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2014-02-21 | Weakly damped acoustic plasmon mode in transition metal dichalcogenides with Zeeman splitting | We analyze the effect of a strong Zeeman field on the spectrum of collective
excitations of monolayer transition metal dichalcogenides. The combination of
the Dresselhaus type spin orbit coupling and an external Zeeman field result in
the lifting of the valley degeneracy in the valence band of these crystals. We
show that this lifting of the valley degeneracy manifests in the appearance of
an additional plasmon mode with linear in wavenumber dispersion along with the
standard square root in wavenumber mode. Despite this novel mode being subject
to the Landau damping, it corresponds to a well defined quasiparticle peak in
the spectral function of the electron gas. | 1402.5274v1 |
2014-05-01 | On the collapse of trial solutions for a damped-driven non-linear Schrödinger equation | We consider the focusing 2D non-linear Schr\"odinger equation, perturbed by a
damping term, and driven by multiplicative noise. We show that a physically
motivated trial solution does not collapse for any admissible initial condition
although the exponent of the non-linearity is critical. Our method is based on
the construction of a global solution to a singular stochastic Hamiltonian
system used to connect trial solution and Schr\"odinger equation. | 1405.0151v3 |
2014-05-02 | Dynamic phase diagram of dc-pumped magnon condensates | We study the effects of nonlinear dynamics and damping by phonons on a system
of interacting electronically pumped magnons in a ferromagnet. The nonlinear
effects are crucial for constructing the dynamic phase diagram, which describes
how "swasing" and Bose-Einstein condensation emerge out of the
quasiequilibrated thermal cloud of magnons. We analyze the system in the
presence of magnon damping and interactions, demonstrating the continuous onset
of stable condensates as well as hysteretic transitions. | 1405.0522v1 |
2014-05-05 | Finite time extinction for nonlinear Schrodinger equation in 1D and 2D | We consider a nonlinear Schrodinger equation with power nonlinearity, either
on a compact manifold without boundary, or on the whole space in the presence
of harmonic confinement, in space dimension one and two. Up to introducing an
extra superlinear damping to prevent finite time blow up, we show that the
presence of a sublinear damping always leads to finite time extinction of the
solution in 1D, and that the same phenomenon is present in the case of small
mass initial data in 2D. | 1405.0995v1 |
2014-05-16 | Investigation of Power-Law Damping/Dissipative Forces | The properties of a one space-dimension, one particle dynamical system under
the influence of a purely dissipative force are investigated. Assuming this
force depends only on the velocity, it is demonstrated, in contrast to the case
of linear damping, that there exist dissipative forces for which the particle
\textquotedblleft stops" in a finite time. It is also shown, by an explicit
example, that other dissipative forces exist such that they produce dynamics in
which the particle achieves zero velocity only after an infinite distance has
been traveled. Possible applications of these results to more complex
situations are discussed. | 1405.4062v1 |
2014-06-02 | Nonlinear coupler operating on Werner-like states - entanglement creation, its enhancement and preservation | We discuss a model of two nonlinear Kerr-like oscillators, mutually coupled
and excited by parametric process. We show that the system's evolution,
starting from Werner-like states, remains closed within a small set of two-mode
n-photon states the system, and pure two-qubit entangled state can be
generated. For some initial Werner-like states delayed entanglement generation
can be observed. We investigate the influence of two damping mechanisms on the
system's evolution. We show that for the both cases, the entanglement can
survive despite the presence of damping, and the effects of sudden entanglement
death and its rebirth can appear in the system. | 1406.0414v1 |
2014-06-10 | A determining form for the damped driven Nonlinear Schrödinger Equation- Fourier modes case | In this paper we show that the global attractor of the 1D damped, driven,
nonlinear Schr\"odinger equation (NLS) is embedded in the long-time dynamics of
a determining form. The determining form is an ordinary differential equation
in a space of trajectories $X=C_b^1(\mathbb{R}, P_mH^2)$ where $P_m$ is the
$L^2$-projector onto the span of the first $m$ Fourier modes. There is a
one-to-one identification with the trajectories in the global attractor of the
NLS and the steady states of the determining form. We also give an improved
estimate for the number of the determining modes. | 1406.2626v1 |
2014-08-20 | Initial Layer and Relaxation Limit of Non-Isentropic Compressible Euler Equations with Damping | In this paper, we study the relaxation limit of the relaxing Cauchy problem
for non-isentropic compressible Euler equations with damping in
multi-dimensions. We prove that the velocity of the relaxing equations
converges weakly to that of the relaxed equations, while other variables of the
relaxing equations converges strongly to the corresponding variables of the
relaxed equations. We show that as relaxation time approaches 0, there exists
an initial layer for the ill-prepared data, the convergence of the velocity is
strong outside the layer; while there is no initial layer for the well-prepared
data, the convergence of the velocity is strong near t=0. | 1408.4784v1 |
2014-08-26 | Exponential decay for the damped wave equation in unbounded domains | We study the decay of the semigroup generated by the damped wave equation in
an unbounded domain. We first prove under the natural geometric control
condition the exponential decay of the semigroup. Then we prove under a weaker
condition the logarithmic decay of the solutions (assuming that the initial
data are smoother). As corollaries, we obtain several extensions of previous
results of stabilisation and control. | 1408.6054v2 |
2014-10-03 | Relaxation of regularity for the Westervelt equation by nonlinear damping with application in acoustic-acoustic and elastic-acoustic coupling | In this paper we show local (and partially global) in time existence for the
Westervelt equation with several versions of nonlinear damping. This enables us
to prove well-posedness with spatially varying $L_\infty$-coefficients, which
includes the situation of interface coupling between linear and nonlinear
acoustics as well as between linear elasticity and nonlinear acoustics, as
relevant, e.g., in high intensity focused ultrasound (HIFU) applications. | 1410.0797v1 |
2014-10-13 | Vortex gyration mediated by spin waves driven by an out-of-plane oscillating magnetic field | In this letter we address the vortex core dynamics involved in gyration
excitation and damping change by out-of-plane oscillating magnetic fields. When
the vortex core is at rest under the effect of in-plane bias magnetic fields,
the spin waves excited by the perpendicular magnetic field can induce obvious
vortex gyration. When simultaneously excite spin waves and vortex gyrotropic
motion, the gyration damping changes. Analysis of the system energy allows us
to explain the origin of the spin-wave-mediated vortex gyration. | 1410.3230v1 |
2014-10-23 | Non-equilibrium thermodynamics approach to open quantum systems | Open quantum systems are studied from the thermodynamical point of view
unifying the principle of maximum informational entropy and the hypothesis of
relaxation times hierarchy. The result of the unification is a non-Markovian
and local in time master equation that provides a direct connection of
dynamical and thermodynamical properties of open quantum systems. The power of
the approach is illustrated with the application to the damped harmonic
oscillator and the damped driven two-level system resulting in analytical
expressions for the non-Markovian and non-equilibrium entropy and inverse
temperature. | 1410.6312v2 |
2014-10-27 | Linear Inviscid Damping for Monotone Shear Flows | In this article, we prove linear stability, scattering and inviscid damping
with optimal decay rates for the linearized 2D Euler equations around a large
class of strictly monotone shear flows, $(U(y),0)$, in a periodic channel under
Sobolev perturbations. Here, we consider the settings of both an infinite
periodic channel of period $L$, $\mathbb{T}_{L}\times \mathbb{R}$, as well as a
finite periodic channel, $\mathbb{T}_{L} \times [0,1]$, with impermeable walls.
The latter setting is shown to not only be technically more challenging, but to
exhibit qualitatively different behavior due to boundary effects. | 1410.7341v2 |
2014-11-08 | Damping of liquid sloshing by foams: from everyday observations to liquid transport | We perform experiments on the sloshing dynamics of liquids in a rectangular
container submitted to an impulse. We show that when foam is placed on top of
the liquid the oscillations of the free interface are significantly damped. The
ability to reduce sloshing and associated splashing could find applications in
numerous industrial processes involving liquid transport. | 1411.2123v1 |
2014-11-17 | A geometric mesh smoothing algorithm related to damped oscillations | We introduce a smoothing algorithm for triangle, quadrilateral, tetrahedral
and hexahedral meshes whose centerpiece is a simple geometric triangle
transformation. The first part focuses on the mathematical properties of the
element transformation. In particular, the transformation gives rise directly
to a continuous model given by a system of coupled damped oscillations. Derived
from this physical model, adaptive parameters are introduced and their benefits
presented. The second part discusses the mesh smoothing algorithm based on the
element transformation and its numerical performance on example meshes. | 1411.4390v3 |
2015-01-07 | Two-photon lasing by a superconducting qubit | We study the response of a magnetic-field-driven superconducting qubit
strongly coupled to a superconducting coplanar waveguide resonator. We observed
a strong amplification/damping of a probing signal at different resonance
points corresponding to a one and two-photon emission/absorption. The sign of
the detuning between the qubit frequency and the probe determines whether
amplification or damping is observed. The larger blue detuned driving leads to
two-photon lasing while the larger red detuning cools the resonator. Our
experimental results are in good agreement with the theoretical model of qubit
lasing and cooling at the Rabi frequency. | 1501.01543v1 |
2015-03-04 | On the Lewis-Riesenfeld (Dodonov-Man'ko) invariant method | We revise the Lewis-Riesenfeld invariant method for solving the quantum
time-dependent harmonic oscillator in light of the Quantum Arnold
Transformation previously introduced and its recent generalization to the
Quantum Arnold-Ermakov-Pinney Transformation. We prove that both methods are
equivalent and show the advantages of the Quantum Arnold-Ermakov-Pinney
transformation over the Lewis-Riesenfeld invariant method. We show that, in the
quantum time-dependent and damped harmonic oscillator, the invariant proposed
by Dodonov & Man'ko is more suitable and provide some examples to illustrate
it, focusing on the damped case. | 1503.01371v1 |
2015-03-06 | On the strongly damped wave equation with constraint | A weak formulation for the so-called "semilinear strongly damped wave
equation with constraint" is introduced and a corresponding notion of solution
is defined. The main idea in this approach consists in the use of duality
techniques in Sobolev-Bochner spaces, aimed at providing a suitable
"relaxation" of the constraint term. A global in time existence result is
proved under the natural condition that the initial data have finite "physical"
energy. | 1503.01911v1 |
2015-03-23 | Spin-Orbit Torques in Two-Dimensional Rashba Ferromagnets | Magnetization dynamics in single-domain ferromagnets can be triggered by
charge current if spin-orbit coupling is sufficiently strong. We apply
functional Keldysh theory to investigate Rashba spin-orbit torques in metallic
two-dimensional ferromagnets. A reactive, anti-damping-like spin-orbit torque
as well as a dissipative, field-like torque are calculated microscopically, to
the leading order in the spin-orbit interaction strength. By calculating the
first vertex correction we show that the intrinsic anti-damping-like torque
vanishes unless the scattering rates are spin-dependent. | 1503.06872v2 |
2015-04-18 | Global Dirichlet Heat Kernel Estimates for Symmetric Lévy Processes in Half-space | In this paper, we derive explicit sharp two-sided estimates for the Dirichlet
heat kernels of a large class of symmetric (but not necessarily rotationally
symmetric) L\'evy processes on half spaces for all $t>0$. These L\'evy
processes may or may not have Gaussian component. When L\'evy density is
comparable to a decreasing function with damping exponent $\beta$,our estimate
is explicit in terms of the distance to the boundary, the L\'evy exponent and
the damping exponent $\beta$ of L\'evy density. | 1504.04673v2 |
2015-05-05 | The transition from the classical to the quantum regime in nonlinear Landau damping | Starting from the Wigner-Moyal equation coupled to Poisson's equation, a
simplified set of equations describing nonlinear Landau damping of Langmuir
waves is derived. This system is studied numerically, with a particular focus
on the transition from the classical to the quantum regime. In the quantum
regime several new features are found. This includes a quantum modified bounce
frequency, and the discovery that bounce-like amplitude oscillations can take
place even in the absence of trapped particles. The implications of our results
are discussed. | 1505.01381v1 |
2015-05-08 | The amplification of weak measurements under quantum noise | The influence of outside quantum noises on the amplification of weak
measurements is investigated. Three typical quantum noises are discussed. The
maximum values of the pointer's shifts decrease sharply with the strength of
the depolarizing channel and phase damping. In order to obtain significant
amplified signals, the preselection quantum systems must be kept away from the
two quantum noises. Interestingly, the amplification effect is immune to the
amplitude damping noise. | 1505.01911v1 |
2015-05-27 | Local energy decay and smoothing effect for the damped Schr{ö}dinger equation | We prove the local energy decay and the smoothing effect for the damped
Schr{\"o}dinger equation on R^d. The self-adjoint part is a Laplacian
associated to a long-range perturbation of the flat metric. The proofs are
based on uniform resolvent estimates obtained by the dissipative Mourre method.
All the results depend on the strength of the dissipation which we consider. | 1505.07200v1 |
2015-05-27 | Logarithmic stability in determining a boundary coefficient in an ibvp for the wave equation | In [2] we introduced a method combining together an observability inequality
and a spectral decomposition to get a logarithmic stability estimate for the
inverse problem of determining both the potential and the damping coefficient
in a dissipative wave equation from boundary measurements. The present work
deals with an adaptation of that method to obtain a logarithmic stability
estimate for the inverse problem of determining a boundary damping coefficient
from boundary measurements. As in our preceding work, the different boundary
measurements are generated by varying one of the initial conditions. | 1505.07248v1 |
2015-06-01 | Local decay for the damped wave equation in the energy space | We improve a previous result about the local energy decay for the damped wave
equation on R^d. The problem is governed by a Laplacian associated with a long
range perturbation of the flat metric and a short range absorption index. Our
purpose is to recover the decay O(t^{--d+$\epsilon$}) in the weighted energy
spaces. The proof is based on uniform resolvent estimates, given by an improved
version of the dissipative Mourre theory. In particular we have to prove the
limiting absorption principle for the powers of the resolvent with inserted
weights. | 1506.00377v1 |
2015-06-03 | Giant Phonon Anomaly associated with Superconducting Fluctuations in the Pseudogap Phase of Cuprates | The opening of the pseudogap in underdoped cuprates breaks up the Fermi
surface, which may lead to a breakup of the d-wave order parameter into two
subband amplitudes and a low energy Leggett mode due to phase fluctuations
between them. This causes a large increase in the temperature range of
superconducting fluctuations with an overdamped Leggett mode. Almost resonant
scattering of inter-subband phonons to a state with a pair of Leggett modes
causes anomalously strong damping. In the ordered state, the Leggett mode
develops a finite energy, suppressing the anomalous phonon damping but leading
to an anomaly in the phonon dispersion. | 1506.01258v1 |
2015-06-06 | On higher regularity for the Westervelt equation with strong nonlinear damping | We show higher interior regularity for the Westervelt equation with strong
nonlinear damping term of the $q$-Laplace type. Secondly, we investigate an
interface coupling problem for these models, which arise, e.g., in the context
of medical applications of high intensity focused ultrasound in the treatment
of kidney stones. We show that the solution to the coupled problem exhibits
piecewise $H^2$ regularity in space, provided that the gradient of the acoustic
pressure is essentially bounded in space and time on the whole domain. This
result is of importance in numerical approximations of the present problem, as
well as in gradient based algorithms for finding the optimal shape of the
focusing acoustic lens in lithotripsy. | 1506.02125v1 |
2015-06-08 | Intermode-coupling modulation in the fermion-boson model: heating effects in the BCS regime | Heating induced by an oscillating modulation of the interaction strength in
an atomic Fermion pair condensate is analyzed. The coupled fermion-boson model,
generalized by incorporating a time-dependent intermode coupling through a
magnetic Feshbach resonance, is applied. The dynamics is analytically
characterized in a perturbative scheme. The results account for experimental
findings which have uncovered a damped and delayed response of the condensate
to the modulation. The delay is due to the variation of the quasiparticle
energies and the subsequent relaxation of the condensate. The detected damping
results from the excitations induced by a nonadiabatic modulation: for driving
frequencies larger than twice the pairing gap, quasiparticles are generated,
and, consequently, heating sets in. | 1506.02612v1 |
2015-06-22 | N-body description of Debye shielding and Landau damping | This paper brings further insight into the recently published N-body
description of Debye shielding and Landau damping [Escande D F, Elskens Y and
Doveil F 2014 Plasma Phys. Control. Fusion 57 025017]. Its fundamental equation
for the electrostatic potential is derived in a simpler and more rigorous way.
Various physical consequences of the new approach are discussed, and this
approach is compared with the seminal one by Pines and Bohm [Pines D and Bohm D
1952 Phys. Rev. 85 338--353]. | 1506.06468v2 |
2015-07-23 | Millisecond newly born pulsars as efficient accelerators of electrons | The newly born millisecond pulsars are investigated as possible energy
sources for creating ultra-high energy electrons. The transfer of energy from
the star rotation to high energy electrons takes place through the Landau
damping of centrifugally driven (via a two stream instability) electrostatic
Langmuir waves. Generated in the bulk magnetosphere plasma, such waves grow to
high amplitudes, and then damp, very effectively, on relativistic electrons
driving them to even higher energies. We show that the rate of transfer of
energy is so efficient that no energy losses might affect the mechanism of
particle acceleration; the electrons might achieve energies of the order of
10^{18}eV for parameters characteristic of a young star. | 1507.06415v1 |
2015-07-28 | Stability of solutions to nonlinear wave equations with switching time-delay | In this paper we study well-posedness and asymptotic stability for a class of
nonlinear second-order evolution equations with intermittent delay damping.
More precisely, a delay feedback and an undelayed one act alternately in time.
We show that, under suitable conditions on the feedback operators, asymptotic
stability results are available. Concrete examples included in our setting are
illustrated. We give also stability results for an abstract model with
alternate positive-negative damping, without delay. | 1507.07787v1 |
2015-08-10 | Theory of the strongly-damped quantum harmonic oscillator | We analyse the properties of a strongly-damped quantum harmonic oscillator by
means of an exact diagonalisation of the full Hamiltonian, including both the
oscillator and the reservoir degrees of freedom to which it is coupled. Many of
the properties of the oscillator, including its steady-state properties and
entanglement with the reservoir can be understood and quantified in terms of a
simple probability density, which we may associate with the ground-state
frequency spectrum of the oscillator. | 1508.02442v1 |
2015-08-20 | Bump-on-tail instability of twisted excitations in rotating cold atomic clouds | We develop a kinetic theory for twisted density waves (phonons), carrying a
finite amount of orbital angular momentum, in large magneto optical traps,
where the collective processes due to the exchange of scattered photons are
considered. Explicit expressions for the dispersion relation and for the
kinetic (Landau) damping are derived and contributions from the orbital angular
momentum are discussed. We show that for rotating clouds, exhibiting
ring-shaped structures, phonons carrying orbital angular momentum can cross the
instability threshold and grow out of noise, while the usual plane wave
solutions are kinetically damped. | 1508.05127v1 |
2015-09-30 | Approximation of Invariant Measure for Damped Stochastic Nonlinear Schrödinger Equation via an Ergodic Numerical Scheme | In order to inherit numerically the ergodicity of the damped stochastic
nonlinear Schr\"odinger equation with additive noise, we propose a fully
discrete scheme, whose spatial direction is based on spectral Galerkin method
and temporal direction is based on a modification of the implicit Euler scheme.
We not only prove the unique ergodicity of the numerical solutions of both
spatial semi-discretization and full discretization, but also present error
estimations on invariant measures, which gives order $2$ in spatial direction
and order ${\frac12}$ in temporal direction. | 1509.09148v2 |
2015-10-02 | Cavity and HOM Coupler Design for CEPC | In this paper we will show a cavity and higher order mode (HOM) coupler
designing scheme for the Circular Electron-Positron Collider (CEPC) main ring.
The cavity radio frequency (RF) design parameters are showed in this paper. The
HOM power is calculated based on the beam parameters in the Preliminary
Conceptual Design Report (Pre-CDR). The damping results of the higher order
modes (HOMs) and same order modes (SOMs) show that they are reached the damping
requirements for beam stability. | 1510.00467v1 |
2015-11-08 | Upper semicontinuity of pullback attractors for damped wave equations | In this paper, we study the upper semicontinuity of pullback attractors for a
strongly damped wave equation. In particular, under some proper assumptions, we
prove that, the pullback attractor $\{A_\varepsilon(t)\}_{t\in\mathbb R}$} of
Eq.(1.1) with $\varepsilon\in[0,1]$ satisfies that for any $[a,b]\subset\mathbb
R$ and $\varepsilon_0\in[0,1]$, $\lim_{\varepsilon\to\varepsilon_0}
\sup_{t\in[a,b]} \mathrm{dist}_{H_0^1\times L^2} (A_\varepsilon(t),
A_{\varepsilon_0}(t))=0$, and $\cup_{t\in[a,b]} \cup_{\varepsilon\in[0,1]}
A_\varepsilon(t)$ is precompact in $H_0^1 (\Omega) \times L^2(\Omega)$. | 1511.02481v2 |
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 |
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 |
2016-04-14 | 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 |
2016-04-20 | Reconstruction for multiwave imaging in attenuating media with large damping coefficient | In this article we study the reconstruction problem in TAT/PAT on an
attenuating media. Namely, we prove a reconstruction procedure of the initial
condition for the damped wave equation via Neumann series that works for
arbitrary large smooth attenuation coefficients extending the result of Homan
in [1]. We also illustrate the theoretical result by including some numerical
experiments at the end of the paper. | 1604.06068v3 |
2016-04-27 | Temperature Dependence Calibration and Correction of the DAMPE BGO Electromagnetic Calorimeter | A BGO electromagnetic calorimeter (ECAL) is built for the DArk Matter
Particle Explorer (DAMPE) mission. The effect of temperature on the BGO ECAL
was investigated with a thermal vacuum experiment. The light output of a BGO
crystal depends on temperature significantly. The temperature coefficient of
each BGO crystal bar has been calibrated, and a correction method is also
presented in this paper. | 1604.08060v1 |
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 |
2016-09-20 | H{ö}lder stability in determining the potential and the damping coefficient in a wave equation | We improve the preceding results obtained by the first and the second authors
in [3]. They concern the stability issue of the inverse problem that consists
in determining the potential and the damping coefficient in a wave equation
from an initial-to-boundary operator. We partially modify the arguments in [3]
to show that actually we have H{\"o}lder stability instead of logarithmic
stability. | 1609.06102v1 |
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 |
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 |
2017-05-15 | 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 |
2017-08-09 | 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 |
2017-11-06 | Linear inviscid damping and enhanced dissipation for the Kolmogorov flow | In this paper, we prove the linear inviscid damping and voticity depletion
phenomena for the linearized Euler equations around the Kolmogorov flow. These
results confirm Bouchet and Morita's predictions based on numerical analysis.
By using the wave operator method introduced by Li, Wei and Zhang, we solve
Beck and Wayne's conjecture on the optimal enhanced dissipation rate for the
2-D linearized Navier-Stokes equations around the bar state called Kolmogorov
flow. The same dissipation rate is proved for the Navier-Stokes equations if
the initial velocity is included in a basin of attraction of the Kolmogorov
flow with the size of $\nu^{\frac 23+}$, here $\nu$ is the viscosity
coefficient. | 1711.01822v1 |
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 |
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 | 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 |
2018-06-30 | 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 |
2019-06-12 | A no-go result for the quantum damped harmonic oscillator | In this letter we show that it is not possible to set up a canonical
quantization for the damped harmonic oscillator using the Bateman lagrangian.
In particular, we prove that no square integrable vacuum exists for the {\em
natural} ladder operators of the system, and that the only vacua can be found
as distributions. This implies that the procedure proposed by some authors is
only formally correct, and requires a much deeper analysis to be made rigorous. | 1906.05121v2 |
2019-06-26 | Mismatched Estimation of Polynomially Damped Signals | In this work, we consider the problem of estimating the parameters of
polynomially damped sinusoidal signals, commonly encountered in, for instance,
spectroscopy. Generally, finding the parameter values of such signals
constitutes a high-dimensional problem, often further complicated by not
knowing the number of signal components or their specific signal structures. In
order to alleviate the computational burden, we herein propose a mismatched
estimation procedure using simplified, approximate signal models. Despite the
approximation, we show that such a procedure is expected to yield predictable
results, allowing for statistically and computationally efficient estimates of
the signal parameters. | 1906.11113v1 |
2019-06-27 | Temperature-Dependent Lifetimes of Low-Frequency Adsorbate Modes from Non-Equilibrium Molecular Dynamics Simulations | We present calculations on the damping of a low-frequency adsorbate mode on a
metal surface, namely the frustrated translation of Na on Cu(100). For the
first time, vibrational lifetimes of excited adlayers are extracted from
non-equilibrium molecular dynamics calculations accounting for both the
phononic and the electronic dissipation channels. The relative contributions of
the two damping mechanisms, which we show to be additive, are found to disagree
with textbook predictions. A simple model based on separable harmonic and
anharmonic contributions is able to semi-quantitatively reproduce the
temperature dependence of the computed lifetimes. | 1906.11776v1 |
2019-08-03 | Lindblad dynamics of the damped and forced quantum harmonic oscillator | The quantum dynamics of a damped and forced harmonic oscillator is
investigated in terms of a Lindblad master equation. Elementary algebraic
techniques are employed allowing for example to analyze the long time behavior,
i.e. the quantum limit cycle. The time evolution of various expectation values
is obtained in closed form as well as the entropy and the Husimi phase space
distribution. We also discuss the related description in terms of a
non-Hermitian Hamiltonian. | 1908.01187v2 |
2019-08-07 | Decay estimates for the linear damped wave equation on the Heisenberg group | This paper is devoted to the derivation of $L^2$ - $L^2$ decay estimates for
the solution of the homogeneous linear damped wave equation on the Heisenberg
group $\mathbf{H}_n$, for its time derivative and for its horizontal gradient.
Moreover, we consider the improvement of these estimates when further
$L^1(\mathbf{H}_n)$ regularity is required for the Cauchy data. Our approach
will rely strongly on the group Fourier transform of $\mathbf{H}_n$ and on the
properties of the Hermite functions that form a maximal orthonormal system for
$L^2(\mathbb{R}^n)$ of eigenfunctions of the harmonic oscillator. | 1908.02657v1 |
2019-08-08 | Critical exponent of Fujita-type for the semilinear damped wave equation on the Heisenberg group with power nonlinearity | In this paper, we consider the Cauchy problem for the semilinear damped wave
equation on the Heisenberg group with power nonlinearity. We prove that the
critical exponent is the Fujita exponent $p_{\mathrm{Fuj}}(\mathscr{Q}) = 1+2 /
\mathscr{Q}$, where $\mathscr{Q}$ is the homogeneous dimension of the
Heisenberg group. On the one hand, we will prove the global existence of small
data solutions for $p >p_{\mathrm{Fuj}}(\mathscr{Q})$ in an exponential
weighted energy space. On the other hand, a blow-up result for $1 < p \leq
p_{\mathrm{Fuj}}(\mathscr{Q})$ under certain integral sign assumptions for the
Cauchy data by using the test function method. | 1908.02989v1 |
2012-10-08 | Comment on "Thermal fluctuations of magnetic nanoparticles" [arXiv:1209.0298] | We comment on some misleading and biased statements appearing in the
manuscript arXiv:1209.0298 ("Thermal fluctuations of magnetic nanoparticles")
about the use of the damped Landau-Lifshitz equation and the kinetic Langer
theory for the calculation of the relaxation rate of magnetic nanoclusters. We
reiterate simple scientific arguments, part of which is well known to the whole
community, demonstrating that the authors' criticisms are unfounded and that
they overstate the issue of damping in the Landau-Lifshitz equation with no
unanimous experimental evidence. | 1210.2436v1 |
2012-10-10 | Phonon momentum and damping of mechanical resonators | The concept of physical momentum associated to phonons in a crystal,
complemented with some fundamental reasoning, implies measurable effects in
crystals even at a macroscopic scale. We show that, in close analogy with the
transfer of momentum in the kinetic theory of gases, physical momentum carried
by of phonons couples the thermal and the velocity field in a vibrating
crystal. Therefore an heat flow applied to a vibrating crystal can sustain or
damp the oscillation, depending on the interplay between the temperature and
the velocity gradient. We derive the general equations of this effect and show
that its experimental confirmation is within reach of current technology. | 1210.2847v1 |
2012-10-12 | HTS wiggler concept for a damping ring | Magnetic design proposed for a damping ring (DR) is based on second
generation HTS cabling technology applied to the DC windings with a yoke and
mu-metal-shimmed pole to achieve ~2T high-quality field within a 86 mm gap and
32-40 cm period. Low levels of current densities (~90-100A/mm2) provide a
robust, reliable operation of the wiggler at higher heat loads, up to LN2
temperatures with long leads, enhanced flexibility for the cryostats and
infrastructure in harsh radiation environment, and reduced failure rate
compared to the baseline SC ILC DR wiggler design at very competitive cost. | 1210.3648v1 |
2012-10-23 | Dynamic response of open cell dry foams | We study the mechanical response of an open cell dry foam subjected to
periodic forcing using experiments and theory. Using the measurements of the
static and dynamic stress-strain relationship, we derive an over-damped model
of the foam, as a set of infinitesimal non-linear springs, where the damping
term depends on the local foam strain. We then analyse the properties of the
foam when subjected to large amplitudes periodic stresses and determine the
conditions for which the foam becomes optimally absorbing. | 1210.6229v1 |
2012-10-31 | Quantum discord of Bell cat-states under amplitude damping | The evolution of pairwise quantum correlations of Bell cat-states under
amplitude damping is examined using the concept of quantum discord which goes
beyond entanglement. A closed expression of the quantum discord is explicitly
derived. We used of the Koashi-Winter relation. A relation which facilitates
the optimization process of the conditional entropy. We also discuss the
temporal evolution of bipartite quantum correlations under a dephasing channel
and compare the behaviors of quantum discord and entanglement whose properties
are characterized through the concurrence. | 1210.8309v1 |
2012-10-31 | Upsilon suppression in PbPb collisions at the LHC | We suggest that the combined effect of screening, gluon-induced dissociation,
collisional damping, and reduced feed-down explains most of the sequential
suppression of Upsilon(nS) states that has been observed in PbPb relative to pp
collisions at sqrt(s_NN) = 2.76 TeV. The suppression is thus a clear, albeit
indirect, indication for the presence of a QGP. The Upsilon(1S) ground state
suppression is essentially due to reduced feed-down, collisional damping and
gluodissociation, whereas screening prevails for the suppression of the excited
states. | 1210.8366v2 |
2012-11-04 | The Threshold between Effective and Noneffective Damping for Semilinear Waves | In this paper we study the global existence of small data solutions to the
Cauchy problem for the semilinear wave equation with scale-invariant damping.
We obtain estimates for the solution and its energy with the same decay rate of
the linear problem. We extend our results to a model with polynomial speed of
propagation and to a model with an exponential speed of propagation. | 1211.0731v2 |
2012-11-10 | Heavy quark quenching from RHIC to LHC and the consequences of gluon damping | In this contribution to the Quark Matter 2012 conference, we study whether
energy loss models established for RHIC energies to describe the quenching of
heavy quarks can be applied at LHC with the same success. We also benefit from
the larger $p_T$-range accessible at this accelerator to test the impact of
gluon damping on observables such as the nuclear modification factor. | 1211.2281v1 |
2012-11-13 | Critical exponent for the semilinear wave equation with scale invariant damping | In this paper we consider the critical exponent problem for the semilinear
damped wave equation with time-dependent coefficients. We treat the scale
invariant cases. In this case the asymptotic behavior of the solution is very
delicate and the size of coefficient plays an essential role. We shall prove
that if the power of the nonlinearity is greater than the Fujita exponent, then
there exists a unique global solution with small data, provided that the size
of the coefficient is sufficiently large. We shall also prove some blow-up
results even in the case that the coefficient is sufficiently small. | 1211.2900v1 |
2012-11-30 | Local feedback stabilisation to a non-stationary solution for a damped non-linear wave equation | We study a damped semi-linear wave equation in a bounded domain with smooth
boundary. It is proved that any sufficiently smooth solution can be stabilised
locally by a finite-dimensional feedback control supported by a given open
subset satisfying a geometric condition. The proof is based on an investigation
of the linearised equation, for which we construct a stabilising control
satisfying the required properties. We next prove that the same control
stabilises locally the non-linear problem. | 1211.7202v1 |
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 |
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