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2010-10-26
Open Quantum Systems in Noninertial Frames
We study the effects of decoherence on the entanglement generated by Unruh effect in noninertial frames by using bit flip, phase damping and depolarizing channels. It is shown that decoherence strongly influences the initial state entanglement. The entanglement sudden death can happens irrespective of the acceleration of the noninertial frame under the action of phase flip and phase damping channels. It is investigated that an early sudden death happens for large acceleration under the depolarizing environment. Moreover, the entanglement increases for a highly decohered phase flip channel.
1010.5395v1
2010-11-17
Faint Resonantly Scattered Lyman Alpha Emission from the Absorption Troughs of Damped Lyman Alpha Systems at z ~ 3
We demonstrate that the Lyman alpha emission in the absorption troughs of a large sample of stacked damped Lyman alpha absorption systems (DLAS) presented by Rahmani et al (2010) is consistent with the spectral profiles and luminosities of a recently detected population of faint Lyman alpha emitters at z ~ 3. This result supports the suggestion that the faint emitters are to be identified with the host galaxies of DLAS at these redshifts.
1011.4061v1
2010-12-19
Quantum damping of Fermi-Pasta-Ulam revivals in ultracold Bose gases
We propose an experimental scheme for studying the Fermi-Pasta-Ulam (FPU) phenomenon in a quantum mechanical regime using ultracold atoms. Specifically, we suggest and analyze a setup of one-dimensional Bose gases confined into an optical lattice. The strength of quantum fluctuations is controlled by tuning the number of atoms per lattice sites (filling factor). By simulating the real-time dynamics of the Bose-Hubbard model by means of the exact numerical method of time-evolving block decimation, we investigate the effects of quantum fluctuations on the FPU recurrence and show that strong quantum fluctuations cause significant damping of the FPU oscillation.
1012.4159v1
2010-12-21
Pullback attractors for a singularly nonautonomous plate equation
We consider the family of singularly nonautonomous plate equation with structural damping \[ u_{tt} + a(t,x)u_{t} + (- \Delta) u_{t} + (-\Delta)^{2} u + \lambda u = f(u), \] in a bounded domain $\Omega \subset \R^n$, with Navier boundary conditions. When the nonlinearity $f$ is dissipative we show that this problem is globally well posed in $H^2_0(\Omega) \times L^2(\Omega)$ and has a family of pullback attractors which is upper-semicontinuous under small perturbations of the damping $a$.
1012.4749v1
2010-12-30
On rotational solutions for elliptically excited pendulum
The author considers the planar rotational motion of the mathematical pendulum with its pivot oscillating both vertically and horizontally, so the trajectory of the pivot is an ellipse close to a circle. The analysis is based on the exact rotational solutions in the case of circular pivot trajectory and zero gravity. The conditions for existence and stability of such solutions are derived. Assuming that the amplitudes of excitations are not small while the pivot trajectory has small ellipticity the approximate solutions are found both for high and small linear damping. Comparison between approximate and numerical solutions is made for different values of the damping parameter.
1101.0062v1
2011-01-28
Entanglement between two atoms in a damping Jaynes-Cummings model
The entanglement between two atoms in a damping Jaynes-Cummings model is investigated with different decay coefficients of the atoms from the upper level to other levels under detuning between the atomic frequency and the quantized light field frequency. The results indicate that the larger the decay coefficient is, the more quickly the entanglement decays. The detuning enhances the entanglement's average value at long times. More importantly, the results show that the so-called sudden death effect can be avoided by enhancing the detuning or the decay coefficient.
1101.5522v1
2011-03-10
Laser-like vibrational instability in rectifying molecular conductors
We study the damping of molecular vibrations due to electron-hole pair excitations in donor-acceptor(D-A) type molecular rectifiers. At finite voltage additional non-equilibrium electron-hole pair excitations involving both electrodes become possible, and contribute to the stimulated emission and absorption of phonons. We point out a generic mechanism for D-A molecules, where the stimulated emission can dominate beyond a certain voltage due to inverted position of the D and A quantum resonances. This leads to current-driven amplification (negative damping) of the phonons similar to laser-action. We investigate the effect in realistic molecular rectifier structures using first principles calculations.
1103.1990v1
2011-03-11
Spin Transport in Polaronic and Superfluid Fermi Gases
We present measurements of spin transport in ultracold gases of fermionic lithium-6 in a mixture of two spin states at a Feshbach resonance. In particular, we study the spin dipole mode, where the two spin components are displaced from each other against a harmonic restoring force. We prepare a highly-imbalanced, or polaronic, spin mixture with a spin dipole excitation and observe strong, unitarity limited damping of the spin dipole mode. In gases with small spin imbalance, below the Pauli limit for superfluidity, we observe strongly damped spin flow despite the presence of a superfluid core.
1103.2337v1
2011-03-14
Tidal Evolution of a Secularly Interacting Planetary System
In a multi-planet system, a gradual change in one planet's semi-major axis will affect the eccentricities of all the planets, as angular momentum is distributed via secular interactions. If tidal dissipation in the planet is the cause of the change in semi-major axis, it also damps that planet's eccentricity, which in turn also contributes to the evolution of all the eccentricities. Formulae quantifying the combined effects on the whole system due to semi-major axis changes, as well as eccentricity damping, are derived here for a two-planet system. The CoRoT 7 system is considered as an example.
1103.2794v1
2011-03-30
Damping in quantum love affairs
In a series of recent papers we have used an operatorial technique to describe stock markets and, in a different context, {\em love affairs} and their time evolutions. The strategy proposed so far does not allow any dumping effect. In this short note we show how, within the same framework, a strictly non periodic or quasi-periodic effect can be introduced in the model by describing in some details a linear Alice-Bob love relation with damping.
1103.5907v1
2011-04-03
Spatially confined Bloch oscillations in semiconductor superlattices
In a semiconductor superlattice with long scattering times, damping of Bloch oscillations due to scattering is so small that convective nonlinearities may compensate it and Bloch oscillations persist even in the hydrodynamic regime. In this case, numerical solutions show that there are stable Bloch oscillations confined to a region near the collector with inhomogeneous field, charge, current density and energy density profiles. These Bloch oscillations disappear when damping due to inelastic collisions becomes sufficiently strong.
1104.0429v2
2011-04-06
Observed damping of the slow magnetoacoustic mode
Spectroscopic and stereoscopic imaging observations of slow magnetoacoustic wave propagation within a coronal loop are investigated to determine the decay length scale of the slow magnetoacoustic mode in three dimensions and the density profile within the loop system. The slow wave is found to have an e-folding decay length scale of $20,000^{+4000}_{-3000}$km with a uniform density profile along the loop base. These observations place quantitive constraints on the modelling of wave propagation within coronal loops. Theoretical forward modelling suggests that magnetic field line divergence is the dominant damping factor and thermal conduction is insufficient, given the observed parameters of the coronal loop temperature, density and wave mode period.
1104.1100v1
2011-04-17
Stochastic Wave Equations with Nonlinear Damping and Source Terms
In this paper, we discuss an initial boundary value problem for the stochastic wave equation involving the nonlinear damping term $|u_t|^{q-2}u_t$ and a source term of the type $|u|^{p-2}u$. We firstly establish the local existence and uniqueness of solution by the Galerkin approximation method and show that the solution is global for $q\geq p$. Secondly, by an appropriate energy inequality, the local solution of the stochastic equations will blow up with positive probability or explosive in energy sense for $p>q$.
1104.3279v2
2011-05-07
Cooperative scattering measurement of coherence in a spatially modulated Bose gas
Correlations of a Bose gas released from an optical lattice are measured using superradiant scattering. Conditions are chosen so that after initial incident light pumping at the Bragg angle for diffraction, due to matter wave amplification and mode competition, superradiant scattering into the Bragg diffracted mode is preponderant. A temporal analysis of the superradiant scattering gain reveals periodical oscillations and damping due to the initial lack of coherence between lattice sites. Such damping is used for characterizing first order spatial correlations in our system with a precision of one lattice period.
1105.1425v1
2011-06-09
Hamiltonian of mean force for damped quantum systems
We consider a quantum system linearly coupled to a reservoir of harmonic oscillators. For finite coupling strengths, the stationary distribution of the damped system is not of the Gibbs form, in contrast to standard thermodynamics. With the help of the quantum Hamiltonian of mean force, we quantify this deviation exactly for a harmonic oscillator and provide approximations in the limit of high and low temperatures, and weak and strong couplings. Moreover, in the semiclassical regime, we use the quantum Smoluchowski equation to obtain results valid for any potential. We, finally, give a physical interpretation of the deviation in terms of the initial system-reservoir coupling.
1106.1775v1
2011-06-17
Current effect on magnetization oscillations in a ferromagnet - antiferromagnet junction
Spin-polarized current effect is studied on the static and dynamic magnetization of the antiferromagnet in a ferromagnet - antiferromagnet junction. The macrospin approximation is generalized to antiferromagnets. Canted antiferromagnetic configuration and resulting magnetic moment are induced by an external magnetic field. The resonance frequency and damping are calculated, as well as the threshold current density corresponding to instability appearance. A possibility is shown of generating low-damping magnetization oscillations in terahertz range. The fluctuation effect is discussed on the canted antiferromagnetic configuration.
1106.3519v1
2011-06-23
Dissipation evidence for the quantum damped harmonic oscillator via pseudo-bosons
It is known that a self-adjoint, time-independent hamiltonian can be defined for the quantum damped harmonic oscillator. We show here that the two vacua naturally associated to this operator, when expressed in terms of pseudo-bosonic lowering and raising operators, appear to be non square-integrable. This fact is interpreted as the evidence of the dissipation effect of the classical oscillator at a purely quantum level.
1106.4638v1
2011-07-15
Aspects of General Relativity: Pseudo-Finsler extensions, Quasi-normal frequencies and Multiplication of tensorial distributions
This thesis is based on three different projects, all of them are directly linked to the classical general theory of relativity, but they might have consequences for quantum gravity as well. The first chapter deals with pseudo-Finsler geometric extensions of the classical theory, these being ways of naturally representing high-energy Lorentz symmetry violations. The second chapter deals with the problem of highly damped quasi-normal modes related to different types of black hole spacetimes. Besides the astrophysical meaning of the quasi-normal modes, there are conjectures about the link between the highly damped modes and black hole thermodynamics. The third chapter is related to the topic of multiplication of tensorial distributions.
1107.2978v1
2011-08-08
Synchrotron radiation damping, intrabeam scattering and beam-beam simulations for HE-LHC
The proposed High-Energy LHC project presents an unusual combination of strong synchrotron radiation (SR) damping and intrabeam scattering (IBS), which is not seen in present-day hadron colliders. The subject of investigation reported in this paper was the simulation of beam-beam effect for the HE-LHC parameters. Parameters of SR and IBS are calculated, and the luminosity evolution is simulated in the absence of beambeam interaction. Then, a weak-strong numerical simulation is used to predict the effect of beam-beam interaction on particle losses and emittance evolution.
1108.1644v1
2011-09-08
On the attenuation coefficient of monomode periodic waveguides
It is widely accepted that, on ensemble average, the transmission T of guided modes decays exponentially with the waveguide length L due to small imperfections, leading to the important figure of merit defined as the attenuation-rate coefficient alpha = -<ln(T)>/L. In this letter, we evidence that the exponential-damping law is not valid in general for periodic monomode waveguides, especially as the group velocity decreases. This result that contradicts common beliefs and experimental practices aiming at measuring alpha is supported by a theoretical study of light transport in the limit of very small imperfections, and by numerical results obtained for two waveguide geometries that offer contrasted damping behaviours.
1109.1642v1
2011-09-09
Delocalization of slowly damped eigenmodes on Anosov manifolds
We look at the properties of high frequency eigenmodes for the damped wave equation on a compact manifold with an Anosov geodesic flow. We study eigenmodes with spectral parameters which are asymptotically close enough to the real axis. We prove that such modes cannot be completely localized on subsets satisfying a condition of negative topological pressure. As an application, one can deduce the existence of a "strip" of logarithmic size without eigenvalues below the real axis under this dynamical assumption on the set of undamped trajectories.
1109.1909v2
2011-10-18
Life times and chirality of spin-waves in antiferromagnetic and ferromagnetic FeRh: time depedent density functional theory perspective
The study of the spin excitations in antiferromagnetic (AFM) and ferromagnetic (FM) phases of FeRh is reported. We demonstrate that although the Fe atomic moments are well defined there is a number of important phenomena absent in the Heisenberg description: Landau damping of spin waves, large Rh moments induced by the AFM magnons, the formation of the optical magnons terminated by Stoner excitations. We relate the properties of the spin-wave damping to the features of the Stoner continuum and compare the chirality of the spin excitations in AFM, FM and paramagnetic (PM) systems.
1110.3913v1
2011-10-21
Environment-Assisted Error Correction of Single-Qubit Phase Damping
Open quantum system dynamics of random unitary type may in principle be fully undone. Closely following the scheme of environment-assisted error correction proposed by Gregoratti and Werner [M. Gregoratti and R. F. Werner, J. Mod. Opt. 50(6), 915-933 (2003)], we explicitly carry out all steps needed to invert a phase-damping error on a single qubit. Furthermore, we extend the scheme to a mixed-state environment. Surprisingly, we find cases for which the uncorrected state is closer to the desired state than any of the corrected ones.
1110.4806v1
2011-11-01
Damping of tensor modes in inflation
We discuss the damping of tensor modes due to anisotropic stress in inflation. The effect is negligible in standard inflation and may be significantly large in inflation models that involve drastic production of free-streaming particles.
1111.0295v3
2011-11-04
Global uniform asymptotic stabilization and k-exponential trajectory tracking of underactuated surface ships with non-diagonal inertia/damping matrices
In this work, we investigate the state stabilization and trajectory tracking problems of underactuated surface ships with full state model of having non-diagonal inertia and damping matrices. By combining the novel state transformations, the direct Lyapunov approach, and the nonlinear time-varying tools, the stabilization and the trajectory tracking controllers are developed respectively guaranteeing global uniform asymptotic convergence of the state to the desired set point and global exponential convergence to the desired reference trajectory via mild persistent exciting conditions. Simulation examples are given to illustrate the effectiveness of the proposed control schemes.
1111.1029v1
2011-11-15
Finite Size Effects of the Surface States in a Lattice Model of Topological Insulator
Energy gap and wave function in thin films of topological insulator is studied, based on tight--binding model. It is revealed that thickness dependence of the magnitude of energy gap is composed of damping and oscillation. The damped behavior originates from the presence of gapless surface Dirac cone in the infinite thickness limit. On the other hand, the oscillatory behavior stems from electronic properties in the thin thickness limit.
1111.3528v2
2011-11-23
Pumping the eccentricity of exoplanets by tidal effect
Planets close to their host stars are believed to undergo significant tidal interactions, leading to a progressive damping of the orbital eccentricity. Here we show that, when the orbit of the planet is excited by an outer companion, tidal effects combined with gravitational interactions may give rise to a secular increasing drift on the eccentricity. As long as this secular drift counterbalances the damping effect, the eccentricity can increase to high values. This mechanism may explain why some of the moderate close-in exoplanets are observed with substantial eccentricity values.
1111.5486v1
2011-11-30
Shear viscosity and damping of collective modes in a two-dimensional Fermi gas
We compute the shear viscosity of a two dimensional Fermi gas interacting via a short range potential with scattering length $a_{2d}$ in kinetic theory. We find that kinetic theory predicts that the shear viscosity to entropy density ratio of a strongly interacting two dimensional gas is comparable to that of the three dimensional unitary gas. We use our results to compute the damping of collective modes in a trapped Fermi gas, and compare to experimental data recently obtained in E. Vogt et al., arXiv:1111.1173.
1111.7242v2
2011-12-13
Drastically suppressing the error of ballistic readout of qubits
The thermal jitter of transmission of magnetic flux quanta in long Josephson junctions is studied. While for large-to-critical damping and small values of bias current the physically obvious dependence of the jitter versus length $\sigma\sim\sqrt{L}$ is confirmed, for small damping starting from the experimentally relevant $\alpha=0.03$ and below strong deviation from $\sigma\sim\sqrt{L}$ is observed, up to nearly complete independence of the jitter versus length, which is exciting from fundamental point of view, but also intriguing from the point of view of possible applications.
1112.2805v1
2011-12-15
Diffusion-Induced Oscillations of Extended Defects
From a simple model for the driven motion of a planar interface under the influence of a diffusion field we derive a damped nonlinear oscillator equation for the interface position. Inside an unstable regime, where the damping term is negative, we find limit-cycle solutions, describing an oscillatory propagation of the interface. In case of a growing solidification front this offers a transparent scenario for the formation of solute bands in binary alloys, and, taking into account the Mullins-Sekerka instability, of banded structures.
1112.3669v1
2011-12-31
Stability of cnoidal waves in the parametrically driven nonlinear Schrödinger equation
The parametrically driven, damped nonlinear Schr\"odinger equation has two cn- and two dn-wave solutions. We show that one pair of the cn and dn solutions is unstable for any combination of the driver's strength, dissipation coefficient and spatial period of the wave; this instability is against periodic perturbations. The second dn-wave solution is shown to be unstable against antiperiodic perturbations --- in a certain region of the parameter space. We also consider quasiperiodic perturbations with long modulation wavelength, in the limit where the driving strength is only weakly exceeding the damping coefficient.
1201.0263v1
2012-01-03
Dynamics of DNA Bubble in Viscous Medium
The damping effect to the DNA bubble is investigated within the Peyrard-Bishop model. In the continuum limit, the dynamics of the bubble of DNA is described by the damped nonlinear Schrodinger equation and studied by means of variational method. It is shown that the propagation of solitary wave pattern is not vanishing in a non-viscous system. Inversely, the solitary wave vanishes soon as the viscous force is introduced.
1201.0689v2
2012-01-18
Magnetohydrodynamic Waves in Partially Ionized Prominence Plasmas
Prominences or filaments are cool clouds of partially ionized plasma living in the solar corona. Ground- and space-based observations have confirmed the presence of oscillatory motions in prominences and they have been interpreted in terms of magnetohydrodynamic (MHD) waves. Existing observational evidence points out that these oscillatory motions are damped in short spatial and temporal scales by some still not well known physical mechanism(s). Since prominences are partially ionized plasmas, a potential mechanism able to damp these oscillations could be ion-neutral collisions. Here, we will review the work done on the effects of partial ionization on MHD waves in prominence plasmas.
1201.3752v1
2012-01-26
Inhomogeneous spin diffusion in traps with cold atoms
The spin diffusion and damped oscillations are studied in the collision of two spin polarized clouds of cold atoms with resonant interactions. The strong density dependence of the diffusion coefficient leads to inhomogeneous spin diffusion that changes from central to surface spin flow as the temperature increases. The inhomogeneity and the smaller finite trap size significantly reduce the spin diffusion rate at low temperatures. The resulting spin diffusion rates, spin drag and initial damped oscillations are compatible with measurements at low to high temperatures for resonant attractive interactions but are incompatible with a metastable ferromagnetic phase.
1201.5526v2
2012-01-30
Volatility-dependent damping of evaporation-driven Bénard-Marangoni instability
The interface between a pure liquid and its vapor is usually close to saturation temperature, hence strongly hindering any thermocapillary flow. In contrast, when the gas phase contains an inert gas such as air, surface-tension-driven convection is easily observed. We here reconcile these two facts by studying the corresponding crossover experimentally, as a function of a new dimensionless number quantifying the degree of damping of interfacial temperature fluctuations. Critical conditions are in convincing agreement with a simple nonlocal one-sided model, in quite a range of evaporation rates.
1201.6334v1
2012-02-18
Dynamics of multi-modes maximum entangled coherent state over amplitude damping channel
The dynamics of maximum entangled coherent state travels through an amplitude damping channel is investigated. For small values of the transmissivity rate the travelling state is very fragile to this noise channel, where it suffers from the phase flip error with high probability. The entanglement decays smoothly for larger values of the transmissivity rate and speedily for smaller values of this rate. As the number of modes increases, the travelling state over this noise channel loses its entanglement hastily. The odd and even states vanish at the same value of the field intensity.
1202.4089v1
2012-03-03
Scaling of intrinsic Gilbert damping with spin-orbital coupling strength
We have experimentally and theoretically investigated the dependence of the intrinsic Gilbert damping parameter $\alpha_0$ on the spin-orbital coupling strength $\xi$ by using L1$_{\mathrm{0}}$ ordered FePd$_{\mathrm{1-x}}$Pt$_{\mathrm{x}}$ ternary alloy films with perpendicular magnetic anisotropy. With the time-resolved magneto-optical Kerr effect, $\alpha_0$ is found to increase by more than a factor of ten when $x$ varies from 0 to 1.0. Since changes of other leading parameters are found to be neglected, the $\alpha_0$ has for the first time been proven to be proportional to $\xi^2$.
1203.0607v1
2012-03-03
Necessary and sufficient conditions of freezing phenomena of quantum discord under phase damping
We investigate the freezing phenomenon of quantum discord occurring in phase damping noise processes. By relating the expression of the time variation of the discord to the convex function of relative entropy, we obtain the necessary and sufficient conditions of the phenomenon for standard Bell-diagonal states. These conditions are applicable also to the phenomenon occurring in a non-Markovian dephasing process. Moreover, we show that the same condition and phenomenon coincide in a new sort of Bell-diagonal states beyond the standard form.
1203.0650v3
2012-03-06
Universal anomalous diffusion of weakly damped particles
We show that anomalous diffusion arises in two different models for the motion of randomly forced and weakly damped particles: one is a generalisation of the Ornstein-Uhlenbeck process with a random force which depends on position as well as time, the other is a generalisation of the Chandrasekhar-Rosenbluth model of stellar dynamics, encompassing non-Coulombic potentials. We show that both models exhibit anomalous diffusion of position $x$ and momentum $p$ with the same exponents: $<x^2> \sim C_x t^2$ and $<p^2> \sim C_p t^{2/5}$. We are able to determine the prefactors $C_x$, $C_p$ analytically.
1203.1354v1
2012-03-13
Monopoles in ferromagnetic metals
The aim of this short review is to give an introduction to monopoles and to present theoretical derivation of two particular monopoles in ferromagnetic metals, a hedgehog monopole and a spin damping monopole. Spin damping monopoles can be generated in simple systems such as a junction of a ferromagnet and a heavy element with strong spin-orbit interaction such as Pt. This monopole is essential in coupling electronics with magnetism, and is thus expected to play an essential role in spintronics.
1203.2709v1
2012-03-16
Report from KEK (High gradient study results from Nextef)
Most up-to-date high gradient test of the CLIC prototype structures as of September 2011 is described in this report. The "T24" undamped structure showed fast processing time, still-decreasing breakdown rate and its breakdown rate was estimated to be as low as the CLIC requirement. The "TD24" damped structure showed not so excellent high gradient performance as undamped "T24" but the characteristics was much improved than the damped "TD18" structure with higher magnetic field. Further R&D is needed and we present some of the present efforts at KEK.
1203.3626v1
2012-03-30
Energy decay rates for solutions of the wave equation with linear damping in exterior domain
In this paper we study the behavior of the energy of solutions of the wave equation with localized damping in exterior domain. We assume that the damper is positive at infinity. Under the Geometric Control Condition of Bardos et al (1992), we prove that: 1) The total energy decay like O(1/t) and L^2-norm is bounded for the solutions with initial data in (H_{0}^{1},L^{2}). 2) The total energy and the square of the L^2-norm, repectively, decay like O(1/t^{2}) and O(1/t) for a kind of the weighted initial data.
1203.6780v4
2012-04-03
Modification in Silling's Peridynamic Formulation of Elasticity Theory for Discontinuities and Long-Range Forces
We suggest modified version of Silling's peridynamic equation of motion within the framework of Silling's peridynamics formulation (J. Mech. Phys. Solids {\bf 48}, pp.175-209, 2000) of elasticity theory. The modified equation contains an additional damping force term. This term can eliminate artificial oscillations in displacement field at large values of time as predicted by Silling's peridynamic equation.
1204.0612v2
2012-04-06
Experimental signatures of the quantum-classical transition in a nanomechanical oscillator modeled as a damped driven double-well problem
We demonstrate robust and reliable signatures for the transition from quantum to classical behavior in the position probability distribution of a damped double-well system using the Qunatum State Diffusion approach to open quantum systems. We argue that these signatures are within experimental reach, for example in a doubly-clamped nanomechanical beam.
1204.1397v1
2012-05-31
The impact of fill patterns on the fast ion instability in the ILC damping ring
The ions produced via collisional ionization of the residual gas molecules in vacuum pipe with the circulating electron beam have deleterious effect on the beam properties and may become a limiting factor for the machine's performance. For the electron damping ring of the International Linear Collider (ILC), the ion instability is noticeable due to the ultra-low beam emittance with many bunches operation. In this paper, the different beam fill patterns are investigated and their effects on the fast ion instability are discussed. The simulations show that the mini train fill patterns can reduce the growth of the fast ion instability significantly.
1205.6977v1
2012-06-11
Damping and decoherence of Fock states in a nanomechanical resonator due to two level systems
We numerically investigate the decay of initial quantum Fock states and their superpositions for a mechanical resonator mode coupled to an environment comprising interacting, damped tunneling two level system (TLS) defects. The cases of one, three, and six near resonant, interacting TLS's are considered in turn and it is found that the resonator displays Ohmic bath like decay behavior with as few as three TLS's.
1206.2200v1
2012-07-13
Magnetic relaxation in bilayers of yttrium iron garnet/platinum due to the dynamic coupling at the interface
We show that in ferromagnetic (FM)/normal metal (NM) bilayers the dynamic coupling at the interface transfers an additional magnetic relaxation from the heavily damped motion of the conduction electron spins in the NM layer to the FM spins. While the FM relaxation rates due to two-magnon scattering and spin pumping decrease rapidly with increasing FM film thickness, the damping due to the dynamic coupling does not depend on the FM film thickness. The proposed mechanism explains the very large broadening of ferromagnetic resonance lines in thick films of yttrium iron garnet after deposition of a Pt layer.
1207.3330v1
2012-07-23
Quantum interference induced by initial system-environment correlations
We investigate the quantum interference induced by a relative phase in the correlated initial state of a system which consists in a two-level atom interacting with a damped mode of the radiation field. We show that the initial relative phase has significant effects on both the evolution of the atomic excited-state population and the information flow between the atom and the reservoir, as quantified by the trace distance. Furthermore, by considering two two-level atoms interacting with a common damped mode of the radiation field, we highlight how initial relative phases can affect the subsequent entanglement dynamics.
1207.5474v1
2012-07-31
An analytic description of the damping of gravitational waves by free streaming neutrinos
We provide an analytic solution to the general wavelength integro-differential equation describing the damping of tensor modes of gravitational waves due to free streaming neutrinos in the early universe. Our result is expressed as a series of spherical Bessel functions whose coefficients are functions of the reduced wave number $Q$.
1207.7285v4
2012-08-21
Dancing bunches as Van Kampen modes
Van Kampen modes are eigen-modes of Jeans-Vlasov equation. Their spectrum consists of continuous and, possibly, discrete parts. Onset of a discrete van Kampen mode means emergence of a coherent mode without any Landau damping; thus, even a tiny couple-bunch wake is sufficient to drive instability. Longitudinal instabilities observed at Tevatron, RHIC and SPS can be explained as loss of Landau damping (LLD), which is shown here to happen at fairly low impedances. For repulsive wakes and single-harmonic RF, LLD is found to be extremely sensitive to steepness of the bunch distribution function at small amplitudes. Based on that, a method of beam stabilization is suggested.
1208.4338v1
2012-08-22
Polynomial stabilization of some dissipative hyperbolic systems
We study the problem of stabilization for the acoustic system with a spatially distributed damping. Imposing various hypotheses on the structural properties of the damping term, we identify either exponential or polynomial decay of solutions with growing time. Expo- nential decay rate is shown by means of a time domain approach, reducing the problem to an observability inequality to be verified for solutions of the associated conservative problem. In addition, we show a polynomial stabilization result, where the proof uses a frequency domain method and combines a contradiction argument with the multiplier technique to carry out a special analysis for the resolvent.
1208.4485v1
2012-09-07
Quantum Damped Harmonic Oscillator
In this chapter we treat the quantum damped harmonic oscillator, and study mathematical structure of the model, and construct general solution with any initial condition, and give a quantum counterpart in the case of taking coherent state as an initial condition. This is a simple and good model of Quantum Mechanics with dissipation which is important to understand real world, and readers will get a powerful weapon for Quantum Physics.
1209.1437v1
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
2012-12-06
The physics of business cycles and inflation
We analyse four consecutive cycles observed in the USA for employment and inflation. They are driven by three oil price shocks and an intended interest rate shock. Non-linear coupling between the rate equations for consumer products as prey and consumers as predators provides the required instability, but its natural damping is too high for spontaneous cycles. Extending the Lotka-Volterra equations with a small term for collective anticipation yields a second analytic solution without damping. It predicts the base period, phase shifts, and the sensitivity to shocks for all six cyclic variables correctly.
1212.1282v1
2012-12-13
CMB Distortions from Damping of Acoustic Waves Produced by Cosmic Strings
We study diffusion damping of acoustic waves in the photon-baryon fluid due to cosmic strings, and calculate the induced $\mu$- and $y$-type spectral distortions of the cosmic microwave background. For cosmic strings with tension within current bounds, their contribution to the spectral distortions is subdominant compared to the distortions from primordial density perturbations.
1212.3283v2
2013-01-21
Asymptotic parabolicity for strongly damped wave equations
For $S$ a positive selfadjoint operator on a Hilbert space, \[ \frac{d^2u}{dt}(t) + 2 F(S)\frac{du}{dt}(t) + S^2u(t)=0 \] describes a class of wave equations with strong friction or damping if $F$ is a positive Borel function. Under suitable hypotheses, it is shown that \[ u(t)=v(t)+ w(t) \] where $v$ satisfies \[ 2F(S)\frac{dv}{dt}(t)+ S^2v(t)=0 \] and \[ \frac{w(t)}{\|v(t)\|} \rightarrow 0, \; \text{as} \; t \rightarrow +\infty. \] The required initial condition $v(0)$ is given in a canonical way in terms of $u(0)$, $u'(0)$.
1301.4979v1
2013-02-04
Gravity waves on the surface of topological superfluid 3He-B
We have observed waves on the free surface of 3He-B sample at temperatures below 0.2mK. The waves are excited by vibrations of the cryostat and detected by coupling the surface to the Bose-Einstein condensate of magnon quasiparticles in the superfluid. The two lowest gravity-wave modes in our cylindrical container are identified. Damping of the waves increases with temperature linearly with the density of thermal quasiparticles, as expected. Additionally finite damping of the waves in the zero-temperature limit and enhancement of magnetic relaxation of magnon condensates by the surface waves are observed. We discuss whether the latter effects may be related to Majorana fermions bound to the surface of the topological superfluid.
1302.0764v1
2013-02-12
On the fractional damped oscillators and fractional forced oscillators
In this paper, we use the fractional calculus to discuss the fractional mechanics, where the time derivative is replaced with the fractional derivative of order $\nu$. We deal with the motion of a body in a resisting medium where the retarding force is assumed to be proportional to the fractional velocity which is obtained by acting the fractional derivative on the position. The fractional harmonic oscillator problem, fractional damped oscillator problem and fractional forced oscillator problem are also studied.
1302.2847v1
2013-02-25
Optimal damping algorithm for unrestricted Hartree-Fock calculations
We have developed a couple of optimal damping algorithms (ODAs) for unrestricted Hartree-Fock (UHF) calculations of open-shell molecular systems. A series of equations were derived for both concurrent and alternate constructions of alpha- and beta-Fock matrices in the integral-direct self-consistent-field (SCF) procedure. Several test calculations were performed to check the convergence behaviors. It was shown that the concurrent algorithm provides better performance than does the alternate one.
1302.6099v1
2013-03-08
Entanglement of Open Quantum Systems in Noninertial Frames
We study the effects of decoherence on the entanglement generated by Unruh effect in accelerated frames by using various combinations of an amplitude damping channel, a phase damping channel and a depolarizing channel in the form of multilocal and collective environments. Using concurrence as entanglement quantifier, we show that the occurrence of entanglement sudden death (ESD) depends on different combinations of the channels. The ESD can be avoided under a particular configuration of the channels. We show that the channels can be used to distinguish between a moving and a stationary frame.
1303.2034v1
2013-03-20
Spin-pumping and Enhanced Gilbert Damping in Thin Magnetic Insulator Films
Precessing magnetization in a thin film magnetic insulator pumps spins into adjacent metals; however, this phenomenon is not quantitatively understood. We present a theory for the dependence of spin-pumping on the transverse mode number and in-plane wave vector. For long-wavelength spin waves, the enhanced Gilbert damping for the transverse mode volume waves is twice that of the macrospin mode, and for surface modes, the enhancement can be ten or more times stronger. Spin-pumping is negligible for short-wavelength exchange spin waves. We corroborate our analytical theory with numerical calculations in agreement with recent experimental results.
1303.4922v1
2013-03-21
Glued trees algorithm under phase damping
We study the behaviour of the glued trees algorithm described by Childs et al. in [STOC `03, Proc. 35th ACM Symposium on Theory of Computing (2004) 59] under decoherence. We consider a discrete time reformulation of the continuous time quantum walk protocol and apply a phase damping channel to the coin state, investigating the effect of such a mechanism on the probability of the walker appearing on the target vertex of the graph. We pay particular attention to any potential advantage coming from the use of weak decoherence for the spreading of the walk across the glued trees graph.
1303.5319v2
2013-05-13
Guaranteed convergence of the Kohn-Sham equations
A sufficiently damped iteration of the Kohn-Sham equations with the exact functional is proven to always converge to the true ground-state density, regardless of the initial density or the strength of electron correlation, for finite Coulomb systems. We numerically implement the exact functional for one-dimensional continuum systems and demonstrate convergence of the damped KS algorithm. More strongly correlated systems converge more slowly.
1305.2967v2
2013-06-25
Decoherence effects in the quantum qubit flip game using Markovian approximation
We are considering a quantum version of the penny flip game, whose implementation is influenced by the environment that causes decoherence of the system. In order to model the decoherence we assume Markovian approximation of open quantum system dynamics. We focus our attention on the phase damping, amplitude damping and amplitude raising channels. Our results show that the Pauli strategy is no longer a Nash equilibrium under decoherence. We attempt to optimize the players' control pulses in the aforementioned setup to allow them to achieve higher probability of winning the game compared to the Pauli strategy.
1306.5957v1
2013-07-06
The 3-dimensional oscillon equation
On a bounded three-dimensional smooth domain, we consider the generalized oscillon equation with Dirichlet boundary conditions, with time-dependent damping and time-dependent squared speed of propagation. Under structural assumptions on the damping and the speed of propagation, which include the relevant physical case of reheating phase of inflation, we establish the existence of a pullback global attractor of optimal regularity, and finite-dimensionality of the kernel sections.
1307.1777v1
2013-07-17
Functional inequalities on path space over a non-compact Riemannian manifold
We prove the existence of the O-U Dirichlet form and the damped O-U Dirichlet form on path space over a general non-compact Riemannian manifold which is complete and stochastically complete. We show a weighted log-Sobolev inequality for the O-U Dirichlet form and the (standard) log-Sobolev inequality for the damped O-U Dirichlet form. In particular, the Poincar\'e inequality (and the super Poincar\'e inequality) can be established for the O-U Dirichlet form on path space over a class of Riemannian manifolds with unbounded Ricci curvatures. Moreover, we construct a large class of quasi-regular local Dirichlet forms with unbounded random diffusion coefficients on the path space over a general non-compact manifold.
1307.4482v2
2013-08-30
A conservative, skew-symmetric Finite Difference Scheme for the compressible Navier--Stokes Equations
We present a fully conservative, skew-symmetric finite difference scheme on transformed grids. The skew-symmetry preserves the kinetic energy by first principles, simultaneously avoiding a central instability mechanism and numerical damping. In contrast to other skew-symmetric schemes no special averaging procedures are needed. Instead, the scheme builds purely on point-wise operations and derivatives. Any explicit and central derivative can be used, permitting high order and great freedom to optimize the scheme otherwise. This also allows the simple adaption of existing finite difference schemes to improve their stability and damping properties.
1308.6672v1
2013-09-09
Classical and quantum capacities of a fully correlated amplitude damping channel
We study information transmission over a fully correlated amplitude damping channel acting on two qubits. We derive the single-shot classical channel capacity and show that entanglement is needed to achieve the channel best performance. We discuss the degradability properties of the channel and evaluate the quantum capacity for any value of the noise parameter. We finally compute the entanglement-assisted classical channel capacity.
1309.2219v3
2013-09-13
Polarization hydrodynamics in a one-dimensional polariton condensate
We study the hydrodynamics of a nonresonantly-pumped polariton condensate in a quasi-one-dimensional quantum wire taking into account the spin degree of freedom. We clarify the relevance of the Landau criterion for superfluidity in this dissipative two-component system. Two Cherenkov-like critical velocities are identified corresponding to the opening of different channels of radiation: one of (damped) density fluctuations and another of (weakly damped) polarization fluctuations. We determine the drag force exerted onto an external obstacle and propose experimentally measurable consequences of the specific features of the fluctuations of polarization.
1309.3494v1
2013-09-26
Imperfect geometric control and overdamping for the damped wave equation
We consider the damped wave equation on a manifold with imperfect geometric control. We show the sub-exponential energy decay estimate in \cite{Chr-NC-erratum} is optimal in the case of one hyperbolic periodic geodesic. We show if the equation is overdamped, then the energy decays exponentially. Finally we show if the equation is overdamped but geometric control fails for one hyperbolic periodic geodesic, then nevertheless the energy decays exponentially.
1309.6967v1
2013-10-01
Scalar filed evolution and area spectrum for Lovelock-AdS black holes
We study the modes of evolution of massless scalar fields in the asymptotically AdS spacetime surrounding maximally symmetric black holes of large and intermediate size in the Lovelock model. It is observed that all modes are purely damped at higher orders. Also, the rate of damping is seen to be independent of order at higher dimensions. The asymptotic form of these frequencies for the case of large black holes is found analytically. Finally, the area spectrum for such black holes is found from these asymptotic modes.
1310.0159v2
2013-10-16
Perturbative quantum damping of cosmological expansion
Perturbative quantum gravity in the framework of the Schwinger-Keldysh formalism is applied to compute lowest-order corrections to the actual expansion of the Universe described in terms of the spatially flat Friedman-Lematre-Robertson-Walker solution. The classical metric is approximated by a third order polynomial perturbation around the Minkowski metric. It is shown that the quantum contribution to the classical expansion, although extremely small, has damping properties (quantum friction), i.e. it slows down the expansion.
1310.4308v2
2013-10-27
Loss of non-Gaussianity for damped photon-subtracted thermal states
We investigate non-Gaussianity properties for a set of classical one-mode states obtained by subtracting photons from a thermal state. Three distance-type degrees of non-Gaussianity used for these states are shown to have a monotonic behaviour with respect to their mean photon number. Decaying of their non-Gaussianity under damping is found to be consistently described by the distance-type measures considered here. We also compare the dissipative evolution of non-Gaussianity when starting from $M$-photon-subtracted and $M$-photon-added thermal states
1310.7229v1
2013-10-27
Landau damping effects and evolutions of energy spread in small isochronous ring
This paper presents the Landau damping effects on the microwave instability of a coasting long bunch in an isochronous ring due to finite energy spread and emittance. Our two-dimensional (2D) dispersion relation gives more accurate predictions of the microwave instability growth rates of short-wavelength perturbations than the conventional 1D formula. The long-term evolution of energy spread is also studied by measurements and simulations.
1310.7253v3
2013-10-28
Robustness of multiparticle entanglement: specific entanglement classes and random states
We investigate the robustness of genuine multiparticle entanglement under decoherence. We consider different kinds of entangled three- and four-qubit states as well as random pure states. For amplitude damping noise, we find that the W-type states are most robust, while other states are not more robust than generic states. For phase damping noise the GHZ state is the most robust state, and for depolarizing noise several states are significantly more robust than random states.
1310.7336v2
2013-11-22
Complexity of the minimum-time damping of a physical pendulum
We study the minimum-time damping of a physical pendulum by means of a bounded control. In the similar problem for a linear oscillator each optimal trajectory possesses a finite number of control switchings from the maximal to the minimal value. If one considers simultaneously all optimal trajectories with any initial state, the number of switchings can be arbitrary large. We show that for the nonlinear pendulum there is a uniform bound for the switching number for all optimal trajectories. We find asymptotics for this bound as the control amplitude goes to zero.
1311.5729v1
2013-12-16
Local Energy Decay for the Damped Wave Equation
We prove local energy decay for the damped wave equation on R^d. The problem which we consider is given by a long range metric perturbation of the Euclidean Laplacian with a short range absorption index. Under a geometric control assumption on the dissipation we obtain an almost optimal polynomial decay for the energy in suitable weighted spaces. The proof relies on uniform estimates for the corresponding "resolvent", both for low and high frequencies. These estimates are given by an improved dissipative version of Mourre's commutators method.
1312.4483v1
2013-12-23
Photonic tuning of quasi-particle decay in a superfluid
We show that the damping rate of elementary excitations of hybrid systems close to a phase transition can undergo a remarkable resonance like enhancement before mode softening takes place. In particular, we consider the friction of a collective density wave in a homogeneous superfluid of weakly interacting bosonic atoms coupled to the electromagnetic field of a single mode optical resonator. Here the Beliaev damping can thus be controlled by an external laser drive and be enhanced by several orders of magnitude.
1312.6719v1
2014-01-04
Entanglement and quantum teleportation via decohered tripartite entangled states
The entanglement behavior of two classes of multi-qubit system, GHZ and GHZ like states passing through a generalized amplitude damping channel is discussed. Despite this channel causes degradation of the entangled properties and consequently their abilities to perform quantum teleportation, one can always improve the lower values of the entanglement and the fidelity of the teleportrd state by controlling on Bell measurements, analyzer angle and channel's strength. Using GHZ-like state within a generalized amplitude damping channel is much better than using the normal GHZ-state, where the decay rate of entanglement and the fidelity of the teleported states are smaller than those depicted for GHZ state.
1401.0796v1
2014-02-11
New approach for Damping in a squeezed bath and its time evolution through Complete Class of Gaussian Quasi-distributions
By virtue of the thermal entangled states representation of density operator and using dissipative interaction picture we solve the master equation of a driven damped harmonic oscillator in a squeezed bath. We show that the essential part of the dynamics can be expressed by the convolution of initial Wigner function with a special kind of normalized Gaussian in phase space and relate the dynamics with the change of Gaussian ordering of density operator.
1402.2545v1
2014-02-11
New approach for solving master equations of density operator for the Jaynes Cummings Model with Cavity Damping
By introducing thermal entangled state representation which can map master equations of density operator in quantum statistics as state vector evolution equations and using dissipative interaction picture we solve the master equation of J-C model with cavity damping. In addition we derive the Wigner function for density operator when the atom is initially in the up state and the cavity mode is in coherent state.
1402.2556v1
2014-02-19
Superfluid Bloch dynamics in an incommensurate lattice
We investigate the interplay of disorder and interactions in the accelerated transport of a Bose-Einstein condensate through an incommensurate optical lattice. We show that interactions can effectively cancel the damping of Bloch oscillations due to the disordered potential and we provide a simple model to qualitatively capture this screening effect. We find that the characteristic interaction energy, above which interactions and disorder cooperate to enhance, rather than reduce, the damping of Bloch oscillations, coincides with the average disorder depth. This is consistent with results of a mean-field simulation.
1402.4830v1
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
2014-04-18
On the Instability and Critical Damping Conditions, $kτ= 1/e$ and $kτ= π/2$ of the equation $\dotθ = -k θ(t-τ)$
In this note, I show that it is possible to use elementary mathematics, instead of the machinery of Lambert function, Laplace Transform, or numerics, to derive the instability condition, $k \tau = \pi/2$, and the critical damping condition, $k\tau = 1/e$, for the time-delayed equation $\dot{\theta} = -k \theta(t-\tau)$. I hope it will be useful for the new comers to this equation, and perhaps even to the experts if this is a simpler method compared to other versions.
1404.4763v1
2014-04-22
Nonlinear-damped Duffing oscillators having finite time dynamics
A class of modified Duffing oscillator differential equations, having nonlinear damping forces, are shown to have finite time dynamics, i.e., the solutions oscillate with only a finite number of cycles, and, thereafter, the motion is zero. The relevance of this feature is briefly discussed in relationship to the mathematical modeling, analysis, and estimation of parameters for the vibrations of carbon nano-tubes and graphene sheets, and macroscopic beams and plates.
1404.5596v1
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