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2019-02-27
|
Necessary and Sufficient Conditions for Passivity of Velocity-Sourced Impedance Control of Series Elastic Actuators
|
Series Elastic Actuation (SEA) has become prevalent in applications involving
physical human-robot interaction as it provides considerable advantages over
traditional stiff actuators in terms of stability robustness and fidelity of
force control. Several impedance control architectures have been proposed for
SEA. Among these alternatives, the cascaded controller with an inner-most
velocity loop, an intermediate torque loop and an outer-most impedance loop is
particularly favoured for its simplicity, robustness, and performance. In this
paper, we derive the \emph{necessary and sufficient conditions} to ensure the
passivity of this cascade-controller architecture for rendering two most common
virtual impedance models. Based on the newly established passivity conditions,
we provide non-conservative design guidelines to haptically display a null
impedance and a pure spring while ensuring the passivity of interaction. We
also demonstrate the importance of including physical damping in the actuator
model during derivation of passivity conditions, when integral controllers are
utilized. In particular, we show the adversary effect of physical damping on
system passivity.
|
1902.10607v2
|
2019-03-01
|
Response to: [Comment on Quantization of the damped harmonic oscillator [Serhan et al, J. Math. Phys. 59, 082105 (2018)]]
|
This is a response to a recently reported comment [1] on paper [J. Math.
Phys.59, 082105 (2018)] regarding the quantization of damped harmonic
oscillator using a non-Hermitian Hamiltonian with real energy eigenvalues. We
assert here that the calculation of Eq. (29) of [2] is incorrect, and thus the
subsequent steps via the Nikiforov-Uvarov method are affected, and the energy
eigenvalues should have been complex. However, we show here that the
Hermiticity of the Hamiltonian should be firstly achieved to make the correct
transition from classical Hamiltonian to quantum counterpart, and this can be
reached using the symmetrization rule. Applying the canonical quantization on
the resulted Hermitian Hamiltonian and then using the Nikiforov-Uvarov method
correctly, the energy eigenvalues will be real and exactly as given by Eq. (35)
of [2].
|
1903.00352v2
|
2019-03-08
|
Protecting quantum correlations in presence of generalised amplitude damping channel: the two-qubit case
|
Any kind of quantum resource useful in different information processing tasks
is vulnerable to several types of environmental noise. Here we study the
behaviour of quantum correlations such as entanglement and steering in
two-qubit systems under the application of the generalised amplitude damping
channel and propose some protocols towards preserving them under this type of
noise. First, we employ the technique of weak measurement and reversal for the
purpose of preservation of correlations. We then show how the evolution under
the channel action can be seen as an unitary process. We use the technique of
weak measurement and most general form of selective positive operator valued
measure (POVM) to achieve preservation of correlations for a significantly
large range of parameter values.
|
1903.03550v2
|
2019-03-17
|
Generalized Euler, Smoluchowski and Schrödinger equations admitting self-similar solutions with a Tsallis invariant profile
|
The damped isothermal Euler equations, the Smoluchowski equation and the
damped logarithmic Schr\"odinger equation with a harmonic potential admit
stationary and self-similar solutions with a Gaussian profile. They satisfy an
$H$-theorem for a free energy functional involving the von Weizs\"acker
functional and the Boltzmann functional. We derive generalized forms of these
equations in order to obtain stationary and self-similar solutions with a
Tsallis profile. In particular, we introduce a nonlinear Schr\"odinger equation
involving a generalized kinetic term characterized by an index $q$ and a
power-law nonlinearity characterized by an index $\gamma$. We derive an
$H$-theorem satisfied by a generalized free energy functional involving a
generalized von Weizs\"acker functional (associated with $q$) and a Tsallis
functional (associated with $\gamma$). This leads to a notion of generalized
quantum mechanics and generalized thermodynamics. When $q=2\gamma-1$, our
nonlinear Schr\"odinger equation admits an exact self-similar solution with a
Tsallis invariant profile. Standard quantum mechanics (Schr\"odinger) and
standard thermodynamics (Boltzmann) are recovered for $q=\gamma=1$.
|
1903.07111v1
|
2019-03-21
|
Creating localized plasma wave by ionization of doped semiconductors
|
Localized plasma waves can be generated by suddenly ionizing extrinsic
semiconductors with spatially periodic dopant densities. The built-in
electrostatic potentials at the metallurgical junctions, combined with electron
density ripples, offer the exact initial condition for exciting long-lasting
plasma waves upon ionization. This method can create plasma waves with a
frequency between a few terahertz to sub-petahertz without substantial damping.
The lingering plasma waves can seed backward Raman amplification in a wide
range of resonance frequencies up to the extreme ultraviolet regime. Chirped
wavevectors and curved wavefronts allow focusing the amplified beam in both
longitudinal and transverse dimensions. The main limitation to this method
appears to be obtaining sufficiently low plasma density from solid-state
materials to avoid collisional damping.
|
1903.09013v2
|
2019-03-22
|
Noncommutative approach to diagnose degenerate Higgs bosons at 125 GeV
|
We propose a noncommutative (NC) version for a global O(2) scalar field
theory, whose damping feature is introduced into the scalar field theory
through the NC parameter. In this context, we investigate how noncommutative
drives spontaneous symmetry breaking (SSB) and Higgs-Kibble mechanisms and how
the damping feature workout. Indeed, we show that the noncommutativity plays an
important role in such mechanisms, i.e., the Higgs mass and VEV dependent on NC
parameter. After that, it is explored the consequences of noncommutativity
dependence of Higgs mass and VEV: for the first, it is shown that there are a
mass-degenerate Higgs bosons near 126.5 GeV, parametrized by the
noncommutativity; for the second, the gauge fields gain masses that present a
noncommutativity contribution.
|
1903.09727v2
|
2019-03-30
|
Uncertainty damping in kinetic traffic models by driver-assist controls
|
In this paper, we propose a kinetic model of traffic flow with uncertain
binary interactions, which explains the scattering of the fundamental diagram
in terms of the macroscopic variability of aggregate quantities, such as the
mean speed and the flux of the vehicles, produced by the microscopic
uncertainty. Moreover, we design control strategies at the level of the
microscopic interactions among the vehicles, by which we prove that it is
possible to dampen the propagation of such an uncertainty across the scales.
Our analytical and numerical results suggest that the aggregate traffic flow
may be made more ordered, hence predictable, by implementing such control
protocols in driver-assist vehicles. Remarkably, they also provide a precise
relationship between a measure of the macroscopic damping of the uncertainty
and the penetration rate of the driver-assist technology in the traffic stream.
|
1904.00257v2
|
2019-04-01
|
Reduction of Kinetic Equations to Liénard-Levinson-Smith Form: Counting Limit Cycles
|
We have presented an unified scheme to express a class of system of equations
in two variables into a Li\'enard-Levinson-Smith (LLS) oscillator form. We have
derived the condition for limit cycle with special reference to Rayleigh and
Li\'enard systems for arbitrary polynomial functions of damping and restoring
force. Krylov-Boguliubov (K-B) method is implemented to determine the maximum
number of limit cycles admissible for a LLS oscillator atleast in the weak
damping limit. Scheme is illustrated by a number of model systems with single
cycle as well as the multiple cycle cases.
|
1904.00604v2
|
2019-04-02
|
Stability of the interface of an isotropic active fluid
|
We study the linear stability of an isotropic active fluid in three different
geometries: a film of active fluid on a rigid substrate, a cylindrical thread
of fluid, and a spherical fluid droplet. The active fluid is modeled by the
hydrodynamic theory of an active nematic liquid crystal in the isotropic phase.
In each geometry, we calculate the growth rate of sinusoidal modes of
deformation of the interface. There are two distinct branches of growth rates;
at long wavelength, one corresponds to the deformation of the interface, and
one corresponds to the evolution of the liquid crystalline degrees of freedom.
The passive cases of the film and the spherical droplet are always stable. For
these geometries, a sufficiently large activity leads to instability. Activity
also leads to propagating damped or growing modes. The passive cylindrical
thread is unstable for perturbations with wavelength longer than the
circumference. A sufficiently large activity can make any wavelength unstable,
and again leads to propagating damped or growing modes.
|
1904.01558v1
|
2019-04-04
|
Shear viscosity of classical fields in scalar theory
|
We investigate the shear viscosity of massless classical scalar fields in the
$\phi^4$ theory on a lattice by using the Green-Kubo formula. Based on the
scaling property of the classical field, the shear viscosity is represented
using a scaling function. Equilibrium expectation value of the time-correlation
function of the energy-momentum tensor is evaluated as the ensemble average of
the classical field configurations, whose time evolution is obtained by solving
the classical equation of motion starting from the initial condition in thermal
equilibrium. It is found that there are two distinct damping time scales in the
time-correlation function, which is found to show damped oscillation behavior
in the early stage around a slow monotonous decay with an exponential form, and
the slow decay part is found to dominate the shear viscosity in the massless
classical field theory. This kind of slow decay is also known to exist in the
molecular dynamics simulation, then it may be a generic feature of dense
matter.
|
1904.02419v3
|
2019-04-08
|
Study of Decoherence in Quantum Computers: A Circuit-Design Perspective
|
Decoherence of quantum states is a major hurdle towards scalable and reliable
quantum computing. Lower decoherence (i.e., higher fidelity) can alleviate the
error correction overhead and obviate the need for energy-intensive noise
reduction techniques e.g., cryogenic cooling. In this paper, we performed a
noise-induced decoherence analysis of single and multi-qubit quantum gates
using physics-based simulations. The analysis indicates that (i) decoherence
depends on the input state and the gate type. Larger number of $|1\rangle$
states worsen the decoherence; (ii) amplitude damping is more detrimental than
phase damping; (iii) shorter depth implementation of a quantum function can
achieve lower decoherence. Simulations indicate 20\% improvement in the
fidelity of a quantum adder when realized using lower depth topology. The
insights developed in this paper can be exploited by the circuit designer to
choose the right gates and logic implementation to optimize the system-level
fidelity.
|
1904.04323v1
|
2019-04-09
|
Ferromagnetic Resonance Studies of Strain tuned Bi:YIG Films
|
Bismuth-doped Yttrium iron garnet (Bi:YIG) thin films known for large
Magneto-optical activity with low losses still needs to get probed for its
magnetization dynamics. We demonstrate a controlled tuning of
magnetocrystalline anisotropy in Bi-doped Y_3 Fe_5 O_12 (Bi:YIG) films of high
crystalline quality using growth induced epitaxial strain on [111]-oriented
Gd_3 Ga_5 O_12 (GGG) substrate. We optimize a growth protocol to get thick
highly-strained epitaxial films showing large magneto-crystalline anisotropy,
compare to thin films prepared using a different protocol. Ferromagnetic
resonance measurements establish a linear dependence of the out-of-plane
uniaxial anisotropy on the strain induced rhombohedral distortion of Bi:YIG
lattice. Interestingly, the enhancement in the magnetoelastic constant due to
an optimum substitution of Bi^(3+) ions with strong spin orbit coupling does
not strongly affect the precessional damping (~2x10^(-3) ). Large
magneto-optical activity, reasonably low damping, large magnetocrystalline
anisotropy and large magnetoelastic coupling in BiYIG are the properties that
may help BiYIG emerge as a possible material for photo-magnonics and other
spintronics applications.
|
1904.04800v2
|
2019-04-23
|
A novel undamped gapless plasmon mode in tilted type-II Dirac semimetal
|
We predict the existence of a novel long-lived gapless plasmon mode in a
type-II Dirac semimetal (DSM). This gapless mode arises from the out-of-phase
oscillations of the density fluctuations in the electron and the hole pockets
of a type-II DSM. It originates beyond a critical wave-vector along the
direction of the tilt axis, owing to the momentum separation of the electron
and hole pockets. A similar out-of-phase plasmon mode arises in other
multi-component charged fluids as well, but generally it is Landau damped and
lies within the particle-hole continuum. In the case of a type-II DSM, the open
Fermi surface prohibits low-energy finite momentum single-particle excitations,
creating a `gap' in the particle-hole continuum. The gapless plasmon mode lies
within this particle-hole continuum gap and, thus, it is protected from Landau
damping.
|
1904.10137v1
|
2019-04-25
|
Interplay between nonclassicality and $\mathcal{PT}$ symmetry in an effective two level system with open system effects
|
A three level atom in $\Lambda$ configuration is reduced to an effective two
level system, under appropriate conditions, and its $\mathcal{PT}$ symmetric
properties are investigated. This effective qubit system when subjected to a
beam-splitter type of interaction, it provides the scope of directly
(indirectly) probing the nonclassical properties of the output (input) state.
Here, we study nonclassical properties of the output state by using some well
known measures of nonclassical correlations like the measurement induced
disturbance, concurrence and negativity. The nonclassical features are found to
enhance in the $\mathcal{PT}$ symmetric (PTS) phase compared to the
$\mathcal{PT}$ symmetry broken (PTSB) phase. Further, the output ports of the
beam-splitter are subjected to different quantum noise channels, both
non-Markovian, e.g., random telegraph noise as well as Markovian, e.g., phase
damping, and amplitude damping noise. The application of noise channels is
found to decrease the degree of nonclassicality, though continuing to exhibit
distinct behavior in PTS and PTSB phases, with the dominant behavior appearing
in the former case.
|
1904.11181v1
|
2019-04-25
|
Low damping magnetic properties and perpendicular magnetic anisotropy with strong volume contribution in the Heusler alloy Fe1.5CoGe
|
We present a study of the dynamic magnetic properties of TiN-buffered
epitaxial thin films of the Heusler alloy Fe$_{1.5}$CoGe. Thickness series
annealed at different temperatures are prepared and the magnetic damping is
measured, a lowest value of $\alpha=2.18\times 10^{-3}$ is obtained. The
perpendicular magnetic anisotropy properties in Fe$_{1.5}$CoGe/MgO are also
characterized. The evolution of the interfacial perpendicular anisotropy
constant $K^{\perp}_{\rm S}$ with the annealing temperature is shown and
compared with the widely used CoFeB/MgO interface. A large volume contribution
to the perpendicular anisotropy of $(4.3\pm0.5)\times 10^{5}$ $\rm J/m^3$ is
also found, in contrast with vanishing bulk contribution in common Co- and
Fe-based Heusler alloys.
|
1904.11247v1
|
2019-04-26
|
Terahertz spin dynamics driven by a field-derivative torque
|
Efficient manipulation of magnetization at ultrashort time scales is of
particular interest for future technology. Here, we numerically investigate the
influence of the so-called field-derivative torque, which was derived earlier
based on relativistic Dirac theory [Mondal et al., Phys. Rev. B 94, 144419
(2016)], on the spin dynamics triggered by ultrashort laser pulses. We find
that only considering the THz Zeeman field can underestimate the spin
excitation in antiferromagnetic oxide systems as, e.g., NiO and CoO. However,
accounting for both, the THz Zeeman torque and the field-derivative torque, the
amplitude of the spin excitation increases significantly. Studying the damping
dependence of field-derivative torque we observe larger effects for materials
having larger damping constants.
|
1904.11768v2
|
2019-04-30
|
A Self-Adaptive Contractive Algorithm for Enhanced Dynamic Phasor Estimation
|
In this paper, a self-adaptive contractive (SAC) algorithm is proposed for
enhanced dynamic phasor estimation in the diverse operating conditions of
modern power systems. At a high-level, the method is composed of three stages:
parameter shifting, filtering and parameter unshifting. The goal of the first
stage is to transform the input signal phasor so that it is approximately
mapped to nominal conditions. The second stage provides estimates of the
phasor, frequency, rate of change of frequency (ROCOF), damping and rate of
change of damping (ROCOD) of the parameter shifted phasor by using a
differentiator filter bank (DFB). The final stage recovers the original signal
phasor parameters while rejecting misleading estimates. The most important
features of the algorithm are that it offers convergence guarantees in a set of
desired conditions, and also great harmonic rejection. Numerical examples,
including the IEEE C37.118.1 standard tests with realistic noise levels, as
well as fault conditions, validate the proposed algorithm.
|
1904.13328v1
|
2019-05-02
|
The floatability of aerosols and waves damping on Titan's seas
|
Titan, Saturn's largest moon, has a dense atmosphere, together with lakes and
seas of liquid hydrocarbons. These liquid bodies, which are in polar regions
and up to several hundred kilometres in diameter, generally have smooth
surfaces despite evidence of near-surface winds. Photochemically generated
organic aerosols form a haze that can settle and potentially interact with the
liquid surface. Here we investigate the floatability of these aerosols on
Titan's seas and their potential to dampen waves. We find that the majority of
aerosols are denser than the liquid hydrocarbons, but that some could have
liquid-repelling properties. From calculation of the capillary forces, we
propose that these 'liquidophobic' aerosols could float and form a persistent
film on Titan's seas. We numerically model the wave damping efficiency of such
a film under the conditions on Titan, demonstrating that even a film one
molecule thick may inhibit formation of waves larger than a few centimetres in
wavelength. We conclude that the presence of a floating film of aerosols
deposited on Titan's lakes and seas could explain the remarkable smoothness of
their surfaces.
|
1905.00760v1
|
2019-05-02
|
Holographic Plasmon Relaxation with and without Broken Translations
|
We study the dynamics and the relaxation of bulk plasmons in strongly coupled
and quantum critical systems using the holographic framework. We analyze the
dispersion relation of the plasmonic modes in detail for an illustrative class
of holographic bottom-up models. Comparing to a simple hydrodynamic formula, we
entangle the complicated interplay between the three least damped modes and
shed light on the underlying physical processes. Such as the dependence of the
plasma frequency and the effective relaxation time in terms of the
electromagnetic coupling, the charge and the temperature of the system.
Introducing momentum dissipation, we then identify its additional contribution
to the damping. Finally, we consider the spontaneous symmetry breaking (SSB) of
translational invariance. Upon dialing the strength of the SSB, we observe an
increase of the longitudinal sound speed controlled by the elastic moduli and a
decrease in the plasma frequency of the gapped plasmon. We comment on the
condensed matter interpretation of this mechanism.
|
1905.00804v2
|
2019-05-05
|
Effective spin-mixing conductance of heavy-metal-ferromagnet interfaces
|
The effective spin-mixing conductance (G_eff) of a heavy metal/ferromagnet
(HM/FM) interface characterizes the efficiency of the interfacial spin
transport.Accurately determining G_eff is critical to the quantitative
understanding of measurements of direct and inverse spin Hall effects. G_eff is
typically ascertained from the inverse dependence of magnetic damping on the FM
thickness under the assumption that spin pumping is the dominant mechanism
affecting this dependence.Here we report that, this assumption fails badly in
many in-plane magnetized prototypical HM/FM systems in the nm-scale thickness
regime. Instead, the majority of the damping is from two-magnon scattering at
the FM interface, while spin-memory-loss scattering at the interface can also
be significant.If these two effects are neglected, the results will be an
unphysical "giant" apparent G_eff and hence considerable underestimation of
both the spin Hall ratio and the spin Hall conductivity in inverse/direct spin
Hall experiments.
|
1905.01577v2
|
2019-05-07
|
Integral representation formulae for the solution of a wave equation with time-dependent damping and mass in the scale-invariant case
|
This paper is devoted to derive integral representation formulae for the
solution of an inhomogeneous linear wave equation with time-dependent damping
and mass terms, that are scale-invariant with respect to the so-called
hyperbolic scaling. Yagdjian's integral transform approach is employed for this
purpose. The main step in our argument consists in determining the kernel
functions for the different integral terms, which are related to the source
term and to initial data. We will start with the one dimensional case (in
space). We point out that we may not apply in a straightforward way Duhamel's
principle to deal with the source term since the coefficients of lower order
terms make our model not invariant by time translation. On the contrary, we
shall begin with the representation formula for the inhomogeneous equation with
vanishing data by using a revised Duhamel's principle. Then, we will derive the
representation of the solution in the homogeneous case with nontrivial data.
After deriving the formula in the one dimensional case, the classical approach
by spherical means is used in order to deal with the odd dimensional case.
Finally, using the method of descent, the representation formula in the even
dimensional case is proved.
|
1905.02408v1
|
2019-05-07
|
Optimal decay for the $n$-dimensional incompressible Oldroyd-B model without damping mechanism
|
By a new energy approach involved in the high frequencies and low frequencies
decomposition in the Besov spaces, we obtain the optimal decay for the
incompressible Oldroyd-B model without damping mechanism in $\mathbb{R}^n$
($n\ge 2$). More precisely, let $(u,\tau)$ be the global small solutions
constructed in [18],
we prove for any $(u_0,\tau_0)\in{\dot{B}_{2,1}^{-s}}(\mathbb{R}^n)$ that
\begin{eqnarray*}
\big\|\Lambda^{\alpha}(u,\Lambda^{-1}\mathbb{P}\mathrm{div}\tau)\big\|_{L^q}
\le C (1+t)^{-\frac n4-\frac {(\alpha+s)q-n}{2q}},
\quad\Lambda\stackrel{\mathrm{def}}{=}\sqrt{-\Delta}, \end{eqnarray*}
with $\frac n2-1<s<\frac np, $ $2\leq p \leq \min(4,{2n}/({n-2})),\ p\not=4\
\hbox{ if }\ n=2,$ and $p\leq q\leq\infty$, $\frac nq-\frac np-s<\alpha
\leq\frac nq-1$. The proof relies heavily on the special dissipative structure
of the equations and some commutator estimates and various interpolations
between Besov type spaces. The method also works for other parabolic-hyperbolic
systems in which the Fourier splitting technique is invalid.
|
1905.02604v1
|
2019-05-12
|
Transport and Phonon Damping in $^{\bf 4}$He
|
The dynamic structure function $S(k,\omega)$ informs about the dispersion and
damping of excitations. We have recently (Phys. Rev. B {\bf 97}, 184520 (2018))
compared experimental results for $S(k,\omega)$ from high-precision neutron
scattering experiment and theoretical results using the ``dynamic many-body
theory'' (DMBT), showing excellent agreement over the whole experimentally
accessible pressure regime. This paper focuses on the specific aspect of the
propagation of low-energy phonons. We report calculations of the phonon
mean-free path and phonon life time in liquid \he4 as a function of wave length
and pressure. Historically, the question was of interest for experiments of
quantum evaporation. More recently, there is interest in the potential use of
$^4$He as a detector for low-energy dark matter (K. Schulz and Kathryn M.
Zurek, Phys. Rev. Lett. {\bf 117}, 121302 (2016)). While the mean free path of
long wave length phonons is large, phonons of intermediate energy can have a
short mean free path of the order of $\mu$m. Comparison of different levels of
theory indicate that reliable predictions of the phonon mean free path can be
made only by using the most advanced many--body method available, namely, DMBT.
|
1905.04759v1
|
2019-05-15
|
Nearly Markovian maps and entanglement-based bound on corresponding non-Markovianity
|
We identify a set of dynamical maps of open quantum system, and refer to them
as "$ \epsilon $-Markovian" maps. It is constituted of maps which, in a higher
dimensional system-environment Hilbert space, possibly violate Born
approximation but only a "little". We characterize the
"$\epsilon$-nonmarkovianity" of a general dynamical map by the minimum distance
of that map from the set of $\epsilon$-Markovian maps. We analytically derive
an inequality which gives a bound on the $ \epsilon$-nonmarkovianity of the
dynamical map, in terms of an entanglement-like resource generated between the
system and its "immediate" environment. In the special case of a vanishing
$\epsilon$, this inequality gives a relation between the
$\epsilon$-nonmarkovianity of the reduced dynamical map on the system and the
entanglement generated between the system and its immediate environment. We
numerically investigate the behavior of the similar distant based measures of
non-Markovianity for classes of amplitude damping and phase damping channels.
|
1905.06198v3
|
2019-05-15
|
A remark on triviality for the two-dimensional stochastic nonlinear wave equation
|
We consider the two-dimensional stochastic damped nonlinear wave equation
(SdNLW) with the cubic nonlinearity, forced by a space-time white noise. In
particular, we investigate the limiting behavior of solutions to SdNLW with
regularized noises and establish triviality results in the spirit of the work
by Hairer, Ryser, and Weber (2012). More precisely, without renormalization of
the nonlinearity, we establish the following two limiting behaviors; (i) in the
strong noise regime, we show that solutions to SdNLW with regularized noises
tend to 0 as the regularization is removed and (ii) in the weak noise regime,
we show that solutions to SdNLW with regularized noises converge to a solution
to a deterministic damped nonlinear wave equation with an additional mass term.
|
1905.06278v3
|
2019-05-17
|
Chiral p-wave superconductors have complex coherence and magnetic field penetration lengths
|
We show that in superconductors that break time reversal symmetry and have
anisotropy, such as p+ip materials, all order parameters and magnetic modes are
mixed. Excitation of the gap fields produces an excitation of the magnetic
field and vice versa. Correspondingly the long-range decay of the magnetic
field and order parameter are in general given by the same exponent. Thus one
cannot characterize p+ip superconductors by the usual coherence and magnetic
field penetration lengths. Instead the system has normal modes that are
associated with linear combinations of magnetic fields, moduli of and phases of
the order parameter components. Each such normal mode has its own decay length
that plays the role of a hybridized coherence/magnetic field penetration
length. On a large part of the parameter space these exponents are complex.
Therefore the system in general has damped oscillatory decay of the magnetic
field accompanied by damped oscillatory variation of the order parameter
fields.
|
1905.07296v2
|
2019-05-20
|
Short time blow-up by negative mass term for semilinear wave equations with small data and scattering damping
|
In this paper we study blow-up and lifespan estimate for solutions to the
Cauchy problem with small data for semilinear wave equations with scattering
damping and negative mass term. We show that the negative mass term will play a
dominant role when the decay of its coefficients is not so fast, thus the
solutions will blow up in a finite time. What is more, we establish a lifespan
estimate from above which is much shorter than the usual one.
|
1905.08100v1
|
2019-05-21
|
Low-pass-filter-based shock response spectrum and the evaluation method of transmissibility between equipment and sensitive components interfaces
|
According to the features of the sources of pyroshock and ballistic shock,
this study considers the pyroshock and ballistic shock generated by their
respective impulsive sources as damped harmonic waves with different
frequencies. According to the linear superposition assumption of damped
harmonic waves in a linear elastic structure, a shock analysis method based on
low-pass-filtered shock signals and their corresponding shock response spectrum
(SRS), termed as low-pass-filter-based shock response spectrum (LPSRS), is
proposed. LPSRS contains rich information of the frequency distribution of the
shock excitation signal. A method to calculate shock transmissibility is
proposed based on LPSRS and basic modal information of the equipment structure.
LPSRS and SRS curves can be predicted at any given position of the equipment
structure. The prediction method is validated by finite element method (FEM)
simulation.
|
1905.10190v1
|
2019-05-24
|
Sound damping in glasses: interplay between anharmonicities and elastic heterogeneities
|
Some facets of the way sound waves travel through glasses are still unclear.
Recent works have shown that in the low-temperature harmonic limit a crucial
role in controlling sound damping is played by local elastic heterogeneity.
Sound waves propagation has been demonstrated to be strongly affected by
inhomogeneous mechanical features of the materials, which add to the anharmonic
couplings at finite temperatures. We describe the interplay between these two
effects by molecular dynamics simulation of a model glass. In particular, we
focus on the transverse components of the vibrational excitations in terms of
dynamic structure factors, and characterize the temperature dependence of sound
attenuation rates in an extended frequency range. We provide a complete picture
of all phenomena, in terms encompassing both theory and experiments.
|
1905.10235v2
|
2019-05-27
|
A blow-up result for a semilinear wave equation with scale-invariant damping and mass and nonlinearity of derivative type
|
In this note, we prove blow-up results for semilinear wave models with
damping and mass in the scale-invariant case and with nonlinear terms of
derivative type. We consider the single equation and the weakly coupled system.
In the first case we get a blow-up result for exponents below a certain shift
of the Glassey exponent. For the weakly coupled system we find as critical
curve a shift of the corresponding curve for the weakly coupled system of
semilinear wave equations with the same kind of nonlinearities. Our approach
follows the one for the respective classical wave equation by Zhou Yi. In
particular, an explicit integral representation formula for a solution of the
corresponding linear scale-invariant wave equation, which is derived by using
Yagdjian's integral transform approach, is employed in the blow-up argument.
While in the case of the single equation we may use a comparison argument, for
the weakly coupled system an iteration argument is applied.
|
1905.11025v2
|
2019-05-28
|
Stationary states for underdamped anharmonic oscillators driven by Cauchy noise
|
Using methods of stochastic dynamics, we have studied stationary states in
the underdamped anharmonic stochastic oscillators driven by Cauchy noise. Shape
of stationary states depend both on the potential type and the damping. If the
damping is strong enough, for potential wells which in the overdamped regime
produce multimodal stationary states, stationary states in the underdamped
regime can be multimodal with the same number of modes like in the overdamped
regime. For the parabolic potential, the stationary density is always unimodal
and it is given by the two dimensional $\alpha$-stable density. For the mixture
of quartic and parabolic single-well potentials the stationary density can be
bimodal. Nevertheless, the parabolic addition, which is strong enough, can
destroy bimodlity of the stationary state.
|
1905.12078v2
|
2019-05-30
|
Intrinsically Undamped Plasmon Modes in Narrow Electron Bands
|
Surface plasmons in 2-dimensional electron systems with narrow Bloch bands
feature an interesting regime in which Landau damping (dissipation via
electron-hole pair excitation) is completely quenched. This surprising behavior
is made possible by strong coupling in narrow-band systems characterized by
large values of the "fine structure" constant $\alpha=e^2/\hbar \kappa v_{\rm
F}$. Dissipation quenching occurs when dispersing plasmon modes rise above the
particle-hole continuum, extending into the forbidden energy gap that is free
from particle-hole excitations. The effect is predicted to be prominent in
moir\'e graphene, where at magic twist-angle values, flat bands feature
$\alpha\gg1$. The extinction of Landau damping enhances spatial optical
coherence. Speckle-like interference, arising in the presence of disorder
scattering, can serve as a telltale signature of undamped plasmons directly
accessible in near-field imaging experiments.
|
1905.13088v2
|
2019-06-04
|
High frequency voltage-induced ferromagnetic resonance in magnetic tunnel junctions
|
Voltage-induced ferromagnetic resonance (V-FMR) in magnetic tunnel junctions
(MTJs) with a W buffer is investigated. Perpendicular magnetic anisotropy (PMA)
energy is controlled by both thickness of a CoFeB free layer deposited directly
on the W buffer and a post-annealing process at different temperatures. The PMA
energy as well as the magnetization damping are determined by analysing
field-dependent FMR signals in different field geometries. An optimized MTJ
structure enabled excitation of V-FMR at frequencies exceeding 30 GHz. The
macrospin modelling is used to analyse the field- and angular-dependence of the
V-FMR signal and to support experimental magnetization damping extraction.
|
1906.01301v1
|
2019-06-04
|
Late time approach to Hawking radiation: terms beyond leading order
|
Black hole evaporation is studied using wave packets for the modes. These
allow for approximate frequency and time resolution. The leading order late
time behavior gives the well known Hawking radiation that is independent of how
the black hole formed. The focus here is on the higher order terms and the rate
at which they damp at late times. Some of these terms carry information about
how the black hole formed. A general argument is given which shows that the
damping is significantly slower (power law) than what might be naively expected
from a stationary phase approximation (exponential). This result is verified by
numerical calculations in the cases of 2D and 4D black holes that form from the
collapse of a null shell.
|
1906.01735v2
|
2019-06-20
|
Time-sliced perturbation theory with primordial non-Gaussianity and effects of large bulk flows on inflationary oscillating features
|
We extend the formalism of time-sliced perturbation theory (TSPT) for
cosmological large-scale structure to include non-Gaussian initial conditions.
We show that in such a case the TSPT interaction vertices acquire new
contributions whose time-dependence factorizes for the Einstein-de Sitter
cosmology. The new formulation is free from spurious infrared (IR) enhancements
and reveals a clear IR structure of non-Gaussian vertices. We use the new
technique to study the evolution of oscillating features in primordial
statistics and show that they are damped due to non-linear effects of large
bulk flows. We derive the damping factors for the oscillating primordial power
spectrum and bispectrum by means of a systematic IR resummation of relevant
Feynman diagrams.
|
1906.08697v2
|
2019-06-21
|
Control of eigenfunctions on surfaces of variable curvature
|
We prove a microlocal lower bound on the mass of high energy eigenfunctions
of the Laplacian on compact surfaces of negative curvature, and more generally
on surfaces with Anosov geodesic flows. This implies controllability for the
Schr\"odinger equation by any nonempty open set, and shows that every
semiclassical measure has full support. We also prove exponential energy decay
for solutions to the damped wave equation on such surfaces, for any nontrivial
damping coefficient. These results extend previous works [arXiv:1705.05019],
[arXiv:1712.02692], which considered the setting of surfaces of constant
negative curvature.
The proofs use the strategy of [arXiv:1705.05019], [arXiv:1712.02692] and
rely on the fractal uncertainty principle of [arXiv:1612.09040]. However, in
the variable curvature case the stable/unstable foliations are not smooth, so
we can no longer associate to these foliations a pseudodifferential calculus of
the type used in [arXiv:1504.06589]. Instead, our argument uses Egorov's
Theorem up to local Ehrenfest time and the hyperbolic parametrix of
[arXiv:0706.3242], together with the $C^{1+}$ regularity of the stable/unstable
foliations.
|
1906.08923v2
|
2019-06-21
|
Exponential damping induced by random and realistic perturbations
|
Given a quantum many-body system and the expectation-value dynamics of some
operator, we study how this reference dynamics is altered due to a perturbation
of the system's Hamiltonian. Based on projection operator techniques, we unveil
that if the perturbation exhibits a random-matrix structure in the eigenbasis
of the unperturbed Hamiltonian, then this perturbation effectively leads to an
exponential damping of the original dynamics. Employing a combination of
dynamical quantum typicality and numerical linked cluster expansions, we
demonstrate that our theoretical findings for random matrices can, in some
cases, be relevant for the dynamics of realistic quantum many-body models as
well. Specifically, we study the decay of current autocorrelation functions in
spin-$1/2$ ladder systems, where the rungs of the ladder are treated as a
perturbation to the otherwise uncoupled legs. We find a convincing agreement
between the exact dynamics and the lowest-order prediction over a wide range of
interchain couplings.
|
1906.09268v2
|
2019-06-27
|
Fast control of dissipation in a superconducting resonator
|
We report on fast tunability of an electromagnetic environment coupled to a
superconducting coplanar waveguide resonator. Namely, we utilize a
recently-developed quantum-circuit refrigerator (QCR) to experimentally
demonstrate a dynamic tunability in the total damping rate of the resonator up
to almost two orders of magnitude. Based on the theory it corresponds to a
change in the internal damping rate by nearly four orders of magnitude. The
control of the QCR is fully electrical, with the shortest implemented operation
times in the range of 10 ns. This experiment constitutes a fast active reset of
a superconducting quantum circuit. In the future, a similar scheme can
potentially be used to initialize superconducting quantum bits.
|
1906.11519v1
|
2019-06-28
|
Ground-state cooling of an magnomechanical resonator induced by magnetic damping
|
Quantum manipulation of mechanical resonators has been widely applied in
fundamental physics and quantum information processing. Among them, cooling the
mechanical system to its quantum ground state is regarded as a key step. In
this work, we propose a scheme which one can realize ground-state cooling of
resonator in a cavity magnomechanical system. The system consists of a
microwave cavity and a small ferromagnetic sphere, in which phonon-magnon
coupling and cavity photon-magnon coupling can be achieved via magnetostrictive
interaction and magnetic dipole interaction, respectively. After adiabatically
eliminating the cavity mode, an effective Hamiltonian which consists of magnon
and mechanical modes is obtained. Within experimentally feasible parameters, we
demonstrate that the ground-state cooling of the magnomechanical resonator can
be achieved by extra magnetic damping. Unlike optomechanical cooling,
magnomechanical interaction is utilized to realize the cooling of resonators.
We further illustrate the ground-state cooling can be effectively controlled by
the external magnetic field.
|
1906.12081v1
|
2019-06-30
|
Non-linear spin torque, pumping and cooling in superconductor/ferromagnet systems
|
We study the effects of the coupling between magnetization dynamics and the
electronic degrees of freedom in a heterostructure of a metallic nanomagnet
with dynamic magnetization coupled with a superconductor containing a steady
spin-splitting field. We predict how this system exhibits a non-linear spin
torque, which can be driven either with a temperature difference or a voltage
across the interface. We generalize this notion to arbitrary magnetization
precession by deriving a Keldysh action for the interface, describing the
coupled charge, heat and spin transport in the presence of a precessing
magnetization. We characterize the effect of superconductivity on the
precession damping and the anti-damping torques. We also predict the full
non-linear characteristic of the Onsager counterparts of the torque, showing up
via pumped charge and heat currents. For the latter, we predict a spin-pumping
cooling effect, where the magnetization dynamics can cool either the nanomagnet
or the superconductor.
|
1907.00424v2
|
2019-07-03
|
Wave-ice interaction in the North-West Barents Sea
|
The results of field work on drift ice during wave propagation are analyzed
and presented. The field work was performed in the Barents Sea, and the main
focus of the paper is on wave processes in the MIZ. A model of wave damping in
broken ice is formulated and applied to interpret the field work results. It is
confirmed that waves of higher frequencies are subjected to stronger damping
when they propagate below the ice. This reduces the frequency of most energetic
wave with increasing distance from the ice edge. Difference of wave spectra
measured in two relatively close locations within the MIZ is discussed. The
complicated geometry and dynamics of the MIZ in the North-West Barents Sea
allow waves from the Atlantic Ocean and south regions of the Barents Sea to
penetrate into different locations of the MIZ.
|
1907.02032v1
|
2019-07-05
|
Nesterov's acceleration and Polyak's heavy ball method in continuous time: convergence rate analysis under geometric conditions and perturbations
|
In this article a family of second order ODEs associated to inertial gradient
descend is studied. These ODEs are widely used to build trajectories converging
to a minimizer $x^*$ of a function $F$, possibly convex. This family includes
the continuous version of the Nesterov inertial scheme and the continuous heavy
ball method. Several damping parameters, not necessarily vanishing, and a
perturbation term $g$ are thus considered. The damping parameter is linked to
the inertia of the associated inertial scheme and the perturbation term $g$ is
linked to the error that can be done on the gradient of the function $F$. This
article presents new asymptotic bounds on $F(x(t))-F(x^*)$ where $x$ is a
solution of the ODE, when $F$ is convex and satisfies local geometrical
properties such as {\L}ojasiewicz properties and under integrability conditions
on $g$. Even if geometrical properties and perturbations were already studied
for most ODEs of these families, it is the first time they are jointly studied.
All these results give an insight on the behavior of these inertial and
perturbed algorithms if $F$ satisfies some {\L}ojasiewicz properties especially
in the setting of stochastic algorithms.
|
1907.02710v1
|
2019-07-08
|
Role of Toll-Like Receptors in the interplay between pathogen and damage associated molecular patterns
|
Various theoretical studies have been carried out to infer relevant
protein-protein interactions among pathogens and their hosts. Such studies are
generally based on preferential attachment of bacteria / virus to their human
receptor homologs. We have analyzed 17 pathogenic species mainly belonging to
bacterial and viral pathogenic classes, with the aim to identify the
interacting human proteins which are targeted by both bacteria and virus
specifically. Our study reveals that the TLRs play a crucial role between the
pathogen-associated molecular patterns (PAMPs) and the damage associated
molecular patterns (DAMPS). PAMPs include bacterial lipopolysaccharides (LPs),
endotoxins, bacterial flagellin, lipoteichoic acid, peptidoglycan in bacterial
organisms and nucleic acid variants associated with viral organisms, whereas
DAMPs are associated with host biomolecules that perpetuate non-infectious
inflammatory responses. We found out the presence of SOD1 and SOD2 (superoxide
dismutase) is crucial, as it acts as an anti-oxidant and helps in eliminating
oxidative stress by preventing damage from reactive oxygen species. Hence, such
strategies can be used as new therapies for anti-inflammatory diseases with
significant clinical outcomes.
|
1907.03512v1
|
2019-07-15
|
Alternating Direction Method of Multipliers (ADMMs) Based Distributed Approach For Wide-Area Control
|
In this paper, an alternating direction method of multipliers based novel
distributed wide-area control architecture is proposed for damping the
interarea oscillations. In this approach, first, an interconnected power system
is divided into areas based on coherency grouping. Second, local processors are
assigned on each area that estimate a black-box transfer function model based
on Lagrange multipliers using measurements. These local area processors are
then used to estimate a global transfer function model of the power system
based on a consensus algorithm through a global processor. After convergence, a
transfer function residue corresponding to the interarea mode of interest is
derived, to determine optimal wide area control loop. Finally, a wide-area
damping controller is designed based on this information. The efficacy of the
controller is validated using two area and IEEE-39 bus test systems on
RTDS/RSCAD and MATLAB cosimulation platform.
|
1907.06340v1
|
2019-07-16
|
Coherency and Online Signal Selection Based Wide Area Control of Wind Integrated Power Grid
|
This paper introduces a novel method of designing wide area control (WAC)
based on a discrete linear quadratic regulator and Kalman filtering based
state-estimation that can be applied for real-time damping of interarea
oscillations of wind integrated power grid. The main advantages of the proposed
method are that the architecture provides online coherency grouping that
properly characterizes real-time changes in the power grid and online wide-area
signal selection based on residue method for proper selection of the WAC
signals. The proposed architecture can, thus, accurately monitors changes in
the power grid and select the appropriate control signal for more effectively
damping the interarea oscillation when compared to the conventional local
signal based power system stabilizers or offline based WAC designs. The
architecture is tested on a wind integrated two-area system and the IEEE 39 bus
system in order to show the capability of the proposed method.
|
1907.06846v1
|
2019-07-20
|
Magnon Bose-Einstein condensate and supercurrents over a wide temperature range
|
Magnon Bose-Einstein Condensates (BECs) and supercurrents are coherent
quantum phenomena, which appear on a macroscopic scale in parametrically
populated solid state spinsystems. One of the most fascinating and attractive
features of these processes is the possibility of magnon condensation and
supercurrent excitation even at room temperature. At the same time, valuable
information about a magnon BEC state, such as its lifetime, its formation
threshold, and coherency, is provided by experiments at various temperatures.
Here, we use Brillouin Light Scattering (BLS) spectroscopy for the
investigation of the magnon BEC dynamics in a single-crystal film of yttrium
iron garnet in a wide temperature range from 30 K to 380 K. By comparing the
BLS results with previous microwave measurements, we re-vealed the direct
relation between the damping of the condensed and the parametrically injected
magnons. The enhanced supercurrent dynamics was detected at 180 K near the
minimum of BEC damping.
|
1907.08805v1
|
2019-07-21
|
Explaining Retrocausality Phenomena in Quantum Mechanics using a Modified Variational Principle
|
A modified lagrangian with causal and retrocausal momenta was used to derive
a first causal wave equation and a second retrocausal wave equation using the
principle of least action. The retrocausal wave function obtained through this
method was found to be equivalent to the complex conjugate of the causal wave
function, thus leading to the conclusion that a retrocausal effect is already
implicit in quantum mechanics through the means of complex conjugation of the
wave function when computing the probability density for a particle. Lastly,
the same variational principle was employed with a fractionary langriangian,
(that is, containing fractional Riemann derivatives) to obtain a pair of
modified wave equations, one causal and other retrocausal, both of which
correspond to the differential equation of a damped oscillator in the free
particle (potential energy V=0) case. The solutions of this damped wave
equations remain to be explored.
|
1907.09688v3
|
2019-07-23
|
Global wellposedness to the $n$-dimensional compressible Oldroyd-B model without damping mechanism
|
The Cauchy problem of the compressible Oldroyd-B model without damping
mechanism in R^n$ with $n\ge2$ is considered. The lack of dissipation in
density and stress tensor in the model is compensated by exploiting an
intrinsic structure and introducing new quantities between density, velocity
and stress tensor. Therefore, global solutions to the system with small initial
data in critical Besov spaces are obtained. As a byproduct, optimal time decay
rates of the solutions are derived by using an energy estimation argument. The
results remain valid for the compressible viscoelastic system without the
`div-curl structure assumption and thus improve those given by Hu and Wang [ J.
Differential Equations, {\bf 250}, 1200--1231, 2011] and Qian and Zhang [Arch.
Ration. Mech. Anal., {\bf 198}, 835--868, 2010].
|
1907.09829v3
|
2019-08-01
|
The $J$-method for the Gross-Pitaevskii eigenvalue problem
|
This paper studies the $J$-method of [E. Jarlebring, S. Kvaal, W. Michiels.
SIAM J. Sci. Comput. 36-4:A1978-A2001, 2014] for nonlinear eigenvector problems
in a general Hilbert space framework. This is the basis for variational
discretization techniques and a mesh-independent numerical analysis. A simple
modification of the method mimics an energy-decreasing discrete gradient flow.
In the case of the Gross-Pitaevskii eigenvalue problem, we prove global
convergence towards an eigenfunction for a damped version of the $J$-method.
More importantly, when the iterations are sufficiently close to an
eigenfunction, the damping can be switched off and we recover a local linear
convergence rate previously known from the discrete setting. This quantitative
convergence analysis is closely connected to the~$J$-method's unique feature of
sensitivity with respect to spectral shifts. Contrary to classical gradient
flows, this allows both the selective approximation of excited states as well
as the amplification of convergence beyond linear rates in the spirit of the
Rayleigh quotient iteration for linear eigenvalue problems. These advantageous
convergence properties are demonstrated in a series of numerical experiments
involving exponentially localized states under disorder potentials and vortex
lattices in rotating traps.
|
1908.00333v2
|
2019-08-02
|
How do Conservative Backbone Curves Perturb into Forced Responses? A Melnikov Function Analysis
|
Weakly damped mechanical systems under small periodic forcing tend to exhibit
periodic response in a close vicinity of certain periodic orbits of their
conservative limit. Specifically, amplitude frequency plots for the
conservative limit have often been noted, both numerically and experimentally,
to serve as backbone curves for the near resonance peaks of the forced
response. In other cases, such a relationship between the unforced and forced
response was not observed. Here we provide a systematic mathematical analysis
that predicts which members of conservative periodic orbit families will serve
as backbone curves for the forced-damped response. We also obtain mathematical
conditions under which approximate numerical and experimental approaches, such
as energy balance and force appropriation, are justifiable. Finally, we derive
analytic criteria for the birth of isolated response branches (isolas) whose
identification is otherwise challenging from numerical continuation.
|
1908.00721v3
|
2019-08-05
|
Tunable strong coupling of two adjacent optical λ/2 Fabry-Pérot microresonators
|
Optical half-wave microresonators enable to control the optical mode density
around a quantum system and thus to modify the temporal emission properties. If
the coupling rate exceeds the damping rate, strong coupling between a
microresonator and a quantum system can be achieved, leading to a coherent
energy exchange and the creation of new hybrid modes. Here, we investigate
strong coupling between two adjacent lambda/2 Fabry-P\'erot microresonators,
where the resonance of one microresonator can be actively tuned across the
resonance of the other microresonator. The transmission spectra of the coupled
microresonators show a clear anticrossing behavior, which proves that the two
cavity modes are strongly coupled. Additionally, we can vary the coupling rate
by changing the resonator geometry and thereby investigate the basic principles
of strong coupling with a well-defined model system. Finally, we will show that
such a coupled system can theoretically be modelled by coupled damped harmonic
oscillators.
|
1908.01566v1
|
2019-07-27
|
An extension of the second order dynamical system that models Nesterov's convex gradient method
|
In this paper we deal with a general second order continuous dynamical system
associated to a convex minimization problem with a Fr\`echet differentiable
objective function. We show that inertial algorithms, such as Nesterov's
algorithm, can be obtained via the natural explicit discretization from our
dynamical system. Our dynamical system can be viewed as a perturbed version of
the heavy ball method with vanishing damping, however the perturbation is made
in the argument of the gradient of the objective function. This perturbation
seems to have a smoothing effect for the energy error and eliminates the
oscillations obtained for this error in the case of the heavy ball method with
vanishing damping, as some numerical experiments show. We prove that the value
of the objective function in a generated trajectory converges in order O(1/t^2)
to the global minimum of the objective function. Moreover, we obtain that a
trajectory generated by the dynamical system converges to a minimum point of
the objective function.
|
1908.02574v1
|
2019-08-07
|
Interfacial contributions to spin-orbit torque and magnetoresistance in ferromagnet/heavy-metal bilayers
|
The thickness dependence of spin-orbit torque and magnetoresistance in
ferromagnet/heavy-metal bilayers is studied using the first-principles
non-equilibrium Green's function formalism combined with the Anderson disorder
model. A systematic expansion in orthogonal vector spherical harmonics is used
for the angular dependence of the torque. The damping-like torque in Co/Pt and
Co/Au bilayers can be described as a sum of the spin-Hall contribution, which
increases with thickness in agreement with the spin-diffusion model, and a
comparable interfacial contribution. The magnetoconductance in the plane
perpendicular to the current in Co/Pt bilayers is of the order of a conductance
quantum per interfacial atom, exceeding the prediction of the spin-Hall model
by more than an order of magnitude. This suggests that the "spin-Hall
magnetoresistance," similarly to the damping-like torque, has a large
interfacial contribution unrelated to the spin-Hall effect.
|
1908.02680v2
|
2019-08-16
|
Dynamics of Hot Bose-Einstein Condensates: stochastic Ehrenfest relations for number and energy damping
|
Describing partially-condensed Bose gases poses a long-standing theoretical
challenge. We present exact stochastic Ehrenfest relations for the stochastic
projected Gross-Pitaevskii equation, including both number and energy damping
mechanisms, and all projector terms that arise from the energy cutoff
separating system from reservoir. We test the theory by applying it to the
centre of mass fluctuations of a harmonically trapped prolate system, finding
close agreement between c-field simulations and analytical results. The
formalism lays the foundation to analytically explore experimentally accessible
hot Bose-Einstein condensates.
|
1908.05809v3
|
2019-08-12
|
On a simple derivation of the very low damping escape rate for classical spins by modifying the method of Kramers
|
The original perturbative Kramers' method (starting from the phase space
coordinates) (Kramers, 1940) of determining the energy-controlled-diffusion
equation for Newtonian particles with separable and additive Hamiltonians is
generalized to yield the energy-controlled diffusion equation and thus the very
low damping (VLD) escape rate including spin-transfer torque for classical
giant magnetic spins with two degrees of freedom. These have dynamics governed
by the magnetic Langevin and Fokker-Planck equations and thus are generally
based on non-separable and non-additive Hamiltonians. The derivation of the VLD
escape rate directly from the (magnetic) Fokker-Planck equation for the surface
distribution of magnetization orientations in the configuration space of the
polar and azimuthal angles $(\vartheta, \varphi)$ is much simpler than those
previously used.
|
1908.06747v1
|
2019-08-22
|
Improving the dynamics of quantum sensors with reinforcement learning
|
Recently proposed quantum-chaotic sensors achieve quantum enhancements in
measurement precision by applying nonlinear control pulses to the dynamics of
the quantum sensor while using classical initial states that are easy to
prepare. Here, we use the cross-entropy method of reinforcement learning to
optimize the strength and position of control pulses. Compared to the
quantum-chaotic sensors with periodic control pulses in the presence of
superradiant damping, we find that decoherence can be fought even better and
measurement precision can be enhanced further by optimizing the control. In
some examples, we find enhancements in sensitivity by more than an order of
magnitude. By visualizing the evolution of the quantum state, the mechanism
exploited by the reinforcement learning method is identified as a kind of
spin-squeezing strategy that is adapted to the superradiant damping.
|
1908.08416v2
|
2019-08-28
|
Spin functional renormalization group for quantum Heisenberg ferromagnets: Magnetization and magnon damping in two dimensions
|
We use the spin functional renormalization group recently developed by two of
us [J. Krieg and P. Kopietz, Phys. Rev. B $\bf{99}$, 060403(R) (2019)] to
calculate the magnetization $M ( H , T )$ and the damping of magnons due to
classical longitudinal fluctuations of quantum Heisenberg ferromagnets. In
order to guarantee that for vanishing magnetic field $H \rightarrow 0$ the
magnon spectrum is gapless when the spin rotational invariance is spontaneously
broken, we use a Ward identity to express the magnon self-energy in terms of
the magnetization. In two dimensions our approach correctly predicts the
absence of long-range magnetic order for $H=0$ at finite temperature $T$. The
magnon spectrum then exhibits a gap from which we obtain the transverse
correlation length. We also calculate the wave-function renormalization factor
of the magnons. As a mathematical by-product, we derive a recursive form of the
generalized Wick theorem for spin operators in frequency space which
facilitates the calculation of arbitrary time-ordered connected correlation
functions of an isolated spin in a magnetic field.
|
1908.10753v2
|
2019-09-03
|
Learning Elastic Constitutive Material and Damping Models
|
Commonly used linear and nonlinear constitutive material models in
deformation simulation contain many simplifications and only cover a tiny part
of possible material behavior. In this work we propose a framework for learning
customized models of deformable materials from example surface trajectories.
The key idea is to iteratively improve a correction to a nominal model of the
elastic and damping properties of the object, which allows new forward
simulations with the learned correction to more accurately predict the behavior
of a given soft object. Space-time optimization is employed to identify gentle
control forces with which we extract necessary data for model inference and to
finally encapsulate the material correction into a compact parametric form.
Furthermore, a patch based position constraint is proposed to tackle the
challenge of handling incomplete and noisy observations arising in real-world
examples. We demonstrate the effectiveness of our method with a set of
synthetic examples, as well with data captured from real world homogeneous
elastic objects.
|
1909.01875v2
|
2019-09-06
|
Effect of Tantalum spacer thickness and deposition conditions on the properties of MgO/CoFeB/Ta/CoFeB/MgO free layers
|
To get stable perpendicularly magnetized tunnel junctions at small device
dimensions, composite free layers that comprise two MgO/FeCoB interfaces as
sources of interface anisotropy are generally used. Proper cristallisation and
annealing robustness is typically ensured by the insertion of a spacer layer of
the early transition metal series within the FeCoB layer. We study the
influence of the spacer thickness and growth condition on the switching metrics
of tunnel junctions thermally annealed at 400$^\circ$C for the case of 1-4
\r{A} Ta spacers. Thick Ta spacer results in a large anisotropies indicative of
a better defined top FeCoB/MgO interface, but this is achieved at the
systematic expense of a stronger damping. For the best anisotropy-damping
compromise, junctions of diameter 22 nm can still be stable and spin-torque
switched. Coercivity and inhomogeneous linewidth broadening, likely arising
from roughness at the FeCoB/Ta interface, can be reduced if a sacrificial Mg
layer is inserted before the Ta spacer deposition.
|
1909.02741v1
|
2019-09-19
|
Blow-up for Strauss type wave equation with damping and potential
|
We study a kind of nonlinear wave equations with damping and potential, whose
coefficients are both critical in the sense of the scaling and depend only on
the spatial variables. Based on the earlier works, one may think there are two
kinds of blow-up phenomenons when the exponent of the nonlinear term is small.
It also means there are two kinds of law to determine the critical exponent. In
this paper, we obtain a blow-up result and get the estimate of the upper bound
of the lifespan in critical and sub-critical cases. All of the results support
such a conjecture, although for now, the existence part is still open.
|
1909.08885v3
|
2019-09-23
|
Inference of modes for linear stochastic processes
|
For dynamical systems that can be modelled as asymptotically stable linear
systems forced by Gaussian noise, this paper develops methods to infer or
estimate their modes from observations in real time. The modes can be real or
complex. For a real mode, we wish to infer its damping rate and mode shape. For
a complex mode, we wish to infer its frequency, damping rate and (complex) mode
shape. Their amplitudes and correlations are encoded in a mode covariance
matrix. The work is motivated and illustrated by the problem of detection of
oscillations in power flow in AC electrical networks. Suggestions of other
applications are given.
|
1909.10247v2
|
2019-10-02
|
Exponential stability for the nonlinear Schrödinger equation with locally distributed damping
|
In this paper, we study the defocusing nonlinear Schr\"{o}dinger equation
with a locally distributed damping on a smooth bounded domain as well as on the
whole space and on an exterior domain. We first construct approximate solutions
using the theory of monotone operators. We show that approximate solutions
decay exponentially fast in the $L^2$-sense by using the multiplier technique
and a unique continuation property. Then, we prove the global existence as well
as the $L^2$-decay of solutions for the original model by passing to the limit
and using a weak lower semicontinuity argument, respectively. The distinctive
feature of the paper is the monotonicity approach, which makes the analysis
independent from the commonly used Strichartz estimates and allows us to work
without artificial smoothing terms inserted into the main equation. We, in
addition, implement a precise and efficient algorithm for studying the
exponential decay established in the first part of the paper numerically. Our
simulations illustrate the efficacy of the proposed control design.
|
1910.00921v1
|
2019-10-07
|
Quantum mechanics at high redshift -- Modelling Damped Lyman-$α$ absorption systems
|
For around 100 years, hydrogen spectral modelling has been based on Voigt
profile fitting. The semi-classical Voigt profile is based on a 2-level atom
approximation. Whilst the Voigt profile is excellent for many circumstances,
the accuracy is insufficient for very high column density damped Lyman-$\alpha$
absorption systems. We have adapted the quantum-mechanical Kramers-Heisenberg
model to include thermal broadening, producing a new profile, the KHT profile.
Interactions involving multiple discrete atomic levels and continuum terms, not
accounted for in the Voigt model, generate asymmetries in the Lyman line wings.
If not modelled, this can lead to significant systematics in parameter
estimation when modelling real data. There are important ramifications in
particular for measurements of the primordial deuterium abundance. However, the
KHT model is complicated. We therefore present a simplified formulation based
on Taylor series expansions and look-up tables, quantifying the impact of the
approximations made. The KHT profile has been implemented within the
widely-used VPFIT code.
|
1910.02913v2
|
2019-10-12
|
Almost Global Solutions to the Three-dimensional Isentropic Inviscid Flows with Damping in Physical Vacuum Around Barenlatt Solutions
|
For the three-dimensional vacuum free boundary problem with physical
singularity that the sound speed is $C^{ {1}/{2}}$-H$\ddot{\rm o}$lder
continuous across the vacuum boundary of the compressible Euler equations with
damping, without any symmetry assumptions, we prove the almost global existence
of smooth solutions when the initial data are small perturbations of the
Barenblatt self-similar solutions to the corresponding porous media equations
simplified via Darcy's law. It is proved that if the initial perturbation is of
the size of $\epsilon$, then the existing time for smooth solutions is at least
of the order of $\exp(\epsilon^{-2/3})$. The key issue for the analysis is the
slow {\em sub-linear} growth of vacuum boundaries of the order of
$t^{1/(3\gamma-1)}$, where $\gamma>1$ is the adiabatic exponent for the gas.
This is in sharp contrast to the currently available global-in-time existence
theory of expanding solutions to the vacuum free boundary problems with
physical singularity of compressible Euler equations for which the expanding
rate of vacuum boundaries is linear. The results obtained in this paper is
closely related to the open question in multiple dimensions since T.-P. Liu's
construction of particular solutions in 1996 .
|
1910.05516v1
|
2019-10-15
|
Nonlocal quantum correlations under amplitude damping decoherence
|
Different nonlocal quantum correlations of entanglement, steering and Bell
nonlocality are defined with the help of local hidden state (LHS) and local
hidden variable (LHV) models. Considering their unique roles in quantum
information processing, it is of importance to understand the individual
nonlocal quantum correlation as well as their relationship. Here, we
investigate the effects of amplitude damping decoherence on different nonlocal
quantum correlations. In particular, we have theoretically and experimentally
shown that the entanglement sudden death phenomenon is distinct from those of
steering and Bell nonlocality. In our scenario, we found that all the initial
states present sudden death of steering and Bell nonlocality, while only some
of the states show entanglement sudden death. These results suggest that the
environmental effect can be different for different nonlocal quantum
correlations, and thus, it provides distinct operational interpretations of
different quantum correlations.
|
1910.06483v1
|
2019-10-17
|
The linearly damped nonlinear Schrödinger equation with localized driving: spatiotemporal decay estimates and the emergence of extreme wave events
|
We prove spatiotemporal algebraically decaying estimates for the density of
the solutions of the linearly damped nonlinear Schr\"odinger equation with
localized driving, when supplemented with vanishing boundary conditions. Their
derivation is made via a scheme, which incorporates suitable weighted Sobolev
spaces and a time-weighted energy method. Numerical simulations examining the
dynamics (in the presence of physically relevant examples of driver types and
driving amplitude/linear loss regimes), showcase that the suggested decaying
rates, are proved relevant in describing the transient dynamics of the
solutions, prior their decay: they support the emergence of waveforms
possessing an algebraic space-time localization (reminiscent of the Peregrine
soliton) as first events of the dynamics, but also effectively capture the
space-time asymptotics of the numerical solutions.
|
1910.08425v2
|
2019-10-24
|
Gapless and gapped holographic phonons
|
We study a holographic model where translations are both spontaneously and
explicitly broken, leading to the presence of (pseudo)-phonons in the spectrum.
The weak explicit breaking is due to two independent mechanisms: a small source
for the condensate itself and additional linearly space-dependent marginal
operators. The low energy dynamics of the model is described by Wigner crystal
hydrodynamics. In absence of a source for the condensate, the phonons remain
gapless, but momentum is relaxed. Turning on a source for the condensate damps
and pins the phonons. Finally, we verify that the universal relation between
the phonon damping rate, mass and diffusivity reported in arXiv:1812.08118
continues to hold in this model for weak enough explicit breaking.
|
1910.11330v2
|
2019-11-06
|
High spin mixing conductance and spin interface transparency at $Co_2Fe_{0.4}Mn_{0.6}Si$ Heusler alloy and Pt interface
|
Ferromagnetic materials exhibiting low magnetic damping ($\alpha$) and
moderately high saturation magnetization are required from the viewpoints of
generation, transmission and detection of spin wave. Since spin-to-charge
conversion efficiency is another important parameter, high spin mixing
conductance ($g_{r}^{\uparrow \downarrow}$) is the key for efficient
spin-to-charge conversion. Full Heusler alloys e.g. $Co_2Fe_{0.4}Mn_{0.6}Si$
(CFMS), which are predicted to be 100$\%$ spin polarized, possess low $\alpha$.
However, the $g_{r}^{\uparrow \downarrow}$ at the interface between CFMS and a
paramagnet has not fully been understood. Here, we report the investigations of
spin pumping and inverse spin Hall effect in $CFMS/Pt$ bilayers. Damping
analysis indicates the presence of significant spin pumping at the interface of
CFMS and Pt, which is also confirmed by the detection of inverse spin Hall
voltage. We show that in CFMS/Pt the $g_{r}^{\uparrow \downarrow}$
(1.77$\times$10$^{20}$m$^{-2}$) and interface transparency (84$\%$) are higher
compared to values reported for other ferromagnet/heavy metal systems.
|
1911.02230v1
|
2019-11-10
|
Influence of resonances on the noise performance of SQUID susceptometers
|
Scanning Superconducting Quantum Interference Device (SQUID) Susceptometry
simultaneously images the local magnetic fields and susceptibilities above a
sample with sub-micron spatial resolution. Further development of this
technique requires a thorough understanding of the current, voltage, and flux
characteristics of scanning SQUID susceptometers. These sensors often have
striking anomalies in their current-voltage characteristics, which we believe
to be due to electromagnetic resonances. The effect of these resonances on the
performance of these SQUIDs is unknown. To explore the origin and impact of the
resonances, we have developed a model that qualitatively reproduces the
experimentally-determined current-voltage characteristics of our scanning SQUID
susceptometers. We use this model to calculate the noise characteristics of
SQUIDs of different designs. We find that the calculated ultimate flux noise is
better in susceptometers with damping resistors that diminish the resonances
than susceptometers without damping resistors. Such calculations will enable
the optimization of the signal-to-noise characteristics of scanning SQUID
susceptometers.
|
1911.03836v2
|
2019-11-13
|
Impact of the crystal orientation on spin-orbit torques in Fe/Pd bilayers
|
Spin-orbit torques in ferromagnetic (FM)/non-magnetic (NM) heterostructures
offer more energy-efficient means to realize spin-logic devices; however, their
strengths are determined by the heterostructure interface. This work examines
crystal orientation impact on the spin-orbit torque efficiency in different
Fe/Pd bilayer systems. Spin torque ferromagnetic measurements evidence that the
damping-like torque efficiency is higher in epitaxial than in polycrystalline
bilayer structures while the field-like torque is negligible in all bilayer
structures. The strength of the damping-like torque decreases with
deterioration of the bilayer epitaxial quality. The present finding provides
fresh insight for the enhancement of spin-orbit torques in magnetic
heterostructures.
|
1911.05487v1
|
2019-12-02
|
Boundary input-to-state stabilization of a damped Euler-Bernoulli beam in the presence of a state-delay
|
This paper is concerned with the point torque boundary feedback stabilization
of a damped Euler-Bernoulli beam model in the presence of a time-varying
state-delay. First, a finite-dimensional truncated model is derived by spectral
reduction. Then, for a given stabilizing state-feedback of the delay-free
truncated model, an LMI-based sufficient condition on the maximum amplitude of
the state-delay is employed to guarantee the stability of the closed-loop
state-delayed truncated model. Second, we assess the exponential stability of
the resulting closed-loop infinite-dimensional system under the assumption that
the number of modes of the original infinite-dimensional system captured by the
truncated model has been selected large enough. Finally, we consider in our
control design the possible presence of a distributed perturbation, as well as
additive boundary perturbations in the control inputs. In this case, we derive
for the closed-loop system an exponential input-to-state estimate with fading
memory of the distributed and boundary disturbances.
|
1912.01117v1
|
2019-12-03
|
The noise fluxes produced by the degree of first-order temporal coherence in a single mode class-A laser amplifier
|
The noise feature of a single mode class-A laser is investigated in the
presence (amplifier) and absence (free-running) of an input signal. The
Maxwell-Bloch equations of motion have been solved after adding the cavity
Langevin force to calculate fluctuations that imposed to the atomic population
inversion and the amplitude and phase of cavity electric field. The correlation
function of these fluctuations is then used to derive the spontaneous emission,
amplitude, and phase noise fluxes in the below and above-threshold states. The
bandwidth of noise fluxes is not only adjusted by the amplitude and frequency
detuning of input signal, but also by the laser pumping and cavity damping
rates. On the other hand, the degree of first-order temporal coherence (DFOTC)
is turned out as the correlation function of the amplitude fluctuation so that
its Fourier transform led to the amplitude noise flux. The coherence time plays
a dual role in order that it is equal to the damping rate invers of DFOTC and
at the same time has an uncertainty relation with the bandwidth of amplitude
noise flux. Finally, the flux conservation requires a balance between the input
pumping noise flux and the output amplitude and spontaneous emission noise
fluxes.
|
1912.01485v1
|
2019-12-05
|
A Fast Implementation for the Canonical Polyadic Decomposition
|
A new implementation of the canonical polyadic decomposition (CPD) is
presented. It features lower computational complexity and memory usage than the
available state of art implementations available. The CPD of tensors is a
challenging problem which has been approached in several manners. Alternating
least squares algorithms were used for a long time, but they convergence
properties are limited. Nonlinear least squares (NLS) algorithms - more
precisely, damped Gauss-Newton (dGN) algorithms - are much better in this
sense, but they require inverting large Hessians, and for this reason there is
just a few implementations using this approach. In this paper, we propose a
fast dGN implementation to compute the CPD. In this paper, we make the case to
always compress the tensor, and propose a fast damped Gauss-Newton
implementation to compute the canonical polyadic decomposition.
|
1912.02366v1
|
2019-12-05
|
Damping of spinful excitons in LaCoO$_3$ by thermal fluctuations: Theory and experiment
|
We present Co $L_3$-edge resonant inelastic x-ray scattering (RIXS) of bulk
LaCoO$_3$ across the thermally-induced spin-state crossover around 100~K. Owing
to a high energy resolution of 25~meV, we observe unambiguously the dispersion
of the intermediate-spin (IS) excitations in the low temperature regime.
Approaching the intermediate temperature regime, the IS excitations are damped
and the bandwidth is reduced. The observed behavior can be well described by a
model of mobile IS excitons with strong attractive interaction, which we solve
using dynamical mean-field theory for hard-core bosons. Our results provide a
detailed mechanism of how high-spin (HS) and IS excitations interact to
establish the physical properties of cobaltite perovskites.
|
1912.02564v3
|
2019-12-09
|
High Frequency Sound in a Unitary Fermi Gas
|
We present an experimental and theoretical study of the phonon mode in a
unitary Fermi gas. Using two-photon Bragg spectroscopy, we measure excitation
spectra at a momentum of approximately half the Fermi momentum, both above and
below the superfluid critical temperature $T_\mathrm{c}$. Below $T_\mathrm{c}$,
the dominant excitation is the Bogoliubov-Anderson (BA) phonon mode, driven by
gradients in the phase of the superfluid order parameter. The temperature
dependence of the BA phonon is consistent with a theoretical model based on the
quasiparticle random phase approximation in which the dominant damping
mechanism is via collisions with thermally excited quasiparticles. As the
temperature is increased above $T_\mathrm{c}$, the phonon evolves into a
strongly damped collisional mode, accompanied by an abrupt increase in spectral
width. Our study reveals strong similarities between sound propagation in the
unitary Fermi gas and liquid helium.
|
1912.03830v1
|
2019-12-10
|
Stability of traveling waves in a driven Frenkel-Kontorova model
|
In this work we revisit a classical problem of traveling waves in a damped
Frenkel-Kontorova lattice driven by a constant external force. We compute these
solutions as fixed points of a nonlinear map and obtain the corresponding
kinetic relation between the driving force and the velocity of the wave for
different values of the damping coefficient. We show that the kinetic curve can
become non-monotone at small velocities, due to resonances with linear modes,
and also at large velocities where the kinetic relation becomes multivalued.
Exploring the spectral stability of the obtained waveforms, we identify, at the
level of numerical accuracy of our computations, a precise criterion for
instability of the traveling wave solutions: monotonically decreasing portions
of the kinetic curve always bear an unstable eigendirection. We discuss why the
validity of this criterion in the {\it dissipative} setting is a rather
remarkable feature offering connections to the Hamiltonian variant of the model
and of lattice traveling waves more generally. Our stability results are
corroborated by direct numerical simulations which also reveal the possible
outcomes of dynamical instabilities.
|
1912.05052v2
|
2019-12-11
|
Quasinormal Modes of Charged Fields in Reissner-Nordstrom Backgrounds by Borel-Pade Summation of Bender-Wu Series
|
We extend recent work of Hatsuda on the computation of quasinormal mode
frequencies via analytic continuation of bound state energies and Borel-Pade
resummation of the Bender-Wu perturbation series to the case of charged fields
in the background of Reissner-Nordstrom black holes. We compare the quasinormal
mode frequencies obtained in this manner to calculations using Leaver's method
of continued fractions, and find good agreement for damped modes (DMs) with
imaginary part remaining finite in the extremal limit. We also present
numerical evidence that the frequencies of certain zero-damped modes (ZDMs)
with imaginary part tending to zero in the extremal limit can be computed when
constructing the Bender-Wu expansion about a peak of the potential inside the
outer horizon of the black hole.
|
1912.05553v2
|
2019-12-19
|
On twin peak quasi-periodic oscillations resulting from the interaction between discoseismic modes and turbulence in accretion discs around black holes
|
Given the peculiar and (in spite of many efforts) unexplained quasi-periodic
oscillation (QPO) twin peak phenomena in accretion disc PSD observations, the
present exploratory analytical article tries to inquire deeper into the
relationship between discoseismic modes and the underlying driving turbulence
in order to assess its importance. We employ a toy model in the form of a
Gaussian white noise driven damped harmonic oscillator with stochastic
frequency. This oscillator represents the discoseismic mode. (Stochastic
damping was also considered, but interestingly found to be less relevant for
the case at hand.) In the context of this model, we find that turbulence
interacts with disc oscillations in interesting ways. In particular, the
stochastic part in the oscillator frequency behaves as a separate driving
agent. This gives rise to 3:2 twin peaks for some values of the physical
parameters, which we find. We conclude with the suggestion that the study of
turbulence be brought to the forefront of disc oscillation dynamics, as opposed
to being a mere background feature. This change of perspective carries
immediate observable consequences, such as considerably shifting the values of
the (discoseismic) oscillator frequencies.
|
1912.09527v1
|
2019-12-28
|
Non-linear damping of superimposed primordial oscillations on the matter power spectrum in galaxy surveys
|
Galaxy surveys are an important probe for superimposed oscillations on the
primordial power spectrum of curvature perturbations, which are predicted in
several theoretical models of inflation and its alternatives. In order to
exploit the full cosmological information in galaxy surveys it is necessary to
study the matter power spectrum to fully non-linear scales. We therefore study
the non-linear clustering in models with superimposed linear and logarithmic
oscillations to the primordial power spectrum by running high-resolution
dark-matter-only N-body simulations. We fit a Gaussian envelope for the
non-linear damping of superimposed oscillations in the matter power spectrum to
the results of the N-body simulations for $k \lesssim 0.6\ h/$Mpc at $0 \leq z
\leq 5$ with an accuracy below the percent. We finally use this fitting formula
to forecast the capabilities of future galaxy surveys, such as Euclid and
Subaru, to probe primordial oscillation down to non-linear scales alone and in
combination with the information contained in CMB anisotropies.
|
1912.12499v3
|
2020-01-04
|
Finite Difference/Galerkin Finite Element Simulation of the Semi-Linear Wave Equation with Scale-Invariant Damping and Mass and Power Non-Linearity
|
This study is concern with the numerical solution of the initial boundary
value problem (IBVP) for the semilinear scale-invariant wave equation with
damping and mass and power non-linearity. Numerical results of the
aforementioned IBVP is obtained by using standart Galerkin finite element
method (GFEM) for the spatial variable and the temporal variable is discretized
with the finite difference method (FDM). The FDM is also used for the
discretization of the spatial variable for the accuracy of the numerical
results. The obtained numerical results with different numerical schemes are
observed compatible. Numerical simulation of the considered problem is given
for the different initial conditions.
|
2001.01075v2
|
2020-01-05
|
Quantifying quantum non-Markovianity based on quantum coherence via skew information
|
Based on the nonincreasing property of quantum coherence via skew information
under incoherent completely positive and trace-preserving maps, we propose a
non-Markovianity measure for open quantum processes. As applications, by
applying the proposed measure to some typical noisy channels, we find that it
is equivalent to the three previous measures of non-Markovianity for phase
damping and amplitude damping channels, i.e., the measures based on the quantum
trace distance, dynamical divisibility, and quantum mutual information. For the
random unitary channel, it is equivalent to the non-Markovianity measure based
on $l_1$ norm of coherence for a class of output states and it is incompletely
equivalent to the measure based on dynamical divisibility. We also use the
modified Tsallis relative $\alpha$ entropy of coherence to detect the
non-Markovianity of dynamics of quantum open systems, the results show that the
modified Tsallis relative $\alpha$ entropy of coherence are more comfortable
than the original Tsallis relative $\alpha$ entropy of coherence for small
$\alpha$.
|
2001.01261v1
|
2020-01-07
|
von Neumann entropy and the entropy production of a damped harmonic oscillator
|
In this paper we analyze the entropy and entropy production of a non-isolated
quantum system described within the quantum Brownian motion framework. This is
a very general and paradigmatic framework for describing non-isolated quantum
systems and can be used in any kind of coupling regime. We start by considering
the application of von Neumann entropy to an arbitrarily damped quantum system
making use of its reduced density operator. We argue that this application is
formally valid and develop a path integral method to evaluate that quantity
analytically. We apply this technique to a harmonic oscillator in contact with
a heat bath and obtain an exact form for its entropy. Then we study the entropy
production of this system and enlighten important characteristics of its
thermodynamical behavior on the pure quantum realm and also address their
transition to the classical limit.
|
2001.02261v1
|
2020-01-09
|
Photon correlation measurements of stochastic limit cycles emerging from high-$Q$ nonlinear silicon photonic crystal microcavities
|
We performed measurements of photon correlation [$g^{(2)}(\tau)$] in driven
nonlinear high-$Q$ silicon (Si) photonic crystal (PhC) microcavities. The
measured $g^{(2)}(\tau)$ exhibits a damped oscillatory behavior when input pump
power exceeds a critical value. From comparison between experiments and
simulations, we attribute the measured oscillation of $g^{(2)}(\tau)$ to
self-pulsing (a limit cycle) emerging from an interplay between photon,
carrier, and thermal dynamics. Namely, the oscillation frequency of
$g^{(2)}(\tau)$ corresponds to the oscillation period of the limit cycle, while
its finite coherence (damping) time originates from the stochastic nature of
the limit cycle. From the standpoint of phase reduction theory, we interpret
the measured coherence time of $g^{(2)}(\tau)$ as the coherence (diffusion)
time of a generalized phase of the limit cycle. Furthermore, we show that an
increase in laser input power enhances the coherence time of $g^{(2)}(\tau)$ up
to the order of microseconds, which could be a demonstration of the
stabilization of a stochastic limit cycle through pumping.
|
2001.02838v2
|
2020-01-12
|
Linear programming bounds for quantum amplitude damping codes
|
Given that approximate quantum error-correcting (AQEC) codes have a
potentially better performance than perfect quantum error correction codes, it
is pertinent to quantify their performance. While quantum weight enumerators
establish some of the best upper bounds on the minimum distance of quantum
error-correcting codes, these bounds do not directly apply to AQEC codes.
Herein, we introduce quantum weight enumerators for amplitude damping (AD)
errors and work within the framework of approximate quantum error correction.
In particular, we introduce an auxiliary exact weight enumerator that is
intrinsic to a code space and moreover, we establish a linear relationship
between the quantum weight enumerators for AD errors and this auxiliary exact
weight enumerator. This allows us to establish a linear program that is
infeasible only when AQEC AD codes with corresponding parameters do not exist.
To illustrate our linear program, we numerically rule out the existence of
three-qubit AD codes that are capable of correcting an arbitrary AD error.
|
2001.03976v1
|
2020-01-22
|
Small data blow-up for the wave equation with a time-dependent scale invariant damping and a cubic convolution for slowly decaying initial data
|
In the present paper, we study the Cauchy problem for the wave equation with
a time-dependent scale invariant damping, i.e.$\frac{2}{1+t}\partial_t v$ and a
cubic convolution $(|x|^{-\gamma}*v^2)v$ with $\gamma\in (0,n)$, where
$v=v(x,t)$ is an unknown function on $\mathbb{R}^n\times[0,T)$. Our aim of the
present paper is to prove a small data blow-up result and show an upper
estimate of lifespan of the problem for slowly decaying positive initial data
$(v(x,0),\partial_t v(x,0))$ such as $\partial_t v(x,0)=O(|x|^{-(1+\nu)})$ as
$|x|\rightarrow\infty$. Here $\nu$ belongs to the scaling supercritical case
$\nu<\frac{n-\gamma}{2}$. Our main new contribution is to estimate the
convolution term in high spatial dimensions, i.e. $n\ge 4$. This paper is the
first blow-up result to treat wave equations with the cubic convolution in high
spatial dimensions ($n\ge 4$).
|
2001.07985v1
|
2020-01-22
|
Testing a Quantum Error-Correcting Code on Various Platforms
|
Quantum error correction plays an important role in fault-tolerant quantum
information processing. It is usually difficult to experimentally realize
quantum error correction, as it requires multiple qubits and quantum gates with
high fidelity. Here we propose a simple quantum error-correcting code for the
detected amplitude damping channel. The code requires only two qubits. We
implement the encoding, the channel, and the recovery on an optical platform,
the IBM Q System, and a nuclear magnetic resonance system. For all of these
systems, the error correction advantage appears when the damping rate exceeds
some threshold. We compare the features of these quantum information processing
systems used and demonstrate the advantage of quantum error correction on
current quantum computing platforms.
|
2001.07998v1
|
2020-01-22
|
Dynamic state reconstruction of quantum systems subject to pure decoherence
|
The article introduces efficient quantum state tomography schemes for qutrits
and entangled qubits subject to pure decoherence. We implement the dynamic
state reconstruction method for open systems sent through phase-damping
channels which was proposed in: Open Syst. Inf. Dyn. 23, 1650019 (2016). In the
current article we prove that two distinct observables measured at four
different time instants suffice to reconstruct the initial density matrix of a
qutrit with evolution given by a phase-damping channel. Furthermore, we
generalize the approach in order to determine the optimal criteria for quantum
tomography of entangled qubits. Finally, we prove two universal theorems
concerning the minimal number of distinct observables required for quantum
tomography of qudits. We believe that dynamic state reconstruction schemes
bring significant advancement and novelty to quantum tomography since they
allow to reduce the number of distinct measurements required to solve the
problem, which is important from the experimental point of view.
|
2001.08167v1
|
2020-01-28
|
Rate of Estimation for the Stationary Distribution of Stochastic Damping Hamiltonian Systems with Continuous Observations
|
We study the problem of the non-parametric estimation for the density $\pi$
of the stationary distribution of a stochastic two-dimensional damping
Hamiltonian system $(Z_t)_{t\in[0,T]}=(X_t,Y_t)_{t \in [0,T]}$. From the
continuous observation of the sampling path on $[0,T]$, we study the rate of
estimation for $\pi(x_0,y_0)$ as $T \to \infty$. We show that kernel based
estimators can achieve the rate $T^{-v}$ for some explicit exponent $v \in
(0,1/2)$. One finding is that the rate of estimation depends on the smoothness
of $\pi$ and is completely different with the rate appearing in the standard
i.i.d.\ setting or in the case of two-dimensional non degenerate diffusion
processes. Especially, this rate depends also on $y_0$. Moreover, we obtain a
minimax lower bound on the $L^2$-risk for pointwise estimation, with the same
rate $T^{-v}$, up to $\log(T)$ terms.
|
2001.10423v1
|
2020-01-28
|
Image polaritons in boron nitride for extreme polariton confinement with low losses
|
Polaritons in two-dimensional materials provide extreme light confinement
that is difficult to achieve with metal plasmonics. However, such tight
confinement inevitably increases optical losses through various damping
channels. Here we demonstrate that hyperbolic phonon polaritons in hexagonal
boron nitride can overcome this fundamental trade-off. Among two observed
polariton modes, featuring a symmetric and antisymmetric charge distribution,
the latter exhibits lower optical losses and tighter polariton confinement.
Far-field excitation and detection of this high-momenta mode becomes possible
with our resonator design that can boost the coupling efficiency via virtual
polariton modes with image charges that we dub image polaritons. Using these
image polaritons, we experimentally observe a record-high effective index of up
to 132 and quality factors as high as 501. Further, our phenomenological theory
suggests an important role of hyperbolic surface scattering in the damping
process of hyperbolic phonon polaritons.
|
2001.10583v2
|
2020-02-06
|
Fractional derivative order determination from harmonic oscillator damping factor
|
This article analysis differential equations which represents damped and
fractional oscillators. First, it is shown that prior to using physical
quantities in fractional calculus, it is imperative that they are turned
dimensionless. Afterwards, approximated expressions that relate the two
equations parameters for the case that the fractional order is close to an
integer number are presented. Following, a numerical regression is made using
power series expansion, and, also from fractional calculus, the fact that both
equations cannot be equivalent is concluded. In the end, from the numerical
regression data, the analytical approximated expressions that relate the two
equations' parameters are refined.
|
2002.02479v1
|
2020-02-11
|
A numerical damped oscillator approach to constrained Schrödinger equations
|
This article explains and illustrates the use of a set of coupled dynamical
equations, second order in a fictitious time, which converges to solutions of
stationary Schr\"{o}dinger equations with additional constraints. We include
three qualitative different numerical examples: the radial Schr\"{o}dinger
equation for the hydrogen atom; the two-dimensional harmonic oscillator with
degenerate excited states; and finally a non-linear Schr\"{o}dinger equation
for rotating states. The presented method is intuitive, with analogies in
classical mechanics for damped oscillators, and easy to implement, either in
own coding, or with software for dynamical systems. Hence, we find it suitable
to introduce it in a continuation course in quantum mechanics or generally in
applied mathematics courses which contain computational parts.
|
2002.04400v2
|
2020-02-12
|
Fast computation of optimal damping parameters for linear vibrational systems
|
We formulate the quadratic eigenvalue problem underlying the mathematical
model of a linear vibrational system as an eigenvalue problem of a
diagonal-plus-low-rank matrix $A$. The eigenvector matrix of $A$ has a
Cauchy-like structure. Optimal viscosities are those for which $trace(X)$ is
minimal, where $X$ is the solution of the Lyapunov equation $AX+XA^{*}=GG^{*}$.
Here $G$ is a low-rank matrix which depends on the eigenfrequencies that need
to be damped. After initial eigenvalue decomposition of linearized problem
which requires $O(n^3)$ operations, our algorithm computes optimal viscosities
for each choice of external dampers in $O(n^2)$ operations, provided that the
number of dampers is small. Hence, the subsequent optimization is order of
magnitude faster than in the standard approach which solves Lyapunov equation
in each step, thus requiring $O(n^3)$ operations. Our algorithm is based on
$O(n^2)$ eigensolver for complex symmetric diagonal-plus-rank-one matrices and
fast $O(n^2)$ multiplication of linked Cauchy-like matrices.
|
2002.04917v2
|
2020-02-13
|
Low-loss two-dimensional plasmon modes in antimonene
|
The effects of spin-orbit (SOC) and electron-phonon coupling on the
collective excitation of doped monolayer Sb$_2$ are investigated using density
functional and many-body perturbation theories. The spin-orbit coupling is
exclusively important for the monolayer Sb$_2$ and it leads to the
reconstruction of the electronic band structure. In particular, plasmon modes
of monolayer Sb$_2$ are quite sensitive to the SOC and are characterized by
very low damping rates owing to small electron-phonon scatterings. Our results
show plasmons in antimonene are significantly less damped compared to monolayer
graphene when plasmon energies are $\hbar \omega> 0.2$ eV due to smaller
plasmon-phonon coupling in the former material.
|
2002.05302v1
|
2020-02-13
|
Quantization of the damped harmonic oscillator based on a modified Bateman Lagrangian
|
An approach to quantization of the damped harmonic oscillator (DHO) is
developed on the basis of a modified Bateman Lagrangian (MBL); thereby some
quantum mechanical aspects of the DHO are clarified. We treat the energy
operator for the DHO, in addition to the Hamiltonian operator that is
determined from the MBL and corresponds to the total energy of the system. It
is demonstrated that the energy eigenvalues of the DHO exponentially decrease
with time and that transitions between the energy eigenstates occur in
accordance with the Schr\"{o}dinger equation. Also, it is pointed out that a
new critical parameter discriminates different behaviours of transition
probabilities.
|
2002.05435v1
|
2020-02-17
|
Charge Transfer Through Redox Molecular Junctions in Non-Equilibrated Solvents
|
Molecular conduction operating in dielectric solvent environments are often
described using kinetic rates based on Marcus theory of electron transfer at a
molecule-metal electrode interface. However, the successive nature of charge
transfer in such system implies that the solvent does not necessarily reach
equilibrium in such process. Here we generalize the theory to account for
solvent nonequilibrium and consider a molecular junction consisting of an
electronic donor-acceptor system coupled to two metallic electrodes and placed
in a polarizable solvent. We determine the nonequilbrium distribution of the
solvent by solving diffusion equations in the strong- and weak-friction limits
and calculate the charge current and its fluctuating behavior. In extreme
limits: the absence of the solvent or fast solvent relaxation, the charge
transfer statistics is Poissonian, while it becomes correlated by the dynamic
solvent in between these limits. A Kramers-like turnover of the nonequilibrium
current as a function of the solvent damping is found. Finally, we propose a
way to tune the solvent-induced damping using geometrical control of the
solvent dielectric response in nanostructured solvent channels.
|
2002.06932v1
|
2020-02-19
|
Diagnostics of plasma ionisation using torsional Alfén waves
|
Using the recently observed torsional Alfv\'en waves in solar prominences, we
determine the ionisation state of the plasma by taking into account that
Alfv\'en waves propagate in a partially ionised prominence plasma. We derive
the evolutionary equation of waves and compare the analytical solutions to
observations to determine the number density of neutrals. Using a single fluid
plasma approximation, where the wave damping is provided by the Cowling
resistivity, we study the temporal evolution of waves. By comparing the
solution of equations with observational data (period, amplitude, propagation
speed), we determined the value of the Cowling resistivity that led us to draw
a conclusion on the amount of neutrals in the partially ionised plasma, a
quantity that cannot be measured directly or indirectly. Our results show that
damped torsional Alfv\'en waves are an ideal diagnostic tool for the ionisation
state of the plasma. Using a simple model, we find that at the observational
temperature of torsional Alfv\'en waves, the number of neutrals is of the order
of $5\times 10^{10}$ cm$^{-3}$.
|
2002.08441v1
|
2020-03-01
|
Optimal Oscillation Damping Control of cable-Suspended Aerial Manipulator with a Single IMU Sensor
|
This paper presents a design of oscillation damping control for the
cable-Suspended Aerial Manipulator (SAM). The SAM is modeled as a double
pendulum, and it can generate a body wrench as a control action. The main
challenge is the fact that there is only one onboard IMU sensor which does not
provide full information on the system state. To overcome this difficulty, we
design a controller motivated by a simplified SAM model. The proposed
controller is very simple yet robust to model uncertainties. Moreover, we
propose a gain tuning rule by formulating the proposed controller in the form
of output feedback linear quadratic regulation problem. Consequently, it is
possible to quickly dampen oscillations with minimal energy consumption. The
proposed approach is validated through simulations and experiments.
|
2003.00472v1
|
2020-03-06
|
Accelerating the Convergence of Higher-Order Coupled Cluster Methods II: Coupled Cluster $Λ$ Equations and Dynamic Damping
|
The method of sub-iteration, which was previously applied to the higher-order
coupled cluster amplitude equations, is extended to the case of the coupled
cluster $\Lambda$ equations. The sub-iteration procedure for the $\Lambda$
equations is found to be highly similar to that for the amplitude equations,
and to exhibit a similar improvement in rate of convergence relative to
extrapolation of all $\hat{T}$ or $\hat{\Lambda}$ amplitudes using DIIS. A
method of dynamic damping is also presented which is found to effectively
recover rapid convergence in the case of oscillatory behavior in the amplitude
or $\Lambda$ equations. Together, these techniques allow for the convergence of
both the amplitude and $\Lambda$ equations necessary for the calculation of
analytic gradients and properties of higher-order coupled cluster methods
without the high memory or disk I/O cost of full DIIS extrapolation.
|
2003.03455v1
|
2020-03-09
|
Forces between Silica Particles in Isopropanol Solutions of 1:1 Electrolytes
|
Interactions between silica surfaces across isopropanol solutions are
measured with colloidal probe technique based on atomic force microscope. In
particular, the influence of 1:1 electrolytes on the interactions between
silica particles is investigated. A plethora of different forces are found in
these systems. Namely, van der Waals, double-layer, attractive non-DLVO,
repulsive solvation, and damped oscillatory interactions are observed. The
measured decay length of the double-layer repulsion is substantially larger
than Debye lengths calculated from nominal salt concentrations. These
deviations are caused by pronounced ion pairing in alcohol solutions. At
separation below 10 nm, additional attractive and repulsive non-DLVO forces are
observed. The former are possibly caused by charge heterogeneities induced by
strong ion adsorption, whereas the latter originate from structuring of
isopropanol molecules close to the surface. Finally, at increased
concentrations the transition from monotonic to damped oscillatory interactions
is uncovered.
|
2003.04058v2
|
2020-03-13
|
Energy localization and transfer in autoresonant weakly dissipative anharmonic chains
|
In this work, we develop an analytical framework to explain the influence of
dissipation and detuning parameters on the emergence and stability of
autoresonance in a strongly nonlinear weakly damped chain subjected to harmonic
forcing with a slowly-varying frequency. Using the asymptotic procedures, we
construct the evolutionary equations, which describe the behavior of the array
under the condition of 1:1 resonance and then approximately compute the slow
amplitudes and phases as well as the duration of autoresonance. It is shown
that, in contrast to autoresonance in a non-dissipative chain with unbounded
growth of energy, the energy in a weakly damped array being initially at rest
is growing only in a bounded time interval up to an instant of simultaneous
escape from resonance of all autoresonant oscillators. Analytical conditions of
the emergence and stability of autoresonance are confirmed by numerical
simulations.
|
2003.06346v1
|
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