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