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2015-11-12 | Strong trajectory and global $\mathbf{W^{1,p}}$-attractors for the damped-driven Euler system in $\mathbb R^2$ | We consider the damped and driven two-dimensional Euler equations in the
plane with weak solutions having finite energy and enstrophy. We show that
these (possibly non-unique) solutions satisfy the energy and enstrophy
equality. It is shown that this system has a strong global and a strong
trajectory attractor in the Sobolev space $H^1$. A similar result on the strong
attraction holds in the spaces $H^1\cap\{u:\ \|\mathrm{curl}
u\|_{L^p}<\infty\}$ for $p\ge2$. | 1511.03873v1 |
2015-11-14 | Infinite energy solutions for critical wave equation with fractional damping in unbounded domains | This work is devoted to infinite-energy solutions of semi-linear wave
equations in unbounded smooth domains of $\mathbb{R}^3$ with fractional damping
of the form $(-\Delta_x+1)^\frac{1}{2}\partial_t u$. The work extends
previously known results for bounded domains in finite energy case.
Furthermore, well-posedness and existence of locally-compact smooth attractors
for the critical quintic non-linearity are obtained under less restrictive
assumptions on non-linearity, relaxing some artificial technical conditions
used before. This is achieved by virtue of new type Lyapunov functional that
allows to establish extra space-time regularity of solutions of Strichartz
type. | 1511.04592v1 |
2015-11-14 | Parametric resonance induced chaos in magnetic damped driven pendulum | A damped driven pendulum with a magnetic driving force, appearing from a
solenoid, where ac current flows is considered. The solenoid acts on the
magnet, which is located at the free end of the pendulum. In this system, the
existence and interrelation of chaos and parametric resonance is theoretically
examined. Derived analytical results are supported by numerical simulations and
conducted experiments. | 1511.04593v2 |
2015-11-19 | Periodic damping gives polynomial energy decay | Let $u$ solve the damped Klein--Gordon equation $$ \big( \partial_t^2-\sum
\partial_{x_j}^2 +m \text{Id} +\gamma(x) \partial_t \big) u=0 $$ on
$\mathbb{R}^n$ with $m>0$ and $\gamma\geq 0$ bounded below on a $2 \pi
\mathbb{Z}^n$-invariant open set by a positive constant. We show that the
energy of the solution $u$ decays at a polynomial rate. This is proved via a
periodic observability estimate on $\mathbb{R}^n.$ | 1511.06144v5 |
2015-12-03 | Evidence for the role of normal-state electrons in nanoelectromechanical damping mechanisms at very low temperatures | We report on experiments performed at low temperatures on aluminum covered
silicon nanoelectromechanical resonators. The substantial difference observed
between the mechanical dissipation in the normal and superconducting states
measured within the same device unambiguously demonstrates the importance of
normal-state electrons in the damping mechanism. The dissipative component
becomes vanishingly small at very low temperatures in the superconducting
state, leading to exceptional values for the quality factor of such small
silicon structures. A critical discussion is given within the framework of the
standard tunneling model. | 1512.01036v1 |
2015-12-31 | Nonlinear stochastic evolution equations of second order with damping | Convergence of a full discretization of a second order stochastic evolution
equation with nonlinear damping is shown and thus existence of a solution is
established. The discretization scheme combines an implicit time stepping
scheme with an internal approximation. Uniqueness is proved as well. | 1512.09260v2 |
2016-01-18 | Stabilizing the Long-time Behavior of the Navier-Stokes Equations and Damped Euler Systems by Fast Oscillating Forces | The paper studies the issue of stability of solutions to the Navier-Stokes
and damped Euler systems in periodic boxes. We show that under action of fast
oscillating-in- time external forces all two dimensional regular solutions
converge to a time periodic flow. Unexpectedly, effects of stabilization can be
also obtained for systems with stationary forces with large total momentum
(average of the velocity). Thanks to the Galilean transformation and space
boundary conditions, the stationary force changes into one with time
oscillations. In the three dimensional case we show an analogical result for
weak solutions to the Navier- Stokes equations. | 1601.04612v1 |
2016-01-27 | Design of a large dynamic range readout unit for the PSD detector of DAMPE | A large dynamic range is required by the Plastic Scintillator Detector (PSD)
of DArk Matter Paricle Explorer (DAMPE), and a double-dynode readout has been
developed. To verify this design, a prototype detector module has been
constructed and tested with cosmic rays and heavy ion beams. The results match
with the estimation and the readout unit could easily cover the required
dynamic range. | 1601.07234v1 |
2016-02-09 | Engineering and Suppression of Decoherence in Two Qubit Systems | In this work, two experimentally feasible methods of decoherence
engineering-one based on the application of stochastic classical kicks and the
other based on temporally randomized pulse sequences are combined. A different
coupling interaction is proposed, which leads to amplitude damping as compared
to existing methods which model phase damping, utilizing the $zz$ coupling
interaction. The decoherence process on combining the stochastic kick method
and the randomized pulse sequence method and the effectiveness of dynamical
decoupling under these coupling interactions are analyzed. Finally, a
counter-intuitive result where decoherence is suppressed in the presence of two
noise sources under certain resonant conditions is presented. | 1602.03026v1 |
2016-02-10 | Attractors for the strongly damped wave equation with $p$-Laplacian | This paper is concerned with the initial boundary value problem for one
dimensional strongly damped wave equation involving $p$-Laplacian. For $p>2$,
we establish the existence of weak local attractors for this problem in
$W_{0}^{1,p}(0,1)\times L^{2}(0,1)$. Under restriction $2<p<4$, we prove that
the semigroup, generated by the considered problem, possesses a strong global
attractor in $W_{0}^{1,p}(0,1)\times L^{2}(0,1)$ and this attractor is a
bounded subset of $W^{1,\infty }(0,1)\times W^{1,\infty }(0,1)$. | 1602.03339v3 |
2016-02-11 | Renormalization Group Study of a Fragile Fermi liquid in $1+ε$ dimensions | We present a calculation of the low energy Greens function in $1+\epsilon$
dimensions using the method of extended poor man's scaling, developed here. We
compute the wave function renormalization $Z(\omega)$ and also the decay rate
near the Fermi energy. Despite the lack of $\omega^2$ damping characteristic of
3-dimensional Fermi liquids, we show that quasiparticles do exist in
$1+\epsilon$ dimensions, in the sense that the quasiparticle weight $Z$ is
finite and that the damping rate is smaller than the energy. We explicitly
compute the crossover from this behavior to a 1-dimensional type
Tomonaga-Luttinger liquid behavior at higher energies. | 1602.03613v2 |
2016-02-20 | Movement of time-delayed hot spots in Euclidean space | We investigate the shape of the solution of the Cauchy problem for the damped
wave equation. In particular, we study the existence, location and number of
spatial maximizers of the solution. Studying the shape of the solution of the
damped wave equation, we prepare a decomposed form of the solution into the
heat part and the wave part. Moreover, as its another application, we give
$L^p$-$L^q$ estimates of the solution. | 1602.06376v1 |
2016-03-04 | Optical realization of the dissipative quantum oscillator | An optical realization of the damped quantum oscillator, based on transverse
light dynamics in an optical resonator with slowly-moving mirrors, is
theoretically suggested. The optical resonator setting provides a simple
implementation of the time-dependent Caldirola-Kanai Hamiltonian of the
dissipative quantum oscillator, and enables to visualize the effects of damped
oscillations in the classical (ray optics) limit and wave packet collapse in
the quantum (wave optics) regime. | 1603.01364v1 |
2016-03-08 | Modifications of the Lifshitz-Kosevich formula in two-dimensional Dirac systems | Starting from the Luttinger-Ward functional we derive an expression for the
oscillatory part of the grand potential of a two dimensional Dirac system in a
magnetic field. We perform the computation for the clean and the disordered
system, and we study the effect of electron-electron interactions on the
oscillations. Unlike in the two dimensional electron gas (2DEG), a finite
temperature and impurity scattering also affects the oscillation frequency.
Furthermore, we find that in graphene, compared to the 2DEG, additional
interaction induced damping effects occur: to two-loop order electron-electron
interactions do lead to an additional damping factor in the amplitude of the
Lifshitz-Kosevich-formula. | 1603.02559v1 |
2016-03-23 | Landau damping for the linearized Vlasov Poisson equation in a weakly collisional regime | In this paper, we consider the linearized Vlasov-Poisson equation around an
homogeneous Maxwellian equilibrium in a weakly collisional regime: there is a
parameter $\eps$ in front of the collision operator which will tend to $0$.
Moreover, we study two cases of collision operators, linear Boltzmann and
Fokker-Planck. We prove a result of Landau damping for those equations in
Sobolev spaces uniformly with respect to the collision parameter $\eps$ as it
goes to $0$. | 1603.07219v2 |
2016-04-14 | Higher order asymptotic expansions to the solutions for a nonlinear damped wave equation | We study the Cauchy problem for a nonlinear damped wave equation. Under
suitable assumptions for the nonlinearity and the initial data, we obtain the
global solution which satisfies weighted $L^1$ and $L^\infty$ estimates.
Furthermore, we establish the higher order asymptotic expansion of the
solution. This means that we construct the nonlinear approximation of the
global solution with respect to the weight of the data. Our proof is based on
the approximation formula of the linear solution, which is given in [36], and
the nonlinear approximation theory for a nonlinear parabolic equation developed
by [18]. | 1604.04100v1 |
2016-04-18 | On the pressureless damped Euler-Poisson equations with non-local forces: Critical thresholds and large-time behavior | We analyse the one-dimensional pressureless Euler-Poisson equations with a
linear damping and non-local interaction forces. These equations are relevant
for modelling collective behavior in mathematical biology. We provide a sharp
threshold between the supercritical region with finite-time breakdown and the
subcritical region with global-in-time existence of the classical solution. We
derive an explicit form of solution in Lagrangian coordinates which enables us
to study the time-asymptotic behavior of classical solutions with the initial
data in the subcritical region. | 1604.05229v1 |
2016-05-24 | Non-existence for fractionally damped fractional differential problems | In this paper, we are concerned with a fractional differential inequality
containing a lower order fractional derivative and a polynomial source term in
the right hand side. A non-existence of non-trivial global solutions result is
proved in an appropriate space by means of the test-function method. The range
of blow up is found to depend only on the lower order derivative. This is in
line with the well-known fact for an internally weakly damped wave equation
that solutions will converge to solutions of the parabolic part. | 1605.07432v1 |
2016-05-31 | On the Benjamin-Bona-Mahony equation with a localized damping | We introduce several mechanisms to dissipate the energy in the
Benjamin-Bona-Mahony (BBM) equation. We consider either a distributed
(localized) feedback law, or a boundary feedback law. In each case, we prove
the global wellposedness of the system and the convergence towards a solution
of the BBM equation which is null on a band. If the Unique Continuation
Property holds for the BBM equation, this implies that the origin is
asymp-totically stable for the damped BBM equation. | 1605.09574v1 |
2016-06-03 | Microscopic derivation of the one qubit Kraus operators for amplitude and phase damping | This article presents microscopic derivation of the Kraus operators for (the
generalized) amplitude and phase damping process. Derivation is based on the
recently developed method [Andersson et al, J. Mod.Opt. 54, 1695 (2007)] which
concerns finite dimensional systems (e.g. qubit). The form of these operators
is usually estimated without insight into the microscopic details of the
dynamics. The behavior of the qubit dynamics is simulated and depicted via
Bloch sphere change. | 1606.01145v1 |
2016-06-08 | Energy Decay in a Wave Guide with Dissipation at Infinity | We prove local and global energy decay for the wave equation in a wave guide
with damping at infinity. More precisely, the absorption index is assumed to
converge slowly to a positive constant, and we obtain the diffusive phenomenon
typical for the contribution of low frequencies when the damping is effective
at infinity. On the other hand, the usual Geometric Control Condition is not
necessarily satisfied so we may have a loss of regularity for the contribution
of high frequencies. Since our results are new even in the Euclidean space, we
also state a similar result in this case. | 1606.02549v2 |
2016-06-29 | Damped Topological Magnons in the Kagomé-Lattice Ferromagnets | We demonstrate that interactions can substantially undermine the
free-particle description of magnons in ferromagnets on geometrically
frustrated lattices. The anharmonic coupling, facilitated by the
Dzyaloshinskii-Moriya interaction, and a highly-degenerate two-magnon continuum
yield a strong, non-perturbative damping of the high-energy magnon modes. We
provide a detailed account of the effect for the $S=1/2$ ferromagnet on the
kagom\'e lattice and propose further experiments. | 1606.09249v3 |
2016-07-06 | Asymptotic profiles of solutions for structural damped wave equations | In this paper, we obtain several asymptotic profiles of solutions to the
Cauchy problem for structurally damped wave equations $\partial_{t}^{2} u -
\Delta u + \nu (-\Delta)^{\sigma} \partial_{t} u=0$, where $\nu >0$ and $0<
\sigma \le1$. Our result is the approximation formula of the solution by a
constant multiple of a special function as $t \to \infty$, which states that
the asymptotic profiles of the solutions are classified into $5$ patterns
depending on the values $\nu$ and $\sigma$. | 1607.01839v1 |
2016-08-01 | Landau-Khalatnikov phonon damping in strongly interacting Fermi gases | We derive the phonon damping rate due to the four-phonon Landau-Khalatnikov
process in low temperature strongly interacting Fermi gases using quantum
hydrodynamics, correcting and extending the original calculation of Landau and
Khalatnikov [ZhETF, 19 (1949) 637]. Our predictions can be tested in
state-of-the-art experiments with cold atomic gases in the collisionless
regime. | 1608.00402v3 |
2016-08-17 | New mechanism of acceleration of particles by stellar black holes | In this paper we study efficiency of particle acceleration in the
magnetospheres of stellar mass black holes. For this purpose we consider the
linearized set of the Euler equation, continuity equation and Poisson equation
respectively. After introducing the varying relativistic centrifugal force, we
show that the charge separation undergoes the parametric instability, leading
to generation of centrifugally excited Langmuir waves. It is shown that these
waves, via the Langmuir collapse damp by means of the Landau damping, as a
result energy transfers to particles accelerating them to energies of the order
of $10^{16}$eV. | 1608.04889v1 |
2016-10-09 | Beam halo study on ATF damping ring | Halo distribution is a key topic for background study. This paper has
developed an analytical method to give an estimation of ATF beam halo
distribution. The equilibrium particle distribution of the beam tail in the ATF
damping ring is calculated analytically with different emittance and different
vacuum degree. The analytical results agree the measurements very well. This is
a general method which can be applied to any electron rings. | 1610.02624v1 |
2016-10-11 | Damping of hard excitations in strongly coupled $\mathcal N\,{=}\,4$ plasma | The damping of high momentum excitations in strongly coupled maximally
supersymmetric Yang-Mills plasma is studied. Previous calculations of the
asymptotic behavior of the quasinormal mode spectrum are extended and
clarified. We confirm that subleading corrections to the lightlike dispersion
relation $\omega({\bf q}) = |{\bf q}|$ have a universal $|{\bf q}|^{-1/3}$
form. Sufficiently narrow, weak planar shocks may be viewed as coherent
superpositions of short wavelength quasinormal modes. The attenuation and
evolution in profile of narrow planar shocks are examined as an application of
our results. | 1610.03491v1 |
2016-10-24 | Assessing the quantumness of a damped two-level system | We perform a detailed analysis of the nonclassical properties of a damped
two-level system. We compute and compare three different criteria of
quantumness, the $l_1$-norm of coherence, the Leggett- Garg inequality and a
quantum witness based on the no-signaling in time condition. We show that all
three quantum indicators decay exponentially in time as a result of the
coupling to the thermal reservoir. We further demonstrate that the
corresponding characteristic times are identical and given by the coherence
half-life. These results quantify how violations of Leggett-Garg inequalities
and nonzero values of the quantum witness are connected to the coherence of the
two-level system. | 1610.07626v1 |
2016-10-26 | Restoring genuine tripartite entanglement under local amplitude damping | We investigate the possibility to restore genuine tripartite entanglement
under local amplitude damping. We show that it is possible to protect genuine
entanglement using CNOT and Hadamard gates. We analyze several ordering of such
recovery operations. We find that for recovery operations applied after
exposing qubits to decoherence, there is no enhancement in lifetime of genuine
entanglement. Actual retrieval of entanglement is only possible when reversal
scheme is applied before and after the decoherence process. We find that
retrieval of entanglement for mixture of $|\widetilde{W}\rangle$ state with
white noise is more evident than the respective mixture of $|W\rangle$ state.
We also find the retrieval of entanglement for similar mixture of $|GHZ\rangle$
state as well. | 1610.08280v1 |
2016-10-27 | Linear Inviscid Damping for Couette Flow in Stratified Fluid | We study the inviscid damping of Couette flow with an exponentially
stratified density. The optimal decay rates of the velocity field and the
density are obtained for general perturbations with minimal regularity. For
Boussinesq approximation model, the decay rates we get are consistent with the
previous results in the literature. We also study the decay rates for the full
Euler equations of stratified fluids, which were not studied before. For both
models, the decay rates depend on the Richardson number in a very similar way.
Besides, we also study the dispersive decay due to the exponential
stratification when there is no shear. | 1610.08924v2 |
2016-11-01 | On the penalty stabilization mechanism for upwind discontinuous Galerkin formulations of first order hyperbolic systems | Penalty fluxes are dissipative numerical fluxes for high order discontinuous
Galerkin (DG) methods which depend on a penalization parameter. We investigate
the dependence of the spectra of high order DG discretizations on this
parameter, and show that as its value increases, the spectra of the DG
discretization splits into two disjoint sets of eigenvalues. One set converges
to the eigenvalues of a conforming discretization, while the other set
corresponds to spurious eigenvalues which are damped proportionally to the
parameter. Numerical experiments also demonstrate that undamped spurious modes
present in both in the limit of zero and large penalization parameters are
damped for moderate values of the upwind parameter. | 1611.00102v2 |
2016-11-26 | Landau damping of surface plasmons in metal nanostructures | We develop a quantum-mechanical theory for Landau damping of surface plasmons
in metal nanostructures larger that the characteristic length for nonlocal
effects. We show that the electron surface scattering, which facilitates
plasmon decay in small nanostructures, can be incorporated into the metal
dielectric function on par with phonon and impurity scattering. The derived
surface scattering rate is determined by the plasmon local field polarization
relative to the metal-dielectric interface and is highly sensitive to the
system geometry. We illustrate our model by providing analytical results for
surface scattering rate in some common shape nanostructures. | 1611.08670v3 |
2016-11-27 | Convergence in probability of an ergodic and conformal multi-symplectic numerical scheme for a damped stochastic NLS equation | In this paper, we investigate the convergence order in probability of a novel
ergodic numerical scheme for damped stochastic nonlinear Schr\"{o}dinger
equation with an additive noise. Theoretical analysis shows that our scheme is
of order one in probability under appropriate assumptions for the initial value
and noise. Meanwhile, we show that our scheme possesses the unique ergodicity
and preserves the discrete conformal multi-symplectic conservation law.
Numerical experiments are given to show the longtime behavior of the discrete
charge and the time average of the numerical solution, and to test the
convergence order, which verify our theoretical results. | 1611.08778v1 |
2016-12-27 | Wiggler for CESR operation at 2 GeV | For low energy operation strategy we advocate utilization of many short
wigglers in contrast with single long wiggler. This allows begin to operate
very naturally with few strong field wigglers giving necessary damping time on
expense of energy spread. By adding more and more wigglers in the ring, as
these wigglers are manufactured and tuned, the field in the wigglers will be
decreased, keeping necessary damping. This strategy allows the mostly effective
operation of CESR with minimum down time. This also gives flexibility in
operation in wider energy scale without non-reversible modifications. | 1612.09227v1 |
2017-01-30 | Energy Transport Property of Charged Particles with Time-Dependent Damping Force via Manifold-Based Analysis Approach | This paper deals with the energy transport properties of charged particles
with time-dependent damping force. Based on the proposed nonlinear
dimensionless mapping,the stability and dynamical evolution of the particle
system is analyzed with the help of manifold-based analysis approach.It has
been found that the particle system possesses two types of energy asymptotic
behaviors. More significantly, the underlying mechanism of an "energy barrier"
is uncovered,i.e., one generalized invariant spanning curve emerges in the
dissipative particle system. These results will be useful to enrich the energy
transport behavior knowledge of the particle system. | 1701.08762v1 |
2017-02-22 | Integration by parts of some non-adapted vector field from Malliavin's lifting approach | In this paper we propose a lift of vector field $X$ on a Riemannian manifold
$M$ to a vector field $\tilde{X}$ on the curved Cameron-Martin space
$H\left(M\right)$ named orthogonal lift. The construction of this lift is based
on a least square spirit with respect to a metric on $H(M)$ reflecting the
damping effect of Ricci curvature. Its stochastic extension gives rise to a
non-adapted Cameron-Martin vector field on $W_o(M)$. In particular, if
$M=\mathbb{R}^d$ with Euclidean metric, then the damp disappears and the lift
reduces to the well-known Malliavin's lift. We establish an integration by
parts formula for these first order differential operators. | 1702.06741v1 |
2017-02-23 | The sharp lifespan estimate for semilinear damped wave equation with Fujita critical power in high dimensions | This paper is concerned about the lifespan estimate to the Cauchy problem of
semilinear damped wave equations with the Fujita critical exponent in high
dimensions$(n\geq 4)$. We establish the sharp upper bound of the lifespan in
the following form \begin{equation}\nonumber\\ \begin{aligned}
T(\varepsilon)\leq \exp(C\varepsilon^{-\frac 2n}), \end{aligned} \end{equation}
by using the heat kernel as the test function. | 1702.07073v2 |
2017-03-09 | Off resonance coupling between a cavity mode and an ensemble of driven spins | We study the interaction between a superconducting cavity and a spin
ensemble. The response of a cavity mode is monitored while simultaneously the
spins are driven at a frequency close to their Larmor frequency, which is tuned
to a value much higher than the cavity resonance. We experimentally find that
the effective damping rate of the cavity mode is shifted by the driven spins.
The measured shift in the damping rate is attributed to the retarded response
of the cavity mode to the driven spins. The experimental results are compared
with theoretical predictions and fair agreement is found. | 1703.03311v1 |
2017-03-10 | Negative Landau damping in bilayer graphene | We theoretically demonstrate that a system formed by two coupled graphene
sheets enables a negative damping regime wherein graphene plasmons are pumped
by a DC current. This effect is triggered by electrons drifting through one of
the graphene sheets and leads to the spontaneous light emission (spasing) and
wave instabilities in the mid-infrared range. It is shown that there is a deep
link between the drift-induced instabilities and wave instabilities in moving
media, as both result from the hybridization of oscillators with oppositely
signed frequencies. With a thickness of few nanometers and wide spectral
tunability, the proposed structure may find interesting applications in
nanophotonic circuitry as an on-chip light source. | 1703.03623v1 |
2017-03-10 | Effects on the CMB from magnetic field dissipation before recombination | Magnetic fields present before decoupling are damped due to radiative
viscosity. This energy injection affects the thermal and ionization history of
the cosmic plasma. The implications for the CMB anisotropies and polarization
are investigated for different parameter choices of a non helical stochastic
magnetic field. Assuming a Gaussian smoothing scale determined by the magnetic
damping wave number at recombination it is found that magnetic fields with
present day strength less than 0.1 nG and negative magnetic spectral indices
have a sizeable effect on the CMB temperature anisotropies and polarization. | 1703.03650v1 |
2017-03-28 | (1+1) Newton-Hooke Group for the Simple and Damped Harmonic Oscillator | It is demonstrated that, in the framework of the orbit method, a simple and
damped harmonic oscillators are indistinguishable at the level of an abstract
Lie algebra. This opens a possibility for treating the dissipative systems
within the orbit method. In depth analysis of the coadjoint orbits of the
$(1+1)$ dimensional Newton-Hooke group are presented. Further, it is argued
that the physical interpretation is carried by a specific realisation of the
Lie algebra of smooth functions on a phase space rather than by an abstract Lie
algebra. | 1703.09583v2 |
2017-04-09 | Controllability of the Strongly Damped Impulsive Semilinear Wave Equation with Memory and Delay | This article is devoted to study the interior approximated controllability of
the strongly damped semilinear wave equation with memory, impulses and delay
terms. The problem is challenging since the state equation contains memory and
impulsive terms yielding to potential unbounded control sequences steering the
system to a neighborhood of the final state, thus fixed point theorems cannot
be used directly. As alternative, the A.E Bashirov and et al. techniques are
applied and together with the delay allow the control solution to be directed
to fixed curve in a short time interval and achieve our result. | 1704.02561v1 |
2017-04-12 | Damping parametric instabilities in future gravitational wave detectors by means of electrostatic actuators | It has been suggested that the next generation of interferometric
gravitational wave detectors may observe spontaneously excited parametric
oscillatory instabilities. We present a method of actively suppressing any such
instability through application of electrostatic forces to the interferometers'
test masses. Using numerical methods we quantify the actuation force required
to damp candidate instabilities and find that such forces are readily
achievable. Our predictions are subsequently verified experimentally using
prototype Advanced LIGO hardware, conclusively demonstrating the effectiveness
of our approach. | 1704.03587v1 |
2017-04-28 | Cross-damping effects in 1S-3S spectroscopy of hydrogen and deuterium | We calculate the cross-damping frequency shift of a laser-induced two-photon
transition monitored through decay fluorescence, by adapting the analogy with
Raman scattering developed by Amaro et al. [P. Amaro et al., PRA 92, 022514
(2015)]. We apply this method to estimate the frequency shift of the 1S-3S
transition in hydrogen and deuterium. Taking into account our experimental
conditions, we find a frequency shift of less than 1 kHz, that is smaller than
our current statistical uncertainty. | 1704.09003v1 |
2017-05-15 | Damping self-forces and Asymptotic Symmetries | Energy conservation in radiating processes requires, at the classical level,
to take into account damping forces on the sources. These forces can be
represented in terms of asymptotic data and lead to charges defined as
integrals over the asymptotic boundary. For scattering processes these charges,
in case of zero radiated energy, are conserved and encode the information about
the sub-leading soft theorems and matching conditions. The QED version of the
self forces is associated with the dependence of the differential cross section
on the infrared resolution scale. | 1705.05297v2 |
2017-05-17 | Exact Model Reduction for Damped-Forced Nonlinear Beams: An Infinite-Dimensional Analysis | We use invariant manifold results on Banach spaces to conclude the existence
of spectral submanifolds (SSMs) in a class of nonlinear, externally forced beam
oscillations. SSMs are the smoothest nonlinear extensions of spectral subspaces
of the linearized beam equation. Reduction of the governing PDE to SSMs
provides an explicit low-dimensional model which captures the correct
asymptotics of the full, infinite-dimensional dynamics. Our approach is general
enough to admit extensions to other types of continuum vibrations. The
model-reduction procedure we employ also gives guidelines for a mathematically
self-consistent modeling of damping in PDEs describing structural vibrations. | 1705.06133v1 |
2017-06-26 | Weighted energy estimates for wave equation with space-dependent damping term for slowly decaying initial data | This paper is concerned with weighted energy estimates for solutions to wave
equation $\partial_t^2u-\Delta u + a(x)\partial_tu=0$ with space-dependent
damping term $a(x)=|x|^{-\alpha}$ $(\alpha\in [0,1))$ in an exterior domain
$\Omega$ having a smooth boundary. The main result asserts that the weighted
energy estimates with weight function like polymonials are given and these
decay rate are almost sharp, even when the initial data do not have compact
support in $\Omega$. The crucial idea is to use special solution of $\partial_t
u=|x|^{\alpha}\Delta u$ including Kummer's confluent hypergeometric functions. | 1706.08311v1 |
2017-08-09 | Global well-posedness for the 2D Boussinesq equations with a velocity damping term | In this paper, we prove global well-posedness of smooth solutions to the
two-dimensional incompressible Boussinesq equations with only a velocity
damping term when the initial data is close to an nontrivial equilibrium state
$(0,x_2)$. As a by-product, under this equilibrium state, our result gives a
positive answer to the question proposed by [ACWX] (see P.3597). | 1708.02695v4 |
2017-08-18 | Second sound in systems of one-dimensional fermions | We study sound in Galilean invariant systems of one-dimensional fermions. At
low temperatures, we find a broad range of frequencies in which in addition to
the waves of density there is a second sound corresponding to ballistic
propagation of heat in the system. The damping of the second sound mode is
weak, provided the frequency is large compared to a relaxation rate that is
exponentially small at low temperatures. At lower frequencies the second sound
mode is damped, and the propagation of heat is diffusive. | 1708.05733v2 |
2017-08-21 | Equilibrium of a Brownian particle with coordinate dependent diffusivity and damping: Generalized Boltzmann distribution | Fick's law for coordinate dependent diffusivity is derived. Corresponding
diffusion current in the presence of coordinate dependent diffusivity is
consistent with the form as given by Kramers-Moyal expansion. We have obtained
the equilibrium solution of the corresponding Smoluchowski equation. The
equilibrium distribution is a generalization of the Boltzmann distribution.
This generalized Boltzmann distribution involves an effective potential which
is a function of coordinate dependent diffusivity. We discuss various
implications of the existence of this generalized Boltzmann distribution for
equilibrium of systems with coordinate dependent diffusivity and damping. | 1708.06132v5 |
2017-08-21 | Global small solutions of 3D incompressible Oldroyd-B model without damping mechanism | In this paper, we prove the global existence of small smooth solutions to the
three-dimensional incompressible Oldroyd-B model without damping on the stress
tensor. The main difficulty is the lack of full dissipation in stress tensor.
To overcome it, we construct some time-weighted energies based on the special
coupled structure of system. Such type energies show the partial dissipation of
stress tensor and the strongly full dissipation of velocity. In the view of
treating "nonlinear term" as a "linear term", we also apply this result to 3D
incompressible viscoelastic system with Hookean elasticity and then prove the
global existence of small solutions without the physical assumption (div-curl
structure) as previous works. | 1708.06172v2 |
2017-10-13 | $L^2$ asymptotic profiles of solutions to linear damped wave equations | In this paper we obtain higher order asymptotic profilles of solutions to the
Cauchy problem of the linear damped wave equation in $\textbf{R}^n$
\begin{equation*} u_{tt}-\Delta u+u_t=0, \qquad u(0,x)=u_0(x), \quad
u_t(0,x)=u_1(x), \end{equation*} where $n\in\textbf{N}$ and $u_0$, $u_1\in
L^2(\textbf{R}^n)$. Established hyperbolic part of asymptotic expansion seems
to be new in the sense that the order of the expansion of the hyperbolic part
depends on the spatial dimension. | 1710.04870v1 |
2017-11-27 | Statistical mechanics of Landau damping | Landau damping is the tendency of solutions to the Vlasov equation towards
spatially homogeneous distribution functions. The distribution functions
however approach the spatially homogeneous manifold only weakly, and Boltzmann
entropy is not changed by Vlasov equation. On the other hand, density and
kinetic energy density, which are integrals of the distribution function,
approach spatially homogeneous states strongly, which is accompanied by growth
of the hydrodynamic entropy. Such a behavior can be seen when Vlasov equation
is reduced to the evolution equations for density and kinetic energy density by
means of the Ehrenfest reduction. | 1711.10022v1 |
2017-11-29 | Lepton-portal Dark Matter in Hidden Valley model and the DAMPE recent results | We study the recent $e^\pm$ cosmic ray excess reported by DAMPE in a Hidden
Valley Model with lepton-portal dark matter. We find the electron-portal can
account for the excess well and satisfy the DM relic density and direct
detection bounds, while electron+muon/electron+muon+tau-portal suffers from
strong constraints from lepton flavor violating observables, such as $\mu \to 3
e$. We also discuss possible collider signatures of our model, both at the LHC
and a future 100 TeV hadron collider. | 1711.11058v3 |
2017-11-30 | Radiative Dirac neutrino mass, DAMPE dark matter and leptogenesis | We explain the electron-positron excess reported by the DAMPE collaboration
recently in a radiative Dirac seesaw model where a dark $U(1)_X$ gauge symmetry
can (i) forbid the tree-level Yukawa couplings of three right-handed neutrinos
to the standard model lepton and Higgs doublets, (ii) predict the existence of
three dark fermions for the gauge anomaly cancellation, (iii) mediate a
testable scattering of the lightest dark fermion off the nucleons. Our model
can also accommodate a successful leptogenesis to generate the cosmic baryon
asymmetry. | 1711.11333v2 |
2017-12-13 | Sub-logistic source can prevent blow-up in the 2D minimal Keller-Segel chemotaxis system | It is well-known that the Neumann initial-boundary value problem for the
minimal-chemotaxis-logistic system in a 2D bounded smooth domain has no blow-up
for any choice of parameters. Here, for a large class of kinetic terms
including sub-logistic sources, we show that the corresponding 2D Neumann
initial-boundary value problems do not possess any blow-up. This illustrates a
new phenomenon that even a class of sub-logistic sources can prevent blow-up
for the 2D problem, indicating that logistic damping is not the weakest damping
to guarantee uniform-in-time boundedness for the 2D minimal Keller-Segel
chemotaxis model. | 1712.04739v1 |
2017-12-16 | Convergence to Equilibrium in Wasserstein distance for damped Euler equations with interaction forces | We develop tools to construct Lyapunov functionals on the space of
probability measures in order to investigate the convergence to global
equilibrium of a damped Euler system under the influence of external and
interaction potential forces with respect to the 2-Wasserstein distance. We
also discuss the overdamped limit to a nonlocal equation used in the modelling
of granular media with respect to the 2-Wasserstein distance, and provide
rigorous proofs for particular examples in one spatial dimension. | 1712.05923v2 |
2017-12-27 | Normal-mode-based analysis of electron plasma waves with second-order Hermitian formalism | The classic problem of the dynamic evolution of Langmuir electron waves in a
collisionless plasma and their Landau damping is cast as a second-order,
self-adjoint problem with a continuum spectrum of real and positive squared
frequencies. The corresponding complete basis of singular normal modes is
obtained, along with their orthogonality relation. This yields easily the
general expression of the time-reversal-invariant solution for any
initial-value problem. An example is given for a specific initial condition
that illustrates the Landau damping of the macroscopic moments of the
perturbation. | 1712.09682v1 |
2018-01-19 | Discontinuous energy shaping control of the Chaplygin sleigh | In this paper we present an energy shaping control law for set-point
regulation of the Chaplygin sleigh. It is well known that nonholonomic
mechanical systems cannot be asymptotically stabilised using smooth control
laws as they do no satisfy Brockett's necessary condition for smooth
stabilisation. Here, we propose a discontinuous control law that can be seen as
a potential energy shaping and damping injection controller. The proposed
controller is shown to be robust against the parameters of both the inertia
matrix and the damping structure of the open-loop system. | 1801.06278v1 |
2018-01-19 | Robust integral action of port-Hamiltonian systems | Interconnection and damping assignment, passivity-based control (IDA-PBC) has
proven to be a successful control technique for the stabilisation of many
nonlinear systems. In this paper, we propose a method to robustify a system
which has been stabilised using IDA-PBC with respect to constant, matched
disturbances via the addition of integral action. The proposed controller
extends previous work on the topic by being robust against the damping of the
system, a quantity which may not be known in many applications. | 1801.06279v1 |
2018-01-19 | A study of Landau damping with random initial inputs | For the Vlasov-Poisson equation with random uncertain initial data, we prove
that the Landau damping solution given by the deterministic counterpart
(Caglioti and Maffei, {\it J. Stat. Phys.}, 92:301-323, 1998) depends smoothly
on the random variable if the time asymptotic profile does, under the
smoothness and smallness assumptions similar to the deterministic case. The
main idea is to generalize the deterministic contraction argument to more
complicated function spaces to estimate derivatives in space, velocity and
random variables. This result suggests that the random space regularity can
persist in long-time even in time-reversible nonlinear kinetic equations. | 1801.06304v1 |
2018-01-31 | Smoluchowski-Kramers approximation for the damped stochastic wave equation with multiplicative noise in any spatial dimension | We show that the solutions to the damped stochastic wave equation converge
pathwise to the solution of a stochastic heat equation. This is called the
Smoluchowski-Kramers approximation. Cerrai and Freidlin have previously
demonstrated that this result holds in the cases where the system is exposed to
additive noise in any spatial dimension or when the system is exposed to
multiplicative noise and the spatial dimension is one. The current paper proves
that the Smoluchowski-Kramers approximation is valid in any spatial dimension
when the system is exposed to multiplicative noise. | 1801.10538v1 |
2018-02-28 | Global-in-time Stability of 2D MHD boundary Layer in the Prandtl-Hartmann Regime | In this paper, we prove global existence of solutions with analytic
regularity to the 2D MHD boundary layer equations in the mixed Prandtl and
Hartmann regime derived by formal multi-scale expansion in \cite{GP}. The
analysis shows that the combined effect of the magnetic diffusivity and
transveral magnetic field on the boundary leads to a linear damping on the
tangential velocity field near the boundary. And this damping effect yields the
global in time analytic norm estimate in the tangential space variable on the
perturbation of the classical steady Hartmann profile. | 1802.10494v3 |
2018-02-28 | Modal approach to the controllability problem of distributed parameter systems with damping | This paper is devoted to the controllability analysis of a class of linear
control systems in a Hilbert space. It is proposed to use the minimum energy
controls of a reduced lumped parameter system for solving the infinite
dimensional steering problem approximately. Sufficient conditions of the
approximate controllability are formulated for a modal representation of a
flexible structure with small damping. | 1803.00129v1 |
2018-03-14 | Study of Quantum Walk over a Square Lattice | Quantum random walk finds application in efficient quantum algorithms as well
as in quantum network theory. Here we study the mixing time of a discrete
quantum walk over a square lattice in presence percolation and decoherence. We
consider bit-flip and phase damping noise, and evaluate the instantaneous
mixing time for both the cases. Using numerical analysis we show that in case
of phase damping noise probability distribution of walker's position is
sufficiently close to the uniform distribution after infinite time. However,
during the action of bit-flip noise, even after infinite time the total
variation distance between the two probability distributions is large enough. | 1803.05152v1 |
2018-04-10 | Motion of a superconducting loop in an inhomogeneous magnetic field: a didactic experiment | We present an experiment conductive to an understanding of both Faraday's law
and the properties of the superconducting state. It consists in the analysis of
the motion of a superconducting loop moving under the influence of gravity in
an inhomogeneous horizontal magnetic field. Gravity, conservation of magnetic
flux, and friction combine to give damped harmonic oscillations. The measured
frequency of oscillation and the damping constant as a function of the magnetic
field strength (the only free parameter) are in good agreement with the
theoretical model. | 1804.03553v1 |
2018-05-08 | Optomechanical damping as the origin of sideband asymmetry | Sideband asymmetry in cavity optomechanics has been explained by particle
creation and annihilation processes, which bestow an amplitude proportional to
'n+1' and 'n' excitations to each of the respective sidebands. We discuss the
issues with this as well as other interpretations, such as quantum backaction
and noise interference, and show that the asymmetry is due to the
optomechanical damping caused by the probe and the cooling lasers instead. | 1805.02952v4 |
2018-05-11 | On the asymptotic stability of stratified solutions for the 2D Boussinesq equations with a velocity damping term | We consider the 2D Boussinesq equations with a velocity damping term in a
strip $\mathbb{T}\times[-1,1]$, with impermeable walls. In this physical
scenario, where the \textit{Boussinesq approximation} is accurate when
density/temperature variations are small, our main result is the asymptotic
stability for a specific type of perturbations of a stratified solution. To
prove this result, we use a suitably weighted energy space combined with linear
decay, Duhamel's formula and "bootstrap" arguments. | 1805.05179v2 |
2018-06-30 | A linearized and conservative Fourier pseudo-spectral method for the damped nonlinear Schrödinger equation in three dimensions | In this paper, we propose a linearized Fourier pseudo-spectral method, which
preserves the total mass and energy conservation laws, for the damped nonlinear
Schr\"{o}dinger equation in three dimensions. With the aid of the semi-norm
equivalence between the Fourier pseudo-spectral method and the finite
difference method, an optimal $L^2$-error estimate for the proposed method
without any restriction on the grid ratio is established by analyzing the real
and imaginary parts of the error function. Numerical results are addressed to
confirm our theoretical analysis. | 1807.00091v3 |
2018-07-11 | Global existence and blow-up for semilinear damped wave equations in three space dimensions | We consider initial value problem for semilinear damped wave equations in
three space dimensions. We show the small data global existence for the problem
without the spherically symmetric assumption and obtain the sharp lifespan of
the solutions. This paper is devoted to a proof of the Takamura's conjecture on
the lifespan of solutions. | 1807.04327v3 |
2018-07-18 | B-field induced mixing between Langmuir waves and axions | We present an analytic study of the dispersion relation for an isotropic
magnetized plasma interacting with axions. We provide a quantitative picture of
the electromagnetic plasma oscillations in both the ultrarelativistic and
nonrelativistic regimes and considering both non-degenerate and degenerate
media, accounting for the dispersion curves as a function of the plasma
temperature and the ratio of the plasma phase velocity to the characteristic
velocity of particles. We include the modifications on the Landau damping of
plasma waves induced by the presence of the axion field, and we comment on the
effects of damping on subluminal plasma oscillations. | 1807.06828v2 |
2018-07-26 | Moment conditions and lower bounds in expanding solutions of wave equations with double damping terms | In this report we obtain higher order asymptotic expansions of solutions to
wave equations with frictional and viscoelastic damping terms. Although the
diffusion phenomena are dominant, differences between the solutions we deal
with and those of heat equations can be seen by comparing the second order
expansions of them. In order to analyze such effects we consider the weighted
L1 initial data. We also give some lower bounds which show the optimality of
obtained expansions. | 1807.10020v1 |
2018-08-16 | Continuity of the set equilibria of non-autonomous damped wave equations with terms concentrating on the boundary | In this paper we are interested in the behavior of the solutions of
non-autonomous damped wave equations when some reaction terms are concentrated
in a neighborhood of the boundary and this neighborhood shrinks to boundary as
a parameter \varepsilon goes to zero. We prove the conti- nuity of the set
equilibria of these equations. Moreover, if an equilibrium solution of the
limit problem is hyperbolic, then we show that the per- turbed equation has one
and only one equilibrium solution nearby. | 1808.05667v1 |
2018-08-30 | Protecting temporal correlations of two-qubit states using quantum channels with memory | Quantum temporal correlations exhibited by violations of Leggett-Garg
Inequality (LGI) and Temporal Steering Inequality (TSI) are in general found to
be non-increasing under decoherence channels when probed on two-qubit pure
entangled states. We study the action of decoherence channels, such as
amplitude damping, phase-damping and depolarising channels when partial memory
is introduced in a way such that two consecutive uses of the channels are
time-correlated. We show that temporal correlations demonstrated by violations
of the above temporal inequalities can be protected against decoherence using
the effect of memory. | 1808.10345v1 |
2018-09-17 | Global existence for weakly coupled systems of semi-linear structurally damped $σ$-evolution models with different power nonlinearities | In this paper, we study the Cauchy problems for weakly coupled systems of
semi-linear structurally damped $\sigma$-evolution models with different power
nonlinearities. By assuming additional $L^m$ regularity on the initial data,
with $m \in [1,2)$, we use $(L^m \cap L^2)- L^2$ and $L^2- L^2$ estimates for
solutions to the corresponding linear Cauchy problems to prove the global (in
time) existence of small data Sobolev solutions to the weakly coupled systems
of semi-linear models from suitable function spaces. | 1809.06744v2 |
2018-10-15 | Global well-posedness in the critical Besov spaces for the incompressible Oldroyd-B model without damping mechanism | We prove the global well-posedness in the critical Besov spaces for the
incompressible Oldroyd-B model without damping mechanism on the stress tensor
in $\mathbb{R}^d$ for the small initial data. Our proof is based on the
observation that the behaviors of Green's matrix to the system of
$\big(u,(-\Delta)^{-\frac12}\mathbb{P}\nabla\cdot\tau\big)$ as well as the
effects of $\tau$ change from the low frequencies to the high frequencies and
the construction of the appropriate energies in different frequencies. | 1810.06171v1 |
2018-10-18 | Global solutions to the $n$-dimensional incompressible Oldroyd-B model without damping mechanism | The present work is dedicated to the global solutions to the incompressible
Oldroyd-B model without damping on the stress tensor in $\mathbb{R}^n(n=2,3)$.
This result allows to construct global solutions for a class of highly
oscillating initial velocity. The proof uses the special structure of the
system. Moreover, our theorem extends the previous result by Zhu [19] and
covers the recent result by Chen and Hao [4]. | 1810.08048v3 |
2018-10-30 | Global well-posedness for nonlinear wave equations with supercritical source and damping terms | We prove the global well-posedness of weak solutions for nonlinear wave
equations with supercritical source and damping terms on a three-dimensional
torus $\mathbb T^3$ of the prototype \begin{align*} &u_{tt}-\Delta
u+|u_t|^{m-1}u_t=|u|^{p-1}u, \;\; (x,t) \in \mathbb T^3 \times \mathbb R^+ ;
\notag\\ &u(0)=u_0 \in H^1(\mathbb T^3)\cap L^{m+1}(\mathbb T^3), \;\;
u_t(0)=u_1\in L^2(\mathbb T^3), \end{align*} where $1\leq p\leq \min\{
\frac{2}{3} m + \frac{5}{3} , m \}$. Notably, $p$ is allowed to be larger than
$6$. | 1810.12476v1 |
2018-11-02 | Nonlinear Damped Timoshenko Systems with Second Sound - Global Existence and Exponential Stability | In this paper, we consider nonlinear thermoelastic systems of Timoshenko type
in a one-dimensional bounded domain. The system has two dissipative mechanisms
being present in the equation for transverse displacement and rotation angle -
a frictional damping and a dissipation through hyperbolic heat conduction
modelled by Cattaneo's law, respectively. The global existence of small, smooth
solutions and the exponential stability in linear and nonlinear cases are
established. | 1811.01128v1 |
2018-11-14 | Quantum witness of a damped qubit with generalized measurements | We evaluate the quantum witness based on the no-signaling-in-time condition
of a damped two-level system for nonselective generalized measurements of
varying strength. We explicitly compute its dependence on the measurement
strength for a generic example. We find a vanishing derivative for weak
measurements and an infinite derivative in the limit of projective
measurements. The quantum witness is hence mostly insensitive to the strength
of the measurement in the weak measurement regime and displays a singular,
extremely sensitive dependence for strong measurements. We finally relate this
behavior to that of the measurement disturbance defined in terms of the
fidelity between pre-measurement and post-measurement states. | 1811.06013v1 |
2018-12-11 | Blow up of solutions to semilinear non-autonomous wave equations under Robin boundary conditions | The problem of blow up of solutions to the initial boundary value problem for
non-autonomous semilinear wave equation with damping and accelerating terms
under the Robin boundary condition is studied. Sufficient conditions of blow up
in a finite time of solutions to semilinear damped wave equations with
arbitrary large initial energy are obtained. A result on blow up of solutions
with negative initial energy of semilinear second order wave equation with
accelerating term is also obtained. | 1812.04595v1 |
2018-12-23 | Global existence of weak solutions for strongly damped wave equations with nonlinear boundary conditions and balanced potentials | We demonstrate the global existence of weak solutions to a class of
semilinear strongly damped wave equations possessing nonlinear hyperbolic
dynamic boundary conditions. Our work assumes $(-\Delta_W)^\theta \partial_tu$
with $\theta\in[\frac{1}{2},1)$ and where $\Delta_W$ is the Wentzell-Laplacian.
Hence, the associated linear operator admits a compact resolvent. A balance
condition is assumed to hold between the nonlinearity defined on the interior
of the domain and the nonlinearity on the boundary. This allows for arbitrary
(supercritical) polynomial growth on each potential, as well as mixed
dissipative/anti-dissipative behavior. Moreover, the nonlinear function defined
on the interior of the domain is assumed to be only $C^0$. | 1812.09781v1 |
2018-12-24 | Cold Damping of an Optically Levitated Nanoparticle to micro-Kelvin Temperatures | We implement a cold damping scheme to cool one mode of the center-of-mass
motion of an optically levitated nanoparticle in ultrahigh vacuum from room
temperature to a record-low temperature of 100 micro-Kelvin. The measured
temperature dependence on feedback gain and thermal decoherence rate is in
excellent agreement with a parameter-free model. We determine the
imprecision-backaction product for our system and provide a roadmap towards
ground-state cooling of optically levitated nanoparticles. | 1812.09875v1 |
2019-01-18 | Decay of semilinear damped wave equations:cases without geometric control condition | We consider the semilinear damped wave equation $\partial_{tt}^2
u(x,t)+\gamma(x)\partial_t u(x,t)=\Delta u(x,t)-\alpha u(x,t)-f(x,u(x,t))$. In
this article, we obtain the first results concerning the stabilization of this
semilinear equation in cases where $\gamma$ does not satisfy the geometric
control condition. When some of the geodesic rays are trapped, the
stabilization of the linear semigroup is semi-uniform in the sense that
$\|e^{At}A^{-1}\|\leq h(t)$ for some function $h$ with $h(t)\rightarrow 0$ when
$t\rightarrow +\infty$. We provide general tools to deal with the semilinear
stabilization problem in the case where $h(t)$ has a sufficiently fast decay. | 1901.06169v1 |
2019-02-04 | Non-Markovian Effects on Overdamped Systems | We study the consequences of adopting the memory dependent, non-Markovian,
physics with the memory-less over-damped approximation usually employed to
investigate Brownian particles. Due to the finite correlation time scale
associated with the noise, the stationary behavior of the system is not
described by the Boltzmann-Gibbs statistics. However, the presence of a very
weak external white noise can be used to regularize the equilibrium properties.
Surprisingly, the coupling to another bath effectively restores the dynamical
aspects missed by the over-damped treatment. | 1902.01356v1 |
2019-02-06 | Stability analysis of a 1D wave equation with a nonmonotone distributed damping | This paper is concerned with the asymptotic stability analysis of a one
dimensional wave equation subject to a nonmonotone distributed damping. A
well-posedness result is provided together with a precise characterization of
the asymptotic behavior of the trajectories of the system under consideration.
The well-posedness is proved in the nonstandard L p functional spaces, with p
$\in$ [2, $\infty$], and relies mostly on some results collected in Haraux
(2009). The asymptotic behavior analysis is based on an attractivity result on
a specific infinite-dimensional linear time-variant system. | 1902.02050v1 |
2019-02-13 | Comment on "Quantization of the damped harmonic oscillator" [Serhan et al, J. Math. Phys. 59, 082105 (2018)] | A recent paper [J. Math. Phys. {\bf 59}, 082105 (2018)] constructs a
Hamiltonian for the (dissipative) damped harmonic oscillator. We point out that
non-Hermiticity of this Hamiltonian has been ignored to find real discrete
eigenvalues which are actually non-real. We emphasize that non-Hermiticity in
Hamiltonian is crucial and it is a quantal signature of dissipation. | 1902.04895v1 |
2019-02-15 | Memory effects teleportation of quantum Fisher information under decoherence | We have investigated how memory effects on the teleportation of quantum
Fisher information(QFI) for a single qubit system using a class of X-states as
resources influenced by decoherence channels with memory, including amplitude
damping, phase-damping and depolarizing channels. Resort to the definition of
QFI, we first derive the explicit analytical results of teleportation of QFI
with respect to weight parameter $\theta$ and phase parameter $\phi$ under the
decoherence channels. Component percentages, the teleportation of QFI for a
two-qubit entanglement system has also been addressed. The remarkable
similarities and differences among these two situations are also analyzed in
detail and some significant results are presented. | 1902.05668v1 |
2019-02-23 | Uniform decay rates for a suspension bridge with locally distributed nonlinear damping | We study a nonlocal evolution equation modeling the deformation of a bridge,
either a footbridge or a suspension bridge. Contrarily to the previous
literature we prove the asymptotic stability of the considered model with a
minimum amount of damping which represents less cost of material. The result is
also numerically proved. | 1902.09963v1 |
2019-03-01 | Spectra of the Dissipative Spin Chain | This paper generalizes the (0+1)-dimensional spin-boson problem to the
corresponding (1+1)-dimensional version. Monte Carlo simulation is used to find
the phase diagram and imaginary time correlation function. The real frequency
spectrum is recovered by the newly developed P\'ade regression analytic
continuation method. We find that, as dissipation strength $\alpha$ is
increased, the sharp quasi-particle spectrum is broadened and the peak
frequency is lower. According to the behavior of the low frequency spectrum, we
classify the dynamical phase into three different regions: weakly damped,
linear $k$-edge, and strongly damped. | 1903.00567v1 |
2019-03-17 | Sensing Kondo correlations in a suspended carbon nanotube mechanical resonator with spin-orbit coupling | We study electron mechanical coupling in a suspended carbon nanotube (CNT)
quantum dot device. Electron spin couples to the flexural vibration mode due to
spin-orbit coupling in the electron tunneling processes. In the weak coupling
limit, i.e. electron-vibration coupling is much smaller than the electron
energy scale, the damping and resonant frequency shift of the CNT resonator can
be obtained by calculating the dynamical spin susceptibility. We find that
strong spin-flip scattering processes in Kondo regime significantly affect the
mechanical motion of the carbon nanotube: Kondo effect induces strong damping
and frequency shift of the CNT resonator. | 1903.07049v1 |
2019-03-27 | Lifespan of semilinear generalized Tricomi equation with Strauss type exponent | In this paper, we consider the blow-up problem of semilinear generalized
Tricomi equation. Two blow-up results with lifespan upper bound are obtained
under subcritical and critical Strauss type exponent. In the subcritical case,
the proof is based on the test function method and the iteration argument. In
the critical case, an iteration procedure with the slicing method is employed.
This approach has been successfully applied to the critical case of semilinear
wave equation with perturbed Laplacian or the damped wave equation of
scattering damping case. The present work gives its application to the
generalized Tricomi equation. | 1903.11351v2 |
2019-04-01 | A remark on semi-linear damped $σ$-evolution equations with a modulus of continuity term in nonlinearity | In this article, we indicate that under suitable assumptions of a modulus of
continuity we obtain either the global (in time) existence of small data
Sobolev solutions or the blow-up result of local (in time) Sobolev solutions to
semi-linear damped $\sigma$-evolution equations with a modulus of continuity
term in nonlinearity. | 1904.00698v3 |
2019-04-05 | Critical regularity of nonlinearities in semilinear classical damped wave equations | In this paper we consider the Cauchy problem for the semilinear damped wave
equation
$u_{tt}-\Delta u + u_t = h(u);\qquad u(0;x) = f(x); \quad u_t(0;x) = g(x);$
where $h(s) = |s|^{1+2/n}\mu(|s|)$. Here n is the space dimension and $\mu$
is a modulus of continuity. Our goal is to obtain sharp conditions on $\mu$ to
obtain a threshold between global (in time) existence of small data solutions
(stability of the zerosolution) and blow-up behavior even of small data
solutions. | 1904.02939v1 |
2019-04-29 | Origin of the DAMPE 1.4 TeV peak | Recent accurate measurements of cosmic ray electron flux by the Dark Matter
Particle Explorer (DAMPE) reveal a sharp peak structure near 1.4 TeV, which is
difficult to explain by standard astrophysical processes. In this letter, we
propose a simple model that the enhanced dark matter annihilation via the
$e^+e^-$ channel and with the thermal relic annihilation cross section around
the current nearest black hole (A0620-00) can satisfactorily account for the
sharp peak structure. The predicted dark matter mass is $\sim 1.5-3$ TeV. | 1904.12418v1 |
2019-05-07 | Decay estimate for the solution of the evolutionary damped $p$-Laplace equation | In this note, we study the asymptotic behavior, as $t$ tends to infinity, of
the solution $u$ to the evolutionary damped $p$-Laplace equation
\begin{equation*}
u_{tt}+a\, u_t =\Delta_p u \end{equation*}
with Dirichlet boundary values. Let $u^*$ denote the stationary solution with
same boundary values, then the $W^{1,p}$-norm of $u(t) - u^{*}$ decays for
large $t$ like $t^{-\frac{1}{(p-1)p}}$, in the degenerate case $ p > 2$. | 1905.03597v2 |
2019-05-10 | Asymptotic profiles for damped plate equations with rotational inertia terms | We consider the Cauchy problem for plate equations with rotational inertia
and frictional damping terms. We will derive asymptotic profiles of the
solution in L^2-sense as time goes to infinity in the case when the initial
data have high and low regularity, respectively. Especially, in the low
regularity case of the initial data one encounters the regularity-loss
structure of the solutions, and the analysis is more delicate. We employ the
so-called Fourier splitting method combined with the explicit expression of the
solutions (high frequency estimates) and the method due to Ikehata (low
frequency estimates). | 1905.04012v1 |
2019-05-20 | Small perturbations for a Duffing-like evolution equation involving non-commuting operators | We consider an abstract evolution equation with linear damping, a nonlinear
term of Duffing type, and a small forcing term. The abstract problem is
inspired by some models for damped oscillations of a beam subject to external
loads or magnetic fields, and shaken by a transversal force.
The main feature is that very natural choices of the boundary conditions lead
to equations whose linear part involves two operators that do not commute.
We extend to this setting the results that are known in the commutative case,
namely that for asymptotically small forcing terms all solutions are eventually
close to the three equilibrium points of the unforced equation, two stable and
one unstable. | 1905.07942v1 |
2019-05-30 | A study of coherence based measure of quantumness in (non) Markovian channels | We make a detailed analysis of quantumness for various quantum noise
channels, both Markovian and non-Markovian. The noise channels considered
include dephasing channels like random telegraph noise, non-Markovian dephasing
and phase damping, as well as the non-dephasing channels such as generalized
amplitude damping and Unruh channels. We make use of a recently introduced
witness for quantumness based on the square $l_1$ norm of coherence. It is
found that the increase in the degree of non-Markovianity increases the
quantumness of the channel. | 1905.12872v1 |
2019-05-30 | Stabilization for vibrating plate with singular structural damping | We consider the dynamic elasticity equation, modeled by the Euler-Bernoulli
plate equation, with a locally distributed singular structural (or viscoelastic
) damping in a boundary domain. Using a frequency domain method combined, based
on the Burq's result, combined with an estimate of Carleman type we provide
precise decay estimate showing that the energy of the system decays
logarithmically as the type goes to the infinity. | 1905.13089v1 |
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