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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 |
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 |
2018-03-15 | Improving the capacity of quantum dense coding by weak measurement and reversal measurement | A protocol of quantum dense coding protection of two qubits is proposed in
amplitude damping (AD) channel using weak measurement and reversal measurement.
It is found that the capacity of quantum dense coding under the weak
measurement and reversal measurement is always greater than that without weak
measurement and reversal measurement. When the protocol is applied, for the AD
channels with different damping coefficient, the result reflects that quantum
entanglement can be protected and quantum dense coding becomes successful. | 1803.05678v1 |
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 |
2018-10-15 | 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 |
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 |
2012-09-07 | Quantum Damped Harmonic Oscillator | In this chapter we treat the quantum damped harmonic oscillator, and study
mathematical structure of the model, and construct general solution with any
initial condition, and give a quantum counterpart in the case of taking
coherent state as an initial condition.
This is a simple and good model of Quantum Mechanics with dissipation which
is important to understand real world, and readers will get a powerful weapon
for Quantum Physics. | 1209.1437v1 |
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 |
2016-08-01 | 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 |
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 |
2007-02-07 | Finite time blow-up results for the damped wave equations with arbitrary initial energy in an inhomogeneous medium | In this paper we consider the long time behavior of solutions of the initial
value problem for the damped wave equation of the form \begin{eqnarray*}
u_{tt}-\rho(x)^{-1}\Delta u+u_t+m^2u=f(u) \end{eqnarray*} with some $\rho(x)$
and $f(u)$ on the whole space $\R^n$ ($n\geq 3$).
For the low initial energy case, which is the non-positive initial energy,
based on concavity argument we prove the blow up result. As for the high
initial energy case, we give out sufficient conditions of the initial datum
such that the corresponding solution blows up in finite time. | 0702190v1 |
2008-11-05 | Spectral function and quasi-particle damping of interacting bosons in two dimensions | We employ the functional renormalization group to study dynamical properties
of the two-dimensional Bose gas. Our approach is free of infrared divergences,
which plague the usual diagrammatic approaches, and is consistent with the
exact Nepomnyashchy identity, which states that the anomalous self-energy
vanishes at zero frequency and momentum. We recover the correct infrared
behavior of the propagators and present explicit results for the spectral
line-shape, from which we extract the quasi-particle dispersion and damping. | 0811.0624v2 |
2008-11-13 | Existence of weak solutions to the Cauchy problem of a semilinear wave equation with supercritical interior source and damping | In this paper we show existence of finite energy solutions for the Cauchy
problem associated with a semilinear wave equation with interior damping and
supercritical source terms. The main contribution consists in dealing with
super-supercritical source terms (terms of the order of $|u|^p$ with $p\geq 5$
in $n=3$ dimensions), an open and highly recognized problem in the literature
on nonlinear wave equations. | 0811.2151v1 |
2008-11-17 | Asymptotic stability and blow up for a semilinear damped wave equation with dynamic boundary conditions | In this paper we consider a multi-dimensional wave equation with dynamic
boundary conditions, related to the Kelvin-Voigt damping. Global existence and
asymptotic stability of solutions starting in a stable set are proved. Blow up
for solutions of the problem with linear dynamic boundary conditions with
initial data in the unstable set is also obtained. | 0811.2783v3 |
2008-11-19 | Weyl laws for partially open quantum maps | We study a toy model for "partially open" wave-mechanical system, like for
instance a dielectric micro-cavity, in the semiclassical limit where ray
dynamics is applicable. Our model is a quantized map on the 2-dimensional
torus, with an additional damping at each time step, resulting in a subunitary
propagator, or "damped quantum map". We obtain analogues of Weyl's laws for
such maps in the semiclassical limit, and draw some more precise estimates when
the classical dynamic is chaotic. | 0811.3134v2 |
2010-04-04 | Quantum information reclaiming after amplitude damping | We investigate the quantum information reclaim from the environment after
amplitude damping has occurred. In particular we address the question of
optimal measurement on the environment to perform the best possible correction
on two and three dimensional quantum systems. Depending on the dimension we
show that the entanglement fidelity (the measure quantifying the correction
performance) is or is not the same for all possible measurements and uncover
the optimal measurement leading to the maximum entanglement fidelity. | 1004.0497v1 |
2010-04-09 | Validity of Landauer's principle in the quantum regime | We demonstrate the validity of Landauer's erasure principle in the strong
coupling quantum regime by treating the system-reservoir interaction in a
consistent way. We show that the initial coupling to the reservoir modifies
both energy and entropy of the system and provide explicit expressions for the
latter in the case of a damped quantum harmonic oscillator. These contributions
are related to the Hamiltonian of mean force and dominate in the strong damping
limit. They need therefore to be fully taken into account in any
low-temperature thermodynamic analysis of quantum systems. | 1004.1599v1 |
2010-04-22 | Critical exponent for damped wave equations with nonlinear memory | We consider the Cauchy problem in $\mathbb{R}^n,$ $n\geq 1,$ for a semilinear
damped wave equation with nonlinear memory. Global existence and asymptotic
behavior as $t\rightarrow\infty$ of small data solutions have been established
in the case when $1\leq n\leq3.$ Moreover, we derive a blow-up result under
some positive data in any dimensional space. | 1004.3850v4 |
2010-04-27 | Radiation Damping in a Non-Abelian Strongly-Coupled Gauge Theory | We study a `dressed' or `composite' quark in strongly-coupled N=4
super-Yang-Mills (SYM), making use of the AdS/CFT correspondence. We show that
the standard string dynamics nicely captures the physics of the quark and its
surrounding quantum non-Abelian field configuration, making it possible to
derive a relativistic equation of motion that incorporates the effects of
radiation damping. From this equation one can deduce a non-standard dispersion
relation for the composite quark, as well as a Lorentz covariant formula for
its rate of radiation. | 1004.4912v1 |
2010-09-09 | The Damped String Problem Revisited | We revisit the damped string equation on a compact interval with a variety of
boundary conditions and derive an infinite sequence of trace formulas
associated with it, employing methods familiar from supersymmetric quantum
mechanics. We also derive completeness and Riesz basis results (with
parentheses) for the associated root functions under less smoothness
assumptions on the coefficients than usual, using operator theoretic methods
(rather than detailed eigenvalue and root function asymptotics) only. | 1009.1858v1 |
2010-09-15 | Anomalous High-Energy Spin Excitations in La2CuO4 | Inelastic neutron scattering is used to investigate the collective magnetic
excitations of the high-temperature superconductor parent antiferromagnet
La2CuO4. We find that while the lower energy excitations are well described by
spin-wave theory, including one- and two-magnon scattering processes, the
high-energy spin waves are strongly damped near the (1/2,0) position in
reciprocal space and merge into a momentum dependent continuum. This anomalous
damping indicates the decay of spin waves into other excitations, possibly
unbound spinon pairs. | 1009.2915v1 |
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 |
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 |
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 |
2018-09-25 | On the energy decay rates for the 1D damped fractional Klein-Gordon equation | We consider the fractional Klein-Gordon equation in one spatial dimension,
subjected to a damping coefficient, which is non-trivial and periodic, or more
generally strictly positive on a periodic set. We show that the energy of the
solution decays at the polynomial rate $O(t^{-\frac{s}{4-2s}})$ for $0< s<2 $
and at some exponential rate when $s\geq 2$. Our approach is based on the
asymptotic theory of $C_0$ semigroups in which one can relate the decay rate of
the energy in terms of the resolvent growth of the semigroup generator. The
main technical result is a new observability estimate for the fractional
Laplacian, which may be of independent interest. | 1809.09531v1 |
2019-09-01 | Invariant measures for stochastic damped 2D Euler equations | We study the two-dimensional Euler equations, damped by a linear term and
driven by an additive noise. The existence of weak solutions has already been
studied; pathwise uniqueness is known for solutions that have vorticity in
$L^\infty$. In this paper, we prove the Markov property and then the existence
of an invariant measure in the space $L^\infty$ by means of a
Krylov-Bogoliubov's type method, working with the weak$\star$ and the bounded
weak$\star$ topologies in $L^\infty$. | 1909.00424v2 |
2019-09-03 | A blow-up result for semi-linear structurally damped $σ$-evolution equations | We would like to prove a blow-up result for semi-linear structurally damped
$\sigma$-evolution equations, where $\sigma \ge 1$ and $\delta\in [0,\sigma)$
are assumed to be any fractional numbers. To deal with the fractional Laplacian
operators $(-\Delta)^\sigma$ and $(-\Delta)^\delta$ as well-known non-local
operators, in general, it seems difficult to apply the standard test function
method directly. For this reason, in this paper we shall construct new test
functions to overcome this difficulty. | 1909.01181v1 |
2019-09-09 | Action Functional for a Particle with Damping | In this brief report we discuss the action functional of a particle with
damping, showing that it can be obtained from the dissipative equation of
motion through a modification which makes the new dissipative equation
invariant for time reversal symmetry. This action functional is exactly the
effective action of Caldeira-Leggett model but, in our approach, it is derived
without the assumption that the particle is weakly coupled to a bath of
infinite harmonic oscillators. | 1909.03694v2 |
2019-09-11 | Equilibrium radiation in a plasma medium with spatial and frequency dispersion | Examination of equilibrium radiation in plasma media shows that the spectral
energy distribution of such radiation is different from the Planck equilibrium
radiation. Using the approach of quantum electrodynamics the general relation
for the spectral energy density of equilibrium radiation in a system of charged
particles is found. The obtained result takes into account the influence of
plasma on equilibrium radiation through the explicit transverse dielectric
permittivity which takes into account spatial and frequency dispersion, as well
as the finite collisional damping. For the limiting case of an infinitesimal
damping the result coincides with the known expression. | 1909.08056v1 |
2019-10-14 | Blow-up of solutions to semilinear strongly damped wave equations with different nonlinear terms in an exterior domain | In this paper, we consider the initial boundary value problem in an exterior
domain for semilinear strongly damped wave equations with power nonlinear term
of the derivative-type $|u_t|^q$ or the mixed-type $|u|^p+|u_t|^q$, where
$p,q>1$. On one hand, employing the Banach fixed-point theorem we prove local
(in time) existence of mild solutions. On the other hand, under some conditions
for initial data and the exponents of power nonlinear terms, the blow-up
results are derived by applying the test function method. | 1910.05981v1 |
2020-03-20 | The Cauchy problem of the semilinear second order evolution equation with fractional Laplacian and damping | In the present paper, we prove time decay estimates of solutions in weighted
Sobolev spaces to the second order evolution equation with fractional Laplacian
and damping for data in Besov spaces. Our estimates generalize the estimates
obtained in the previous studies. The second aim of this article is to apply
these estimates to prove small data global well-posedness for the Cauchy
problem of the equation with power nonlinearities. Especially, the estimates
obtained in this paper enable us to treat more general conditions on the
nonlinearities and the spatial dimension than the results in the previous
studies. | 2003.09239v1 |
2020-03-31 | Time-Asymptotics of Physical Vacuum Free Boundaries for Compressible Inviscid Flows with Damping | In this paper, we prove the leading term of time-asymptotics of the moving
vacuum boundary for compressible inviscid flows with damping to be that for
Barenblatt self-similar solutions to the corresponding porous media equations
obtained by simplifying momentum equations via Darcy's law plus the possible
shift due to the movement of the center of mass, in the one-dimensional and
three-dimensional spherically symmetric motions, respectively. This gives a
complete description of the large time asymptotic behavior of solutions to the
corresponding vacuum free boundary problems. The results obtained in this paper
are the first ones concerning the large time asymptotics of physical vacuum
boundaries for compressible inviscid fluids, to the best of our knowledge. | 2003.14072v2 |
2020-04-13 | Landau damping for analytic and Gevrey data | In this paper, we give an elementary proof of the nonlinear Landau damping
for the Vlasov-Poisson system near Penrose stable equilibria on the torus
$\mathbb{T}^d \times \mathbb{R}^d$ that was first obtained by Mouhot and
Villani in \cite{MV} for analytic data and subsequently extended by Bedrossian,
Masmoudi, and Mouhot \cite{BMM} for Gevrey-$\gamma$ data,
$\gamma\in(\frac13,1]$. Our proof relies on simple pointwise resolvent
estimates and a standard nonlinear bootstrap analysis, using an ad-hoc family
of analytic and Gevrey-$\gamma$ norms. | 2004.05979v3 |
2020-04-16 | Strichartz estimates for mixed homogeneous surfaces in three dimensions | We obtain sharp mixed norm Strichartz estimates associated to mixed
homogeneous surfaces in $\mathbb{R}^3$. Both cases with and without a damping
factor are considered. In the case when a damping factor is considered our
results yield a wide generalization of a result of Carbery, Kenig, and Ziesler
[CKZ13]. The approach we use is to first classify all possible singularities
locally, after which one can tackle the problem by appropriately modifying the
methods from the paper of Ginibre and Velo [GV92], and by using the recently
developed methods by Ikromov and M\"uller [IM16]. | 2004.07751v1 |
2020-04-17 | Critical exponent for semi-linear structurally damped wave equation of derivative type | Main purpose of this paper is to study the following semi-linear structurally
damped wave equation with nonlinearity of derivative type: $$u_{tt}- \Delta u+
\mu(-\Delta)^{\sigma/2} u_t= |u_t|^p,\quad u(0,x)= u_0(x),\quad
u_t(0,x)=u_1(x),$$ with $\mu>0$, $n\geq1$, $\sigma \in (0,2]$ and $p>1$. In
particular, we are going to prove the non-existence of global weak solutions by
using a new test function and suitable sign assumptions on the initial data in
both the subcritical case and the critical case. | 2004.08486v2 |
2020-04-29 | Exponential decay for damped Klein-Gordon equations on asymptotically cylindrical and conic manifolds | We study the decay of the global energy for the damped Klein-Gordon equation
on non-compact manifolds with finitely many cylindrical and subconic ends up to
bounded perturbation. We prove that under the Geometric Control Condition, the
decay is exponential, and that under the weaker Network Control Condition, the
decay is logarithmic, by developing the global Carleman estimate with multiple
weights. | 2004.13894v2 |
2020-08-17 | Dynamics of spatially indistinguishable particles and entanglement protection | We provide a general framework which allows one to obtain the dynamics of $N$
noninteracting spatially indistinguishable particles locally coupled to
separated environments. The approach is universal, being valid for both bosons
and fermions and for any type of system-environment interaction. It is then
applied to study the dynamics of two identical qubits under paradigmatic
Markovian noises, such as phase damping, depolarizing and amplitude damping. We
find that spatial indistinguishability of identical qubits is a controllable
intrinsic property of the system which protects quantum entanglement against
detrimental noise. | 2008.07471v1 |
2021-04-06 | Realising Einstein's mirror: Optomechanical damping with a thermal photon gas | In 1909 Einstein described the thermalization of a mirror within a blackbody
cavity by collisions with thermal photons. While the time to thermalize the
motion of even a microscale or nanoscale object is so long that it is not
feasible, we show that it is using the high intensity light from an amplified
thermal light source with a well-defined chemical potential. We predict damping
of the center-of mass motion due to this effect on times scales of seconds for
small optomechanical systems, such as levitated nanoparticles, allowing
experimental observation. | 2104.02708v2 |
2021-04-12 | Fractional time stepping and adjoint based gradient computation in an inverse problem for a fractionally damped wave equation | In this paper we consider the inverse problem of identifying the initial data
in a fractionally damped wave equation from time trace measurements on a
surface, as relevant in photoacoustic or thermoacoustic tomography. We derive
and analyze a time stepping method for the numerical solution of the
corresponding forward problem. Moreover, to efficiently obtain reconstructions
by minimizing a Tikhonov regularization functional (or alternatively, by
computing the MAP estimator in a Bayesian approach), we develop an adjoint
based scheme for gradient computation. Numerical reconstructions in two space
dimensions illustrate the performance of the devised methods. | 2104.05577v1 |
2021-04-15 | Explaining Neptune's Eccentricity | Early migration damped Neptune's eccentricity. Here, we assume that the
damped value was much smaller than the value observed today, and show that the
closest flyby of $\sim 0.1 \; \mathrm{M_{\odot}}$ star over $\sim 4.5
\mathrm{\; Gyr}$ in the field, at a distance of $\sim 10^3 \mathrm{\; AU}$
would explain the value of Neptune's eccentricity observed today. | 2104.07672v3 |
2021-04-17 | Lifespan estimates for wave equations with damping and potential posed on asymptotically Euclidean manifolds | In this work, we investigate the problem of finite time blow up as well as
the upper bound estimates of lifespan for solutions to small-amplitude
semilinear wave equations with time dependent damping and potential, and mixed
nonlinearities $c_1 |u_t|^p+c_2 |u|^q$, posed on asymptotically Euclidean
manifolds, which is related to both the Strauss conjecture and the Glassey
conjecture. | 2104.08497v2 |
2007-07-15 | Enhancement of Carrier Mobility in Semiconductor Nanostructures by Dielectric Engineering | We propose a technique for achieving large improvements in carrier mobilities
in 2- and 1-dimensional semiconductor nanostructures by modifying their
dielectric environments. We show that by coating the nanostructures with
high-$\kappa$ dielectrics, scattering from Coulombic impurities can be strongly
damped. Though screening is also weakened, the damping of Coulombic scattering
is much larger, and the resulting improvement in mobilities of carriers can be
as much as an order of magnitude for thin 2D semiconductor membranes, and more
for semiconductor nanowires. | 0707.2244v1 |
2007-07-23 | Causal vs. Noncausal Description of Nonlinear Wave Mixing; Resolving the Damping-Sign Controversy | Frequency-domain nonlinear wave mixing processes may be described either
using response functions whereby the signal is generated after all interactions
with the incoming fields, or in terms of scattering amplitudes where all fields
are treated symetrically with no specific time ordering. Closed Green's
function expressions derived for the two types of signals have different
analytical properties. The recent controversy regarding the sign of radiative
damping in the linear (Kramers Heisenberg) formula is put in a broader context. | 0707.3458v1 |
2007-07-27 | Excitation of spin dynamics by spin-polarized current in vortex state disks | A spin-polarized current with the polarization perpendicular to the plane of
a vortex-state disk results in renormalization of the effective damping for a
given magnetization mode, and the effective damping becomes zero if the current
exceeds a threshold value. The lowest threshold current corresponds to the
lowest frequency vortex gyroscopic mode. For larger values of the current the
dynamic magnetization state is characterized by precession of the vortex around
the dot center with non-small amplitude and higher frequency. | 0707.4128v1 |
2009-07-14 | Quantum Monty Hall problem under decoherence | We study the effect of decoherence on quantum Monty Hall problem under the
influence of amplitude damping, depolarizing and dephasing channels. It is
shown that under the effect of decoherence, there is a Nash equilibrium of the
game in case of depolarizing channel for Alice's quantum strategy. Where as in
case of dephasing noise, the game is not influenced by the quantum channel. For
amplitude damping channel, the Bob's payoffs are found symmetrical with maximum
at p=0.5 against his classical strategy. However, it is worth-mentioning that
in case of depolarizing channel, Bob's classical strategy remains always
dominant against any choice of Alice's strategy. | 0907.2293v1 |
2012-02-18 | Dynamics of multi-modes maximum entangled coherent state over amplitude damping channel | The dynamics of maximum entangled coherent state travels through an amplitude
damping channel is investigated. For small values of the transmissivity rate
the travelling state is very fragile to this noise channel, where it suffers
from the phase flip error with high probability. The entanglement decays
smoothly for larger values of the transmissivity rate and speedily for smaller
values of this rate. As the number of modes increases, the travelling state
over this noise channel loses its entanglement hastily. The odd and even states
vanish at the same value of the field intensity. | 1202.4089v1 |
2013-11-22 | Complexity of the minimum-time damping of a physical pendulum | We study the minimum-time damping of a physical pendulum by means of a
bounded control. In the similar problem for a linear oscillator each optimal
trajectory possesses a finite number of control switchings from the maximal to
the minimal value. If one considers simultaneously all optimal trajectories
with any initial state, the number of switchings can be arbitrary large. We
show that for the nonlinear pendulum there is a uniform bound for the switching
number for all optimal trajectories. We find asymptotics for this bound as the
control amplitude goes to zero. | 1311.5729v1 |
2014-01-04 | Entanglement and quantum teleportation via decohered tripartite entangled states | The entanglement behavior of two classes of multi-qubit system, GHZ and GHZ
like states passing through a generalized amplitude damping channel is
discussed. Despite this channel causes degradation of the entangled properties
and consequently their abilities to perform quantum teleportation, one can
always improve the lower values of the entanglement and the fidelity of the
teleportrd state by controlling on Bell measurements, analyzer angle and
channel's strength. Using GHZ-like state within a generalized amplitude damping
channel is much better than using the normal GHZ-state, where the decay rate of
entanglement and the fidelity of the teleported states are smaller than those
depicted for GHZ state. | 1401.0796v1 |
2014-04-18 | On the Instability and Critical Damping Conditions, $kτ= 1/e$ and $kτ= π/2$ of the equation $\dotθ = -k θ(t-τ)$ | In this note, I show that it is possible to use elementary mathematics,
instead of the machinery of Lambert function, Laplace Transform, or numerics,
to derive the instability condition, $k \tau = \pi/2$, and the critical damping
condition, $k\tau = 1/e$, for the time-delayed equation $\dot{\theta} = -k
\theta(t-\tau)$. I hope it will be useful for the new comers to this equation,
and perhaps even to the experts if this is a simpler method compared to other
versions. | 1404.4763v1 |
2014-04-22 | Nonlinear-damped Duffing oscillators having finite time dynamics | A class of modified Duffing oscillator differential equations, having
nonlinear damping forces, are shown to have finite time dynamics, i.e., the
solutions oscillate with only a finite number of cycles, and, thereafter, the
motion is zero. The relevance of this feature is briefly discussed in
relationship to the mathematical modeling, analysis, and estimation of
parameters for the vibrations of carbon nano-tubes and graphene sheets, and
macroscopic beams and plates. | 1404.5596v1 |
2015-02-02 | Enhanced oscillation lifetime of a Bose-Einstein condensate in the 3D/1D crossover | We have measured the damped motion of a trapped Bose-Einstein condensate,
oscillating with respect to a thermal cloud. The cigar-shaped trapping
potential provides enough transverse confinement that the dynamics of the
system are intermediate between three-dimensional and one-dimensional. We find
that oscillations persist for longer than expected for a three-dimensional gas.
We attribute this to the suppressed occupation of transverse momentum states,
which are essential for damping. | 1502.00430v2 |
2015-02-03 | Nonequilibrium dynamics of an ultracold dipolar gas | We study the relaxation and damping dynamics of an ultracold, but not quantum
degenerate, gas consisting of dipolar particles. These simulations are
performed using a direct simulation Monte Carlo method and employing the highly
anisotropic differential cross section of dipoles in the Wigner threshold
regime. We find that both cross-dimensional relaxation and damping of breathing
modes occur at rates that are strongly dependent on the orientation of the
dipole moments relative to the trap axis. The relaxation simulations are in
excellent agreement with recent experimental results in erbium. The results
direct our interest toward a less explored regime in dipolar gases where
interactions are dominated by collision processes rather than mean-field
interactions. | 1502.00960v1 |
2015-02-01 | On the Stability of Cylindrical Tangential Discontinuity, Generation and Damping of Helical Waves | Stability of cylindrical interface between two ideal incompressible fluids,
including the magnetic field, surface tension and gravitational field is
studied in linear approximation. We found that helical waves arising both in
plasma comet tails and on the vertical cylindrical water jet in the air are
described by the same dispersion equation where the comet tail magnetic field
plays the same stabilizing role as surface tension for water jet. Hence they
represent the same phenomenon of Kelvin-Helmholtz instability. Thus helical
waves in comet tails and astrophysical jets may be simulated in the laboratory.
The resonance nature of the Kelvin- instability damping is demonstrated. | 1502.00989v1 |
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 |
2016-06-29 | 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 |
2016-12-27 | 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 |
2017-12-13 | 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 |
2018-02-26 | Controllability and observability for non-autonomous evolution equations: the averaged Hautus test | We consider the observability problem for non-autonomous evolution systems
(i.e., the operators governing the system depend on time). We introduce an
averaged Hautus condition and prove that for skew-adjoint operators it
characterizes exact observability. Next, we extend this to more general class
of operators under a growth condition on the associated evolution family. We
give an application to the Schr\"odinger equation with time dependent potential
and the damped wave equation with a time dependent damping coefficient. | 1802.09224v1 |
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 |
2018-05-08 | 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 |
2018-11-02 | 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 |
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 |
2019-07-10 | Formal expansions in stochastic model for wave turbulence 1: kinetic limit | We consider the damped/driver (modified) cubic NLS equation on a large torus
with a properly scaled forcing and dissipation, and decompose its solutions to
formal series in the amplitude. We study the second order truncation of this
series and prove that when the amplitude goes to zero and the torus' size goes
to infinity the energy spectrum of the truncated solutions becomes close to a
solution of the damped/driven wave kinetic equation. Next we discuss higher
order truncations of the series. | 1907.04531v4 |
2019-07-22 | Thresholds for low regularity solutions to wave equations with structural damping | We study the asymptotic behavior of solutions to wave equations with a
structural damping term \[ u_{tt}-\Delta u+\Delta^2 u_t=0, \qquad
u(0,x)=u_0(x), \,\,\, u_t(0,x)=u_1(x), \] in the whole space. New thresholds
are reported in this paper that indicate which of the diffusion wave property
and the non-diffusive structure dominates in low regularity cases. We develop
to that end the previous author's research in 2019 where they have proposed a
threshold that expresses whether the parabolic-like property or the wave-like
property strongly appears in the solution to some regularity-loss type
dissipative wave equation. | 1907.09299v1 |
2019-11-03 | Linear Inviscid Damping in Sobolev and Gevrey Spaces | In a recent article Jia established linear inviscid damping in Gevrey
regularity for compactly supported Gevrey regular shear flows in a finite
channel, which is of great interest in view of existing nonlinear results. In
this article we provide an alternative very short proof of stability in Gevrey
regularity as a consequence of stability in high Sobolev regularity. Here, we
consider both the setting of a finite channel with compactly supported
perturbations and of an infinite channel without this restriction. Furthermore,
we consider the setting where perturbations vanish only of finite order. | 1911.00880v1 |
2019-11-03 | A global existence result for two-dimensional semilinear strongly damped wave equation with mixed nonlinearity in an exterior domain | We study two-dimensional semilinear strongly damped wave equation with mixed
nonlinearity $|u|^p+|u_t|^q$ in an exterior domain, where $p,q>1$. Assuming the
smallness of initial data in exponentially weighted spaces and some conditions
on powers of nonlinearity, we prove global (in time) existence of small data
energy solution with suitable higher regularity by using a weighted energy
method. | 1911.00899v1 |
2019-11-05 | Critical exponent for a weakly coupled system of semi-linear $σ$-evolution equations with frictional damping | We are interested in studying the Cauchy problem for a weakly coupled system
of semi-linear $\sigma$-evolution equations with frictional damping. The main
purpose of this paper is two-fold. We would like to not only prove the global
(in time) existence of small data energy solutions but also indicate the
blow-up result for Sobolev solutions when $\sigma$ is assumed to be any
fractional number. | 1911.01946v1 |
2019-11-11 | Existence and nonexistence of global solutions for a structurally damped wave system with power nonlinearities | Our interest itself of this paper is strongly inspired from an open problem
in the paper [1] published by D'Abbicco. In this article, we would like to
study the Cauchy problem for a weakly coupled system of semi-linear
structurally damped wave equations. Main goal is to find the threshold, which
classifies the global (in time) existence of small data solutions or the
nonexistence of global solutions under the growth condition of the
nonlinearities. | 1911.04412v1 |
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