approximations. The main result shows that, in
dimension one, the scheme admits a convergence rate of order $\tfrac12$ in
space and order $1$ in time. In dimension two, the error analysis is more
subtle and can be done at the expense of an order reduction due to an
infinitesimal factor. Numerical experiments are performed and confirm our
theoretical findings. | 2307.01975v1 |
2023-07-12 | Decoherence effects on lepton number violation from heavy neutrino-antineutrino oscillations | We study decoherence effects and phase corrections in heavy
neutrino-antineutrino oscillations (NNOs), based on quantum field theory with
external wave packets. Decoherence damps the oscillation pattern, making it
harder to resolve experimentally. Additionally, it enhances lepton number
violation (LNV) for processes in symmetry-protected low-scale seesaw models by
reducing the destructive interference between mass eigenstates. We discuss a
novel time-independent shift in the phase and derive formulae for calculating
decoherence effects and the phase shift in the relevant regimes, which are the
no dispersion regime and transverse dispersion regime. We find that the phase
shift can be neglected in the parameter region under consideration since it is
small apart from parameter regions with large damping. In the oscillation
formulae, decoherence can be included by an effective damping parameter. We
discuss this parameter and present averaged results, which apply to simulations
of NNOs in the dilepton-dijet channel at the HL-LHC. We show that including
decoherence effects can dramatically change the theoretical prediction for the
ratio of LNV over LNC events. | 2307.06208v1 |
2023-07-24 | Phonon damping in a 2D superfluid: insufficiency of Fermi's golden rule at low temperature | It is generally accepted that the phonon gas of a superfluid always enters a
weak coupling regime at sufficiently low temperatures, whatever the strength of
the interactions between the underlying particles (constitutive of the
superfluid). Thus, in this limit, we should always be able to calculate the
damping rate of thermal phonons by applying Fermi's golden rule to the $H\_3$
Hamiltonian of cubic phonon-phonon coupling taken from quantum hydrodynamics,
at least in the case of a convex acoustic branch and in the collisionless
regime (where the eigenfrequency of the considered phonons remains much greater
than the gas thermalization rate). Using the many-body Green's function method,
we predict that, unexpectedly, this is not true in two dimensions, contrary to
the three-dimensional case. We confirm this prediction with classical
phonon-field simulations and a non-perturbative theory in $H\_3$, where the
fourth order is regularized by hand, giving a complex energy to the virtual
phonons of the four-phonon collisional processes. For a weakly interacting
fluid and a phonon mode in the long-wavelength limit, we predict a damping rate
about three times lower than that of the golden rule. | 2307.12705v1 |
2023-08-01 | Regularity for the Timoshenko system with fractional damping | We study, the Regularity of the Timoshenko system with two fractional
dampings $(-\Delta)^\tau u_t$ and $(-\Delta)^\sigma \psi_t$; both of the
parameters $(\tau, \sigma)$ vary in the interval $[0,1]$. We note that
($\tau=0$ or $\sigma=0$) and ($\tau=1$ or $\sigma=1$) the dampings are called
frictional and viscous, respectively. Our main contribution is to show that the
corresponding semigroup $S(t)=e^{\mathcal{B}t}$, is analytic for
$(\tau,\sigma)\in R_A:=[1/2,1]\times[ 1/2,1]$ and determine the Gevrey's class
$\nu>\dfrac{1}{\phi}$, where $\phi=\left\{\begin{array}{ccc}
\dfrac{2\sigma}{\sigma+1} &{\rm for} & \sigma\leq \tau,\\\\
\dfrac{2\tau}{\tau+1} &{\rm for} & \tau\leq \sigma. \end{array}\right.$ \quad
and \quad $(\tau,\sigma)\in R_{CG}:= (0,1)^2$. | 2308.00573v2 |
2023-08-16 | Large time asymptotics for partially dissipative hyperbolic systems without Fourier analysis: application to the nonlinearly damped p-system | A new framework to obtain time-decay estimates for partially dissipative
hyperbolic systems set on the real line is developed. Under the classical
Shizuta-Kawashima (SK) stability condition, equivalent to the Kalman rank
condition in control theory, the solutions of these systems decay exponentially
in time for high frequencies and polynomially for low ones. This allows to
derive a sharp description of the space-time decay of solutions for large time.
However, such analysis relies heavily on the use of the Fourier transform that
we avoid here, developing the "physical space version" of the hyperbolic
hypocoercivity approach introduced by Beauchard and Zuazua, to prove new
asymptotic results in the linear and nonlinear settings. The new physical space
version of the hyperbolic hypocoercivity approach allows to recover the natural
heat-like time-decay of solutions under sharp rank conditions, without
employing Fourier analysis or $L^1$ assumptions on the initial data. Taking
advantage of this Fourier-free framework, we establish new enhanced time-decay
estimates for initial data belonging to weighted Sobolev spaces. These results
are then applied to the nonlinear compressible Euler equations with linear
damping. We also prove the logarithmic stability of the nonlinearly damped
$p$-system. | 2308.08280v1 |
2023-09-06 | Effective Description of the Quantum Damped Harmonic Oscillator: Revisiting the Bateman Dual System | In this work, we present a quantization scheme for the damped harmonic
oscillator (QDHO) using a framework known as momentous quantum mechanics. Our
method relies on a semiclassical dynamical system derived from an extended
classical Hamiltonian, where the phase-space variables are given by expectation
values of observables and quantum dispersions. The significance of our study
lies in its potential to serve as a foundational basis for the effective
description of open quantum systems (OQS), and the description of dissipation
in quantum mechanics. By employing the Bateman's dual model as the initial
classical framework, and undergoing quantization, we demonstrate that our
description aligns exceptionally well with the well-established Lindblad master
equation. Furthermore, our approach exhibits robustness and broad applicability
in the context of OQS, rendering it a versatile and powerful tool for studying
various phenomena. We intend to contribute to the advancement of quantum
physics by providing an effective means of quantizing the damped harmonic
oscillator and shedding light on the behavior of open quantum systems. | 2309.02689v1 |
2023-09-09 | Secondary cosmic-ray nuclei in the model of Galactic halo with nonlinear Landau damping | We employ our recent model of the cosmic-ray (CR) halo by Chernyshov et al.
(2022) to compute the Galactic spectra of stable and unstable secondary nuclei.
In this model, confinement of the Galactic CRs is entirely determined by the
self-generated Alfvenic turbulence whose spectrum is controlled by nonlinear
Landau damping. We analyze the physical parameters affecting propagation
characteristics of CRs, and estimate the best set of free parameters providing
accurate description of available observational data. We also show that
agreement with observations at lower energies may be further improved by taking
into account the effect of ion-neutral damping which operates near the Galactic
disk. | 2309.04772v1 |
2023-09-20 | On the damping of tidally driven oscillations | Expansions in the oscillation modes of tidally perturbed bodies provide a
useful framework for representing tidally induced flows. However, recent work
has demonstrated that such expansions produce inaccurate predictions for
secular orbital evolution when mode damping rates are computed independently.
We explore the coupling of collectively driven modes by frictional and viscous
dissipation, in tidally perturbed bodies that are both non-rotating and rigidly
rotating. This exploration leads us to propose an alternative approach to
treating the damping of tidally driven oscillations that accounts for
dissipative mode coupling, but which does not require any information beyond
the eigenfunctions and eigenfrequencies of adiabatic modes. | 2309.11502v1 |
2023-09-25 | Linearly implicit exponential integrators for damped Hamiltonian PDEs | Structure-preserving linearly implicit exponential integrators are
constructed for Hamiltonian partial differential equations with linear constant
damping. Linearly implicit integrators are derived by polarizing the polynomial
terms of the Hamiltonian function and portioning out the nonlinearly of
consecutive time steps. They require only a solution of one linear system at
each time step. Therefore they are computationally more advantageous than
implicit integrators. We also construct an exponential version of the
well-known one-step Kahan's method by polarizing the quadratic vector field.
These integrators are applied to one-dimensional damped Burger's,
Korteweg-de-Vries, and nonlinear Schr{\"o}dinger equations. Preservation of the
dissipation rate of linear and quadratic conformal invariants and the
Hamiltonian is illustrated by numerical experiments. | 2309.14184v2 |
2023-10-12 | Plasmon dispersion and Landau damping in the nonlinear quantum regime | We study the dispersion properties of electron plasma waves, or plasmons,
which can be excited in quantum plasmas in the nonlinear regime. In order to
describe nonlinear electron response to finite amplitude plasmons, we apply the
Volkov approach to non-relativistic electrons. For that purpose, we use the
Schr\"odinger equation and describe the electron population of a quantum plasma
as a mixture of quantum states. Within the kinetic framework that we are able
to derive from the Volkov solutions, we discuss the role of the wave amplitude
on the nonlinear plasma response. Finally, we focus on the quantum properties
of nonlinear Landau damping and study the contributions of multi-plasmon
absorption and emission processes. | 2310.08544v1 |
2023-11-09 | Landau Damping in an Electron Gas | Material science methods aim at developing efficient computational schemes
for describing complex many-body effects and how they are revealed in
experimentally measurable properties. Bethe-Salpeter equation in the
self-consistent Hartree-Fock basis is often used for this purpose, and in this
paper we employ the real-frequency diagrammatic Monte Carlo framework for
solving the ladder-type Bethe-Salpeter equation for the 3-point vertex function
(and, ultimately, for the system's polarization) to study the effect of
electron-hole Coulomb scattering on Landau damping in the homogeneous electron
gas. We establish how this damping mechanism depends on the Coulomb parameter
$r_s$ and changes with temperature between the correlated liquid and thermal
gas regimes. In a broader context of dielectric response in metals, we also
present the full polarization and the typical dependence of the
exchange-correlation kernel on frequency at finite momentum and temperature
within the same computational framework. | 2311.05611v2 |
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