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2019-02-27
Necessary and Sufficient Conditions for Passivity of Velocity-Sourced Impedance Control of Series Elastic Actuators
Series Elastic Actuation (SEA) has become prevalent in applications involving physical human-robot interaction as it provides considerable advantages over traditional stiff actuators in terms of stability robustness and fidelity of force control. Several impedance control architectures have been proposed for SEA. Among these alternatives, the cascaded controller with an inner-most velocity loop, an intermediate torque loop and an outer-most impedance loop is particularly favoured for its simplicity, robustness, and performance. In this paper, we derive the \emph{necessary and sufficient conditions} to ensure the passivity of this cascade-controller architecture for rendering two most common virtual impedance models. Based on the newly established passivity conditions, we provide non-conservative design guidelines to haptically display a null impedance and a pure spring while ensuring the passivity of interaction. We also demonstrate the importance of including physical damping in the actuator model during derivation of passivity conditions, when integral controllers are utilized. In particular, we show the adversary effect of physical damping on system passivity.
1902.10607v2
2019-03-01
Response to: [Comment on Quantization of the damped harmonic oscillator [Serhan et al, J. Math. Phys. 59, 082105 (2018)]]
This is a response to a recently reported comment [1] on paper [J. Math. Phys.59, 082105 (2018)] regarding the quantization of damped harmonic oscillator using a non-Hermitian Hamiltonian with real energy eigenvalues. We assert here that the calculation of Eq. (29) of [2] is incorrect, and thus the subsequent steps via the Nikiforov-Uvarov method are affected, and the energy eigenvalues should have been complex. However, we show here that the Hermiticity of the Hamiltonian should be firstly achieved to make the correct transition from classical Hamiltonian to quantum counterpart, and this can be reached using the symmetrization rule. Applying the canonical quantization on the resulted Hermitian Hamiltonian and then using the Nikiforov-Uvarov method correctly, the energy eigenvalues will be real and exactly as given by Eq. (35) of [2].
1903.00352v2
2019-03-08
Protecting quantum correlations in presence of generalised amplitude damping channel: the two-qubit case
Any kind of quantum resource useful in different information processing tasks is vulnerable to several types of environmental noise. Here we study the behaviour of quantum correlations such as entanglement and steering in two-qubit systems under the application of the generalised amplitude damping channel and propose some protocols towards preserving them under this type of noise. First, we employ the technique of weak measurement and reversal for the purpose of preservation of correlations. We then show how the evolution under the channel action can be seen as an unitary process. We use the technique of weak measurement and most general form of selective positive operator valued measure (POVM) to achieve preservation of correlations for a significantly large range of parameter values.
1903.03550v2
2019-03-17
Generalized Euler, Smoluchowski and Schrödinger equations admitting self-similar solutions with a Tsallis invariant profile
The damped isothermal Euler equations, the Smoluchowski equation and the damped logarithmic Schr\"odinger equation with a harmonic potential admit stationary and self-similar solutions with a Gaussian profile. They satisfy an $H$-theorem for a free energy functional involving the von Weizs\"acker functional and the Boltzmann functional. We derive generalized forms of these equations in order to obtain stationary and self-similar solutions with a Tsallis profile. In particular, we introduce a nonlinear Schr\"odinger equation involving a generalized kinetic term characterized by an index $q$ and a power-law nonlinearity characterized by an index $\gamma$. We derive an $H$-theorem satisfied by a generalized free energy functional involving a generalized von Weizs\"acker functional (associated with $q$) and a Tsallis functional (associated with $\gamma$). This leads to a notion of generalized quantum mechanics and generalized thermodynamics. When $q=2\gamma-1$, our nonlinear Schr\"odinger equation admits an exact self-similar solution with a Tsallis invariant profile. Standard quantum mechanics (Schr\"odinger) and standard thermodynamics (Boltzmann) are recovered for $q=\gamma=1$.
1903.07111v1
2019-03-21
Creating localized plasma wave by ionization of doped semiconductors
Localized plasma waves can be generated by suddenly ionizing extrinsic semiconductors with spatially periodic dopant densities. The built-in electrostatic potentials at the metallurgical junctions, combined with electron density ripples, offer the exact initial condition for exciting long-lasting plasma waves upon ionization. This method can create plasma waves with a frequency between a few terahertz to sub-petahertz without substantial damping. The lingering plasma waves can seed backward Raman amplification in a wide range of resonance frequencies up to the extreme ultraviolet regime. Chirped wavevectors and curved wavefronts allow focusing the amplified beam in both longitudinal and transverse dimensions. The main limitation to this method appears to be obtaining sufficiently low plasma density from solid-state materials to avoid collisional damping.
1903.09013v2
2019-03-22
Noncommutative approach to diagnose degenerate Higgs bosons at 125 GeV
We propose a noncommutative (NC) version for a global O(2) scalar field theory, whose damping feature is introduced into the scalar field theory through the NC parameter. In this context, we investigate how noncommutative drives spontaneous symmetry breaking (SSB) and Higgs-Kibble mechanisms and how the damping feature workout. Indeed, we show that the noncommutativity plays an important role in such mechanisms, i.e., the Higgs mass and VEV dependent on NC parameter. After that, it is explored the consequences of noncommutativity dependence of Higgs mass and VEV: for the first, it is shown that there are a mass-degenerate Higgs bosons near 126.5 GeV, parametrized by the noncommutativity; for the second, the gauge fields gain masses that present a noncommutativity contribution.
1903.09727v2
2019-03-30
Uncertainty damping in kinetic traffic models by driver-assist controls
In this paper, we propose a kinetic model of traffic flow with uncertain binary interactions, which explains the scattering of the fundamental diagram in terms of the macroscopic variability of aggregate quantities, such as the mean speed and the flux of the vehicles, produced by the microscopic uncertainty. Moreover, we design control strategies at the level of the microscopic interactions among the vehicles, by which we prove that it is possible to dampen the propagation of such an uncertainty across the scales. Our analytical and numerical results suggest that the aggregate traffic flow may be made more ordered, hence predictable, by implementing such control protocols in driver-assist vehicles. Remarkably, they also provide a precise relationship between a measure of the macroscopic damping of the uncertainty and the penetration rate of the driver-assist technology in the traffic stream.
1904.00257v2
2019-04-01
Reduction of Kinetic Equations to Liénard-Levinson-Smith Form: Counting Limit Cycles
We have presented an unified scheme to express a class of system of equations in two variables into a Li\'enard-Levinson-Smith (LLS) oscillator form. We have derived the condition for limit cycle with special reference to Rayleigh and Li\'enard systems for arbitrary polynomial functions of damping and restoring force. Krylov-Boguliubov (K-B) method is implemented to determine the maximum number of limit cycles admissible for a LLS oscillator atleast in the weak damping limit. Scheme is illustrated by a number of model systems with single cycle as well as the multiple cycle cases.
1904.00604v2
2019-04-02
Stability of the interface of an isotropic active fluid
We study the linear stability of an isotropic active fluid in three different geometries: a film of active fluid on a rigid substrate, a cylindrical thread of fluid, and a spherical fluid droplet. The active fluid is modeled by the hydrodynamic theory of an active nematic liquid crystal in the isotropic phase. In each geometry, we calculate the growth rate of sinusoidal modes of deformation of the interface. There are two distinct branches of growth rates; at long wavelength, one corresponds to the deformation of the interface, and one corresponds to the evolution of the liquid crystalline degrees of freedom. The passive cases of the film and the spherical droplet are always stable. For these geometries, a sufficiently large activity leads to instability. Activity also leads to propagating damped or growing modes. The passive cylindrical thread is unstable for perturbations with wavelength longer than the circumference. A sufficiently large activity can make any wavelength unstable, and again leads to propagating damped or growing modes.
1904.01558v1
2019-04-04
Shear viscosity of classical fields in scalar theory
We investigate the shear viscosity of massless classical scalar fields in the $\phi^4$ theory on a lattice by using the Green-Kubo formula. Based on the scaling property of the classical field, the shear viscosity is represented using a scaling function. Equilibrium expectation value of the time-correlation function of the energy-momentum tensor is evaluated as the ensemble average of the classical field configurations, whose time evolution is obtained by solving the classical equation of motion starting from the initial condition in thermal equilibrium. It is found that there are two distinct damping time scales in the time-correlation function, which is found to show damped oscillation behavior in the early stage around a slow monotonous decay with an exponential form, and the slow decay part is found to dominate the shear viscosity in the massless classical field theory. This kind of slow decay is also known to exist in the molecular dynamics simulation, then it may be a generic feature of dense matter.
1904.02419v3
2019-04-08
Study of Decoherence in Quantum Computers: A Circuit-Design Perspective
Decoherence of quantum states is a major hurdle towards scalable and reliable quantum computing. Lower decoherence (i.e., higher fidelity) can alleviate the error correction overhead and obviate the need for energy-intensive noise reduction techniques e.g., cryogenic cooling. In this paper, we performed a noise-induced decoherence analysis of single and multi-qubit quantum gates using physics-based simulations. The analysis indicates that (i) decoherence depends on the input state and the gate type. Larger number of $|1\rangle$ states worsen the decoherence; (ii) amplitude damping is more detrimental than phase damping; (iii) shorter depth implementation of a quantum function can achieve lower decoherence. Simulations indicate 20\% improvement in the fidelity of a quantum adder when realized using lower depth topology. The insights developed in this paper can be exploited by the circuit designer to choose the right gates and logic implementation to optimize the system-level fidelity.
1904.04323v1
2019-04-09
Ferromagnetic Resonance Studies of Strain tuned Bi:YIG Films
Bismuth-doped Yttrium iron garnet (Bi:YIG) thin films known for large Magneto-optical activity with low losses still needs to get probed for its magnetization dynamics. We demonstrate a controlled tuning of magnetocrystalline anisotropy in Bi-doped Y_3 Fe_5 O_12 (Bi:YIG) films of high crystalline quality using growth induced epitaxial strain on [111]-oriented Gd_3 Ga_5 O_12 (GGG) substrate. We optimize a growth protocol to get thick highly-strained epitaxial films showing large magneto-crystalline anisotropy, compare to thin films prepared using a different protocol. Ferromagnetic resonance measurements establish a linear dependence of the out-of-plane uniaxial anisotropy on the strain induced rhombohedral distortion of Bi:YIG lattice. Interestingly, the enhancement in the magnetoelastic constant due to an optimum substitution of Bi^(3+) ions with strong spin orbit coupling does not strongly affect the precessional damping (~2x10^(-3) ). Large magneto-optical activity, reasonably low damping, large magnetocrystalline anisotropy and large magnetoelastic coupling in BiYIG are the properties that may help BiYIG emerge as a possible material for photo-magnonics and other spintronics applications.
1904.04800v2
2019-04-23
A novel undamped gapless plasmon mode in tilted type-II Dirac semimetal
We predict the existence of a novel long-lived gapless plasmon mode in a type-II Dirac semimetal (DSM). This gapless mode arises from the out-of-phase oscillations of the density fluctuations in the electron and the hole pockets of a type-II DSM. It originates beyond a critical wave-vector along the direction of the tilt axis, owing to the momentum separation of the electron and hole pockets. A similar out-of-phase plasmon mode arises in other multi-component charged fluids as well, but generally it is Landau damped and lies within the particle-hole continuum. In the case of a type-II DSM, the open Fermi surface prohibits low-energy finite momentum single-particle excitations, creating a `gap' in the particle-hole continuum. The gapless plasmon mode lies within this particle-hole continuum gap and, thus, it is protected from Landau damping.
1904.10137v1
2019-04-25
Interplay between nonclassicality and $\mathcal{PT}$ symmetry in an effective two level system with open system effects
A three level atom in $\Lambda$ configuration is reduced to an effective two level system, under appropriate conditions, and its $\mathcal{PT}$ symmetric properties are investigated. This effective qubit system when subjected to a beam-splitter type of interaction, it provides the scope of directly (indirectly) probing the nonclassical properties of the output (input) state. Here, we study nonclassical properties of the output state by using some well known measures of nonclassical correlations like the measurement induced disturbance, concurrence and negativity. The nonclassical features are found to enhance in the $\mathcal{PT}$ symmetric (PTS) phase compared to the $\mathcal{PT}$ symmetry broken (PTSB) phase. Further, the output ports of the beam-splitter are subjected to different quantum noise channels, both non-Markovian, e.g., random telegraph noise as well as Markovian, e.g., phase damping, and amplitude damping noise. The application of noise channels is found to decrease the degree of nonclassicality, though continuing to exhibit distinct behavior in PTS and PTSB phases, with the dominant behavior appearing in the former case.
1904.11181v1
2019-04-25
Low damping magnetic properties and perpendicular magnetic anisotropy with strong volume contribution in the Heusler alloy Fe1.5CoGe
We present a study of the dynamic magnetic properties of TiN-buffered epitaxial thin films of the Heusler alloy Fe$_{1.5}$CoGe. Thickness series annealed at different temperatures are prepared and the magnetic damping is measured, a lowest value of $\alpha=2.18\times 10^{-3}$ is obtained. The perpendicular magnetic anisotropy properties in Fe$_{1.5}$CoGe/MgO are also characterized. The evolution of the interfacial perpendicular anisotropy constant $K^{\perp}_{\rm S}$ with the annealing temperature is shown and compared with the widely used CoFeB/MgO interface. A large volume contribution to the perpendicular anisotropy of $(4.3\pm0.5)\times 10^{5}$ $\rm J/m^3$ is also found, in contrast with vanishing bulk contribution in common Co- and Fe-based Heusler alloys.
1904.11247v1
2019-04-26
Terahertz spin dynamics driven by a field-derivative torque
Efficient manipulation of magnetization at ultrashort time scales is of particular interest for future technology. Here, we numerically investigate the influence of the so-called field-derivative torque, which was derived earlier based on relativistic Dirac theory [Mondal et al., Phys. Rev. B 94, 144419 (2016)], on the spin dynamics triggered by ultrashort laser pulses. We find that only considering the THz Zeeman field can underestimate the spin excitation in antiferromagnetic oxide systems as, e.g., NiO and CoO. However, accounting for both, the THz Zeeman torque and the field-derivative torque, the amplitude of the spin excitation increases significantly. Studying the damping dependence of field-derivative torque we observe larger effects for materials having larger damping constants.
1904.11768v2
2019-04-30
A Self-Adaptive Contractive Algorithm for Enhanced Dynamic Phasor Estimation
In this paper, a self-adaptive contractive (SAC) algorithm is proposed for enhanced dynamic phasor estimation in the diverse operating conditions of modern power systems. At a high-level, the method is composed of three stages: parameter shifting, filtering and parameter unshifting. The goal of the first stage is to transform the input signal phasor so that it is approximately mapped to nominal conditions. The second stage provides estimates of the phasor, frequency, rate of change of frequency (ROCOF), damping and rate of change of damping (ROCOD) of the parameter shifted phasor by using a differentiator filter bank (DFB). The final stage recovers the original signal phasor parameters while rejecting misleading estimates. The most important features of the algorithm are that it offers convergence guarantees in a set of desired conditions, and also great harmonic rejection. Numerical examples, including the IEEE C37.118.1 standard tests with realistic noise levels, as well as fault conditions, validate the proposed algorithm.
1904.13328v1
2019-05-02
The floatability of aerosols and waves damping on Titan's seas
Titan, Saturn's largest moon, has a dense atmosphere, together with lakes and seas of liquid hydrocarbons. These liquid bodies, which are in polar regions and up to several hundred kilometres in diameter, generally have smooth surfaces despite evidence of near-surface winds. Photochemically generated organic aerosols form a haze that can settle and potentially interact with the liquid surface. Here we investigate the floatability of these aerosols on Titan's seas and their potential to dampen waves. We find that the majority of aerosols are denser than the liquid hydrocarbons, but that some could have liquid-repelling properties. From calculation of the capillary forces, we propose that these 'liquidophobic' aerosols could float and form a persistent film on Titan's seas. We numerically model the wave damping efficiency of such a film under the conditions on Titan, demonstrating that even a film one molecule thick may inhibit formation of waves larger than a few centimetres in wavelength. We conclude that the presence of a floating film of aerosols deposited on Titan's lakes and seas could explain the remarkable smoothness of their surfaces.
1905.00760v1
2019-05-02
Holographic Plasmon Relaxation with and without Broken Translations
We study the dynamics and the relaxation of bulk plasmons in strongly coupled and quantum critical systems using the holographic framework. We analyze the dispersion relation of the plasmonic modes in detail for an illustrative class of holographic bottom-up models. Comparing to a simple hydrodynamic formula, we entangle the complicated interplay between the three least damped modes and shed light on the underlying physical processes. Such as the dependence of the plasma frequency and the effective relaxation time in terms of the electromagnetic coupling, the charge and the temperature of the system. Introducing momentum dissipation, we then identify its additional contribution to the damping. Finally, we consider the spontaneous symmetry breaking (SSB) of translational invariance. Upon dialing the strength of the SSB, we observe an increase of the longitudinal sound speed controlled by the elastic moduli and a decrease in the plasma frequency of the gapped plasmon. We comment on the condensed matter interpretation of this mechanism.
1905.00804v2
2019-05-05
Effective spin-mixing conductance of heavy-metal-ferromagnet interfaces
The effective spin-mixing conductance (G_eff) of a heavy metal/ferromagnet (HM/FM) interface characterizes the efficiency of the interfacial spin transport.Accurately determining G_eff is critical to the quantitative understanding of measurements of direct and inverse spin Hall effects. G_eff is typically ascertained from the inverse dependence of magnetic damping on the FM thickness under the assumption that spin pumping is the dominant mechanism affecting this dependence.Here we report that, this assumption fails badly in many in-plane magnetized prototypical HM/FM systems in the nm-scale thickness regime. Instead, the majority of the damping is from two-magnon scattering at the FM interface, while spin-memory-loss scattering at the interface can also be significant.If these two effects are neglected, the results will be an unphysical "giant" apparent G_eff and hence considerable underestimation of both the spin Hall ratio and the spin Hall conductivity in inverse/direct spin Hall experiments.
1905.01577v2
2019-05-07
Integral representation formulae for the solution of a wave equation with time-dependent damping and mass in the scale-invariant case
This paper is devoted to derive integral representation formulae for the solution of an inhomogeneous linear wave equation with time-dependent damping and mass terms, that are scale-invariant with respect to the so-called hyperbolic scaling. Yagdjian's integral transform approach is employed for this purpose. The main step in our argument consists in determining the kernel functions for the different integral terms, which are related to the source term and to initial data. We will start with the one dimensional case (in space). We point out that we may not apply in a straightforward way Duhamel's principle to deal with the source term since the coefficients of lower order terms make our model not invariant by time translation. On the contrary, we shall begin with the representation formula for the inhomogeneous equation with vanishing data by using a revised Duhamel's principle. Then, we will derive the representation of the solution in the homogeneous case with nontrivial data. After deriving the formula in the one dimensional case, the classical approach by spherical means is used in order to deal with the odd dimensional case. Finally, using the method of descent, the representation formula in the even dimensional case is proved.
1905.02408v1
2019-05-07
Optimal decay for the $n$-dimensional incompressible Oldroyd-B model without damping mechanism
By a new energy approach involved in the high frequencies and low frequencies decomposition in the Besov spaces, we obtain the optimal decay for the incompressible Oldroyd-B model without damping mechanism in $\mathbb{R}^n$ ($n\ge 2$). More precisely, let $(u,\tau)$ be the global small solutions constructed in [18], we prove for any $(u_0,\tau_0)\in{\dot{B}_{2,1}^{-s}}(\mathbb{R}^n)$ that \begin{eqnarray*} \big\|\Lambda^{\alpha}(u,\Lambda^{-1}\mathbb{P}\mathrm{div}\tau)\big\|_{L^q} \le C (1+t)^{-\frac n4-\frac {(\alpha+s)q-n}{2q}}, \quad\Lambda\stackrel{\mathrm{def}}{=}\sqrt{-\Delta}, \end{eqnarray*} with $\frac n2-1<s<\frac np, $ $2\leq p \leq \min(4,{2n}/({n-2})),\ p\not=4\ \hbox{ if }\ n=2,$ and $p\leq q\leq\infty$, $\frac nq-\frac np-s<\alpha \leq\frac nq-1$. The proof relies heavily on the special dissipative structure of the equations and some commutator estimates and various interpolations between Besov type spaces. The method also works for other parabolic-hyperbolic systems in which the Fourier splitting technique is invalid.
1905.02604v1
2019-05-12
Transport and Phonon Damping in $^{\bf 4}$He
The dynamic structure function $S(k,\omega)$ informs about the dispersion and damping of excitations. We have recently (Phys. Rev. B {\bf 97}, 184520 (2018)) compared experimental results for $S(k,\omega)$ from high-precision neutron scattering experiment and theoretical results using the ``dynamic many-body theory'' (DMBT), showing excellent agreement over the whole experimentally accessible pressure regime. This paper focuses on the specific aspect of the propagation of low-energy phonons. We report calculations of the phonon mean-free path and phonon life time in liquid \he4 as a function of wave length and pressure. Historically, the question was of interest for experiments of quantum evaporation. More recently, there is interest in the potential use of $^4$He as a detector for low-energy dark matter (K. Schulz and Kathryn M. Zurek, Phys. Rev. Lett. {\bf 117}, 121302 (2016)). While the mean free path of long wave length phonons is large, phonons of intermediate energy can have a short mean free path of the order of $\mu$m. Comparison of different levels of theory indicate that reliable predictions of the phonon mean free path can be made only by using the most advanced many--body method available, namely, DMBT.
1905.04759v1
2019-05-15
Nearly Markovian maps and entanglement-based bound on corresponding non-Markovianity
We identify a set of dynamical maps of open quantum system, and refer to them as "$ \epsilon $-Markovian" maps. It is constituted of maps which, in a higher dimensional system-environment Hilbert space, possibly violate Born approximation but only a "little". We characterize the "$\epsilon$-nonmarkovianity" of a general dynamical map by the minimum distance of that map from the set of $\epsilon$-Markovian maps. We analytically derive an inequality which gives a bound on the $ \epsilon$-nonmarkovianity of the dynamical map, in terms of an entanglement-like resource generated between the system and its "immediate" environment. In the special case of a vanishing $\epsilon$, this inequality gives a relation between the $\epsilon$-nonmarkovianity of the reduced dynamical map on the system and the entanglement generated between the system and its immediate environment. We numerically investigate the behavior of the similar distant based measures of non-Markovianity for classes of amplitude damping and phase damping channels.
1905.06198v3
2019-05-15
A remark on triviality for the two-dimensional stochastic nonlinear wave equation
We consider the two-dimensional stochastic damped nonlinear wave equation (SdNLW) with the cubic nonlinearity, forced by a space-time white noise. In particular, we investigate the limiting behavior of solutions to SdNLW with regularized noises and establish triviality results in the spirit of the work by Hairer, Ryser, and Weber (2012). More precisely, without renormalization of the nonlinearity, we establish the following two limiting behaviors; (i) in the strong noise regime, we show that solutions to SdNLW with regularized noises tend to 0 as the regularization is removed and (ii) in the weak noise regime, we show that solutions to SdNLW with regularized noises converge to a solution to a deterministic damped nonlinear wave equation with an additional mass term.
1905.06278v3
2019-05-17
Chiral p-wave superconductors have complex coherence and magnetic field penetration lengths
We show that in superconductors that break time reversal symmetry and have anisotropy, such as p+ip materials, all order parameters and magnetic modes are mixed. Excitation of the gap fields produces an excitation of the magnetic field and vice versa. Correspondingly the long-range decay of the magnetic field and order parameter are in general given by the same exponent. Thus one cannot characterize p+ip superconductors by the usual coherence and magnetic field penetration lengths. Instead the system has normal modes that are associated with linear combinations of magnetic fields, moduli of and phases of the order parameter components. Each such normal mode has its own decay length that plays the role of a hybridized coherence/magnetic field penetration length. On a large part of the parameter space these exponents are complex. Therefore the system in general has damped oscillatory decay of the magnetic field accompanied by damped oscillatory variation of the order parameter fields.
1905.07296v2
2019-05-20
Short time blow-up by negative mass term for semilinear wave equations with small data and scattering damping
In this paper we study blow-up and lifespan estimate for solutions to the Cauchy problem with small data for semilinear wave equations with scattering damping and negative mass term. We show that the negative mass term will play a dominant role when the decay of its coefficients is not so fast, thus the solutions will blow up in a finite time. What is more, we establish a lifespan estimate from above which is much shorter than the usual one.
1905.08100v1
2019-05-21
Low-pass-filter-based shock response spectrum and the evaluation method of transmissibility between equipment and sensitive components interfaces
According to the features of the sources of pyroshock and ballistic shock, this study considers the pyroshock and ballistic shock generated by their respective impulsive sources as damped harmonic waves with different frequencies. According to the linear superposition assumption of damped harmonic waves in a linear elastic structure, a shock analysis method based on low-pass-filtered shock signals and their corresponding shock response spectrum (SRS), termed as low-pass-filter-based shock response spectrum (LPSRS), is proposed. LPSRS contains rich information of the frequency distribution of the shock excitation signal. A method to calculate shock transmissibility is proposed based on LPSRS and basic modal information of the equipment structure. LPSRS and SRS curves can be predicted at any given position of the equipment structure. The prediction method is validated by finite element method (FEM) simulation.
1905.10190v1
2019-05-24
Sound damping in glasses: interplay between anharmonicities and elastic heterogeneities
Some facets of the way sound waves travel through glasses are still unclear. Recent works have shown that in the low-temperature harmonic limit a crucial role in controlling sound damping is played by local elastic heterogeneity. Sound waves propagation has been demonstrated to be strongly affected by inhomogeneous mechanical features of the materials, which add to the anharmonic couplings at finite temperatures. We describe the interplay between these two effects by molecular dynamics simulation of a model glass. In particular, we focus on the transverse components of the vibrational excitations in terms of dynamic structure factors, and characterize the temperature dependence of sound attenuation rates in an extended frequency range. We provide a complete picture of all phenomena, in terms encompassing both theory and experiments.
1905.10235v2
2019-05-27
A blow-up result for a semilinear wave equation with scale-invariant damping and mass and nonlinearity of derivative type
In this note, we prove blow-up results for semilinear wave models with damping and mass in the scale-invariant case and with nonlinear terms of derivative type. We consider the single equation and the weakly coupled system. In the first case we get a blow-up result for exponents below a certain shift of the Glassey exponent. For the weakly coupled system we find as critical curve a shift of the corresponding curve for the weakly coupled system of semilinear wave equations with the same kind of nonlinearities. Our approach follows the one for the respective classical wave equation by Zhou Yi. In particular, an explicit integral representation formula for a solution of the corresponding linear scale-invariant wave equation, which is derived by using Yagdjian's integral transform approach, is employed in the blow-up argument. While in the case of the single equation we may use a comparison argument, for the weakly coupled system an iteration argument is applied.
1905.11025v2
2019-05-28
Stationary states for underdamped anharmonic oscillators driven by Cauchy noise
Using methods of stochastic dynamics, we have studied stationary states in the underdamped anharmonic stochastic oscillators driven by Cauchy noise. Shape of stationary states depend both on the potential type and the damping. If the damping is strong enough, for potential wells which in the overdamped regime produce multimodal stationary states, stationary states in the underdamped regime can be multimodal with the same number of modes like in the overdamped regime. For the parabolic potential, the stationary density is always unimodal and it is given by the two dimensional $\alpha$-stable density. For the mixture of quartic and parabolic single-well potentials the stationary density can be bimodal. Nevertheless, the parabolic addition, which is strong enough, can destroy bimodlity of the stationary state.
1905.12078v2
2019-05-30
Intrinsically Undamped Plasmon Modes in Narrow Electron Bands
Surface plasmons in 2-dimensional electron systems with narrow Bloch bands feature an interesting regime in which Landau damping (dissipation via electron-hole pair excitation) is completely quenched. This surprising behavior is made possible by strong coupling in narrow-band systems characterized by large values of the "fine structure" constant $\alpha=e^2/\hbar \kappa v_{\rm F}$. Dissipation quenching occurs when dispersing plasmon modes rise above the particle-hole continuum, extending into the forbidden energy gap that is free from particle-hole excitations. The effect is predicted to be prominent in moir\'e graphene, where at magic twist-angle values, flat bands feature $\alpha\gg1$. The extinction of Landau damping enhances spatial optical coherence. Speckle-like interference, arising in the presence of disorder scattering, can serve as a telltale signature of undamped plasmons directly accessible in near-field imaging experiments.
1905.13088v2
2019-06-04
High frequency voltage-induced ferromagnetic resonance in magnetic tunnel junctions
Voltage-induced ferromagnetic resonance (V-FMR) in magnetic tunnel junctions (MTJs) with a W buffer is investigated. Perpendicular magnetic anisotropy (PMA) energy is controlled by both thickness of a CoFeB free layer deposited directly on the W buffer and a post-annealing process at different temperatures. The PMA energy as well as the magnetization damping are determined by analysing field-dependent FMR signals in different field geometries. An optimized MTJ structure enabled excitation of V-FMR at frequencies exceeding 30 GHz. The macrospin modelling is used to analyse the field- and angular-dependence of the V-FMR signal and to support experimental magnetization damping extraction.
1906.01301v1
2019-06-04
Late time approach to Hawking radiation: terms beyond leading order
Black hole evaporation is studied using wave packets for the modes. These allow for approximate frequency and time resolution. The leading order late time behavior gives the well known Hawking radiation that is independent of how the black hole formed. The focus here is on the higher order terms and the rate at which they damp at late times. Some of these terms carry information about how the black hole formed. A general argument is given which shows that the damping is significantly slower (power law) than what might be naively expected from a stationary phase approximation (exponential). This result is verified by numerical calculations in the cases of 2D and 4D black holes that form from the collapse of a null shell.
1906.01735v2
2019-06-20
Time-sliced perturbation theory with primordial non-Gaussianity and effects of large bulk flows on inflationary oscillating features
We extend the formalism of time-sliced perturbation theory (TSPT) for cosmological large-scale structure to include non-Gaussian initial conditions. We show that in such a case the TSPT interaction vertices acquire new contributions whose time-dependence factorizes for the Einstein-de Sitter cosmology. The new formulation is free from spurious infrared (IR) enhancements and reveals a clear IR structure of non-Gaussian vertices. We use the new technique to study the evolution of oscillating features in primordial statistics and show that they are damped due to non-linear effects of large bulk flows. We derive the damping factors for the oscillating primordial power spectrum and bispectrum by means of a systematic IR resummation of relevant Feynman diagrams.
1906.08697v2
2019-06-21
Control of eigenfunctions on surfaces of variable curvature
We prove a microlocal lower bound on the mass of high energy eigenfunctions of the Laplacian on compact surfaces of negative curvature, and more generally on surfaces with Anosov geodesic flows. This implies controllability for the Schr\"odinger equation by any nonempty open set, and shows that every semiclassical measure has full support. We also prove exponential energy decay for solutions to the damped wave equation on such surfaces, for any nontrivial damping coefficient. These results extend previous works [arXiv:1705.05019], [arXiv:1712.02692], which considered the setting of surfaces of constant negative curvature. The proofs use the strategy of [arXiv:1705.05019], [arXiv:1712.02692] and rely on the fractal uncertainty principle of [arXiv:1612.09040]. However, in the variable curvature case the stable/unstable foliations are not smooth, so we can no longer associate to these foliations a pseudodifferential calculus of the type used in [arXiv:1504.06589]. Instead, our argument uses Egorov's Theorem up to local Ehrenfest time and the hyperbolic parametrix of [arXiv:0706.3242], together with the $C^{1+}$ regularity of the stable/unstable foliations.
1906.08923v2
2019-06-21
Exponential damping induced by random and realistic perturbations
Given a quantum many-body system and the expectation-value dynamics of some operator, we study how this reference dynamics is altered due to a perturbation of the system's Hamiltonian. Based on projection operator techniques, we unveil that if the perturbation exhibits a random-matrix structure in the eigenbasis of the unperturbed Hamiltonian, then this perturbation effectively leads to an exponential damping of the original dynamics. Employing a combination of dynamical quantum typicality and numerical linked cluster expansions, we demonstrate that our theoretical findings for random matrices can, in some cases, be relevant for the dynamics of realistic quantum many-body models as well. Specifically, we study the decay of current autocorrelation functions in spin-$1/2$ ladder systems, where the rungs of the ladder are treated as a perturbation to the otherwise uncoupled legs. We find a convincing agreement between the exact dynamics and the lowest-order prediction over a wide range of interchain couplings.
1906.09268v2
2019-06-27
Fast control of dissipation in a superconducting resonator
We report on fast tunability of an electromagnetic environment coupled to a superconducting coplanar waveguide resonator. Namely, we utilize a recently-developed quantum-circuit refrigerator (QCR) to experimentally demonstrate a dynamic tunability in the total damping rate of the resonator up to almost two orders of magnitude. Based on the theory it corresponds to a change in the internal damping rate by nearly four orders of magnitude. The control of the QCR is fully electrical, with the shortest implemented operation times in the range of 10 ns. This experiment constitutes a fast active reset of a superconducting quantum circuit. In the future, a similar scheme can potentially be used to initialize superconducting quantum bits.
1906.11519v1
2019-06-28
Ground-state cooling of an magnomechanical resonator induced by magnetic damping
Quantum manipulation of mechanical resonators has been widely applied in fundamental physics and quantum information processing. Among them, cooling the mechanical system to its quantum ground state is regarded as a key step. In this work, we propose a scheme which one can realize ground-state cooling of resonator in a cavity magnomechanical system. The system consists of a microwave cavity and a small ferromagnetic sphere, in which phonon-magnon coupling and cavity photon-magnon coupling can be achieved via magnetostrictive interaction and magnetic dipole interaction, respectively. After adiabatically eliminating the cavity mode, an effective Hamiltonian which consists of magnon and mechanical modes is obtained. Within experimentally feasible parameters, we demonstrate that the ground-state cooling of the magnomechanical resonator can be achieved by extra magnetic damping. Unlike optomechanical cooling, magnomechanical interaction is utilized to realize the cooling of resonators. We further illustrate the ground-state cooling can be effectively controlled by the external magnetic field.
1906.12081v1
2019-06-30
Non-linear spin torque, pumping and cooling in superconductor/ferromagnet systems
We study the effects of the coupling between magnetization dynamics and the electronic degrees of freedom in a heterostructure of a metallic nanomagnet with dynamic magnetization coupled with a superconductor containing a steady spin-splitting field. We predict how this system exhibits a non-linear spin torque, which can be driven either with a temperature difference or a voltage across the interface. We generalize this notion to arbitrary magnetization precession by deriving a Keldysh action for the interface, describing the coupled charge, heat and spin transport in the presence of a precessing magnetization. We characterize the effect of superconductivity on the precession damping and the anti-damping torques. We also predict the full non-linear characteristic of the Onsager counterparts of the torque, showing up via pumped charge and heat currents. For the latter, we predict a spin-pumping cooling effect, where the magnetization dynamics can cool either the nanomagnet or the superconductor.
1907.00424v2
2019-07-03
Wave-ice interaction in the North-West Barents Sea
The results of field work on drift ice during wave propagation are analyzed and presented. The field work was performed in the Barents Sea, and the main focus of the paper is on wave processes in the MIZ. A model of wave damping in broken ice is formulated and applied to interpret the field work results. It is confirmed that waves of higher frequencies are subjected to stronger damping when they propagate below the ice. This reduces the frequency of most energetic wave with increasing distance from the ice edge. Difference of wave spectra measured in two relatively close locations within the MIZ is discussed. The complicated geometry and dynamics of the MIZ in the North-West Barents Sea allow waves from the Atlantic Ocean and south regions of the Barents Sea to penetrate into different locations of the MIZ.
1907.02032v1
2019-07-05
Nesterov's acceleration and Polyak's heavy ball method in continuous time: convergence rate analysis under geometric conditions and perturbations
In this article a family of second order ODEs associated to inertial gradient descend is studied. These ODEs are widely used to build trajectories converging to a minimizer $x^*$ of a function $F$, possibly convex. This family includes the continuous version of the Nesterov inertial scheme and the continuous heavy ball method. Several damping parameters, not necessarily vanishing, and a perturbation term $g$ are thus considered. The damping parameter is linked to the inertia of the associated inertial scheme and the perturbation term $g$ is linked to the error that can be done on the gradient of the function $F$. This article presents new asymptotic bounds on $F(x(t))-F(x^*)$ where $x$ is a solution of the ODE, when $F$ is convex and satisfies local geometrical properties such as {\L}ojasiewicz properties and under integrability conditions on $g$. Even if geometrical properties and perturbations were already studied for most ODEs of these families, it is the first time they are jointly studied. All these results give an insight on the behavior of these inertial and perturbed algorithms if $F$ satisfies some {\L}ojasiewicz properties especially in the setting of stochastic algorithms.
1907.02710v1
2019-07-08
Role of Toll-Like Receptors in the interplay between pathogen and damage associated molecular patterns
Various theoretical studies have been carried out to infer relevant protein-protein interactions among pathogens and their hosts. Such studies are generally based on preferential attachment of bacteria / virus to their human receptor homologs. We have analyzed 17 pathogenic species mainly belonging to bacterial and viral pathogenic classes, with the aim to identify the interacting human proteins which are targeted by both bacteria and virus specifically. Our study reveals that the TLRs play a crucial role between the pathogen-associated molecular patterns (PAMPs) and the damage associated molecular patterns (DAMPS). PAMPs include bacterial lipopolysaccharides (LPs), endotoxins, bacterial flagellin, lipoteichoic acid, peptidoglycan in bacterial organisms and nucleic acid variants associated with viral organisms, whereas DAMPs are associated with host biomolecules that perpetuate non-infectious inflammatory responses. We found out the presence of SOD1 and SOD2 (superoxide dismutase) is crucial, as it acts as an anti-oxidant and helps in eliminating oxidative stress by preventing damage from reactive oxygen species. Hence, such strategies can be used as new therapies for anti-inflammatory diseases with significant clinical outcomes.
1907.03512v1
2019-07-15
Alternating Direction Method of Multipliers (ADMMs) Based Distributed Approach For Wide-Area Control
In this paper, an alternating direction method of multipliers based novel distributed wide-area control architecture is proposed for damping the interarea oscillations. In this approach, first, an interconnected power system is divided into areas based on coherency grouping. Second, local processors are assigned on each area that estimate a black-box transfer function model based on Lagrange multipliers using measurements. These local area processors are then used to estimate a global transfer function model of the power system based on a consensus algorithm through a global processor. After convergence, a transfer function residue corresponding to the interarea mode of interest is derived, to determine optimal wide area control loop. Finally, a wide-area damping controller is designed based on this information. The efficacy of the controller is validated using two area and IEEE-39 bus test systems on RTDS/RSCAD and MATLAB cosimulation platform.
1907.06340v1
2019-07-16
Coherency and Online Signal Selection Based Wide Area Control of Wind Integrated Power Grid
This paper introduces a novel method of designing wide area control (WAC) based on a discrete linear quadratic regulator and Kalman filtering based state-estimation that can be applied for real-time damping of interarea oscillations of wind integrated power grid. The main advantages of the proposed method are that the architecture provides online coherency grouping that properly characterizes real-time changes in the power grid and online wide-area signal selection based on residue method for proper selection of the WAC signals. The proposed architecture can, thus, accurately monitors changes in the power grid and select the appropriate control signal for more effectively damping the interarea oscillation when compared to the conventional local signal based power system stabilizers or offline based WAC designs. The architecture is tested on a wind integrated two-area system and the IEEE 39 bus system in order to show the capability of the proposed method.
1907.06846v1
2019-07-20
Magnon Bose-Einstein condensate and supercurrents over a wide temperature range
Magnon Bose-Einstein Condensates (BECs) and supercurrents are coherent quantum phenomena, which appear on a macroscopic scale in parametrically populated solid state spinsystems. One of the most fascinating and attractive features of these processes is the possibility of magnon condensation and supercurrent excitation even at room temperature. At the same time, valuable information about a magnon BEC state, such as its lifetime, its formation threshold, and coherency, is provided by experiments at various temperatures. Here, we use Brillouin Light Scattering (BLS) spectroscopy for the investigation of the magnon BEC dynamics in a single-crystal film of yttrium iron garnet in a wide temperature range from 30 K to 380 K. By comparing the BLS results with previous microwave measurements, we re-vealed the direct relation between the damping of the condensed and the parametrically injected magnons. The enhanced supercurrent dynamics was detected at 180 K near the minimum of BEC damping.
1907.08805v1
2019-07-21
Explaining Retrocausality Phenomena in Quantum Mechanics using a Modified Variational Principle
A modified lagrangian with causal and retrocausal momenta was used to derive a first causal wave equation and a second retrocausal wave equation using the principle of least action. The retrocausal wave function obtained through this method was found to be equivalent to the complex conjugate of the causal wave function, thus leading to the conclusion that a retrocausal effect is already implicit in quantum mechanics through the means of complex conjugation of the wave function when computing the probability density for a particle. Lastly, the same variational principle was employed with a fractionary langriangian, (that is, containing fractional Riemann derivatives) to obtain a pair of modified wave equations, one causal and other retrocausal, both of which correspond to the differential equation of a damped oscillator in the free particle (potential energy V=0) case. The solutions of this damped wave equations remain to be explored.
1907.09688v3
2019-07-23
Global wellposedness to the $n$-dimensional compressible Oldroyd-B model without damping mechanism
The Cauchy problem of the compressible Oldroyd-B model without damping mechanism in R^n$ with $n\ge2$ is considered. The lack of dissipation in density and stress tensor in the model is compensated by exploiting an intrinsic structure and introducing new quantities between density, velocity and stress tensor. Therefore, global solutions to the system with small initial data in critical Besov spaces are obtained. As a byproduct, optimal time decay rates of the solutions are derived by using an energy estimation argument. The results remain valid for the compressible viscoelastic system without the `div-curl structure assumption and thus improve those given by Hu and Wang [ J. Differential Equations, {\bf 250}, 1200--1231, 2011] and Qian and Zhang [Arch. Ration. Mech. Anal., {\bf 198}, 835--868, 2010].
1907.09829v3
2019-08-01
The $J$-method for the Gross-Pitaevskii eigenvalue problem
This paper studies the $J$-method of [E. Jarlebring, S. Kvaal, W. Michiels. SIAM J. Sci. Comput. 36-4:A1978-A2001, 2014] for nonlinear eigenvector problems in a general Hilbert space framework. This is the basis for variational discretization techniques and a mesh-independent numerical analysis. A simple modification of the method mimics an energy-decreasing discrete gradient flow. In the case of the Gross-Pitaevskii eigenvalue problem, we prove global convergence towards an eigenfunction for a damped version of the $J$-method. More importantly, when the iterations are sufficiently close to an eigenfunction, the damping can be switched off and we recover a local linear convergence rate previously known from the discrete setting. This quantitative convergence analysis is closely connected to the~$J$-method's unique feature of sensitivity with respect to spectral shifts. Contrary to classical gradient flows, this allows both the selective approximation of excited states as well as the amplification of convergence beyond linear rates in the spirit of the Rayleigh quotient iteration for linear eigenvalue problems. These advantageous convergence properties are demonstrated in a series of numerical experiments involving exponentially localized states under disorder potentials and vortex lattices in rotating traps.
1908.00333v2
2019-08-02
How do Conservative Backbone Curves Perturb into Forced Responses? A Melnikov Function Analysis
Weakly damped mechanical systems under small periodic forcing tend to exhibit periodic response in a close vicinity of certain periodic orbits of their conservative limit. Specifically, amplitude frequency plots for the conservative limit have often been noted, both numerically and experimentally, to serve as backbone curves for the near resonance peaks of the forced response. In other cases, such a relationship between the unforced and forced response was not observed. Here we provide a systematic mathematical analysis that predicts which members of conservative periodic orbit families will serve as backbone curves for the forced-damped response. We also obtain mathematical conditions under which approximate numerical and experimental approaches, such as energy balance and force appropriation, are justifiable. Finally, we derive analytic criteria for the birth of isolated response branches (isolas) whose identification is otherwise challenging from numerical continuation.
1908.00721v3
2019-08-05
Tunable strong coupling of two adjacent optical λ/2 Fabry-Pérot microresonators
Optical half-wave microresonators enable to control the optical mode density around a quantum system and thus to modify the temporal emission properties. If the coupling rate exceeds the damping rate, strong coupling between a microresonator and a quantum system can be achieved, leading to a coherent energy exchange and the creation of new hybrid modes. Here, we investigate strong coupling between two adjacent lambda/2 Fabry-P\'erot microresonators, where the resonance of one microresonator can be actively tuned across the resonance of the other microresonator. The transmission spectra of the coupled microresonators show a clear anticrossing behavior, which proves that the two cavity modes are strongly coupled. Additionally, we can vary the coupling rate by changing the resonator geometry and thereby investigate the basic principles of strong coupling with a well-defined model system. Finally, we will show that such a coupled system can theoretically be modelled by coupled damped harmonic oscillators.
1908.01566v1
2019-07-27
An extension of the second order dynamical system that models Nesterov's convex gradient method
In this paper we deal with a general second order continuous dynamical system associated to a convex minimization problem with a Fr\`echet differentiable objective function. We show that inertial algorithms, such as Nesterov's algorithm, can be obtained via the natural explicit discretization from our dynamical system. Our dynamical system can be viewed as a perturbed version of the heavy ball method with vanishing damping, however the perturbation is made in the argument of the gradient of the objective function. This perturbation seems to have a smoothing effect for the energy error and eliminates the oscillations obtained for this error in the case of the heavy ball method with vanishing damping, as some numerical experiments show. We prove that the value of the objective function in a generated trajectory converges in order O(1/t^2) to the global minimum of the objective function. Moreover, we obtain that a trajectory generated by the dynamical system converges to a minimum point of the objective function.
1908.02574v1
2019-08-07
Interfacial contributions to spin-orbit torque and magnetoresistance in ferromagnet/heavy-metal bilayers
The thickness dependence of spin-orbit torque and magnetoresistance in ferromagnet/heavy-metal bilayers is studied using the first-principles non-equilibrium Green's function formalism combined with the Anderson disorder model. A systematic expansion in orthogonal vector spherical harmonics is used for the angular dependence of the torque. The damping-like torque in Co/Pt and Co/Au bilayers can be described as a sum of the spin-Hall contribution, which increases with thickness in agreement with the spin-diffusion model, and a comparable interfacial contribution. The magnetoconductance in the plane perpendicular to the current in Co/Pt bilayers is of the order of a conductance quantum per interfacial atom, exceeding the prediction of the spin-Hall model by more than an order of magnitude. This suggests that the "spin-Hall magnetoresistance," similarly to the damping-like torque, has a large interfacial contribution unrelated to the spin-Hall effect.
1908.02680v2
2019-08-16
Dynamics of Hot Bose-Einstein Condensates: stochastic Ehrenfest relations for number and energy damping
Describing partially-condensed Bose gases poses a long-standing theoretical challenge. We present exact stochastic Ehrenfest relations for the stochastic projected Gross-Pitaevskii equation, including both number and energy damping mechanisms, and all projector terms that arise from the energy cutoff separating system from reservoir. We test the theory by applying it to the centre of mass fluctuations of a harmonically trapped prolate system, finding close agreement between c-field simulations and analytical results. The formalism lays the foundation to analytically explore experimentally accessible hot Bose-Einstein condensates.
1908.05809v3
2019-08-12
On a simple derivation of the very low damping escape rate for classical spins by modifying the method of Kramers
The original perturbative Kramers' method (starting from the phase space coordinates) (Kramers, 1940) of determining the energy-controlled-diffusion equation for Newtonian particles with separable and additive Hamiltonians is generalized to yield the energy-controlled diffusion equation and thus the very low damping (VLD) escape rate including spin-transfer torque for classical giant magnetic spins with two degrees of freedom. These have dynamics governed by the magnetic Langevin and Fokker-Planck equations and thus are generally based on non-separable and non-additive Hamiltonians. The derivation of the VLD escape rate directly from the (magnetic) Fokker-Planck equation for the surface distribution of magnetization orientations in the configuration space of the polar and azimuthal angles $(\vartheta, \varphi)$ is much simpler than those previously used.
1908.06747v1
2019-08-22
Improving the dynamics of quantum sensors with reinforcement learning
Recently proposed quantum-chaotic sensors achieve quantum enhancements in measurement precision by applying nonlinear control pulses to the dynamics of the quantum sensor while using classical initial states that are easy to prepare. Here, we use the cross-entropy method of reinforcement learning to optimize the strength and position of control pulses. Compared to the quantum-chaotic sensors with periodic control pulses in the presence of superradiant damping, we find that decoherence can be fought even better and measurement precision can be enhanced further by optimizing the control. In some examples, we find enhancements in sensitivity by more than an order of magnitude. By visualizing the evolution of the quantum state, the mechanism exploited by the reinforcement learning method is identified as a kind of spin-squeezing strategy that is adapted to the superradiant damping.
1908.08416v2
2019-08-28
Spin functional renormalization group for quantum Heisenberg ferromagnets: Magnetization and magnon damping in two dimensions
We use the spin functional renormalization group recently developed by two of us [J. Krieg and P. Kopietz, Phys. Rev. B $\bf{99}$, 060403(R) (2019)] to calculate the magnetization $M ( H , T )$ and the damping of magnons due to classical longitudinal fluctuations of quantum Heisenberg ferromagnets. In order to guarantee that for vanishing magnetic field $H \rightarrow 0$ the magnon spectrum is gapless when the spin rotational invariance is spontaneously broken, we use a Ward identity to express the magnon self-energy in terms of the magnetization. In two dimensions our approach correctly predicts the absence of long-range magnetic order for $H=0$ at finite temperature $T$. The magnon spectrum then exhibits a gap from which we obtain the transverse correlation length. We also calculate the wave-function renormalization factor of the magnons. As a mathematical by-product, we derive a recursive form of the generalized Wick theorem for spin operators in frequency space which facilitates the calculation of arbitrary time-ordered connected correlation functions of an isolated spin in a magnetic field.
1908.10753v2
2019-09-03
Learning Elastic Constitutive Material and Damping Models
Commonly used linear and nonlinear constitutive material models in deformation simulation contain many simplifications and only cover a tiny part of possible material behavior. In this work we propose a framework for learning customized models of deformable materials from example surface trajectories. The key idea is to iteratively improve a correction to a nominal model of the elastic and damping properties of the object, which allows new forward simulations with the learned correction to more accurately predict the behavior of a given soft object. Space-time optimization is employed to identify gentle control forces with which we extract necessary data for model inference and to finally encapsulate the material correction into a compact parametric form. Furthermore, a patch based position constraint is proposed to tackle the challenge of handling incomplete and noisy observations arising in real-world examples. We demonstrate the effectiveness of our method with a set of synthetic examples, as well with data captured from real world homogeneous elastic objects.
1909.01875v2
2019-09-06
Effect of Tantalum spacer thickness and deposition conditions on the properties of MgO/CoFeB/Ta/CoFeB/MgO free layers
To get stable perpendicularly magnetized tunnel junctions at small device dimensions, composite free layers that comprise two MgO/FeCoB interfaces as sources of interface anisotropy are generally used. Proper cristallisation and annealing robustness is typically ensured by the insertion of a spacer layer of the early transition metal series within the FeCoB layer. We study the influence of the spacer thickness and growth condition on the switching metrics of tunnel junctions thermally annealed at 400$^\circ$C for the case of 1-4 \r{A} Ta spacers. Thick Ta spacer results in a large anisotropies indicative of a better defined top FeCoB/MgO interface, but this is achieved at the systematic expense of a stronger damping. For the best anisotropy-damping compromise, junctions of diameter 22 nm can still be stable and spin-torque switched. Coercivity and inhomogeneous linewidth broadening, likely arising from roughness at the FeCoB/Ta interface, can be reduced if a sacrificial Mg layer is inserted before the Ta spacer deposition.
1909.02741v1
2019-09-19
Blow-up for Strauss type wave equation with damping and potential
We study a kind of nonlinear wave equations with damping and potential, whose coefficients are both critical in the sense of the scaling and depend only on the spatial variables. Based on the earlier works, one may think there are two kinds of blow-up phenomenons when the exponent of the nonlinear term is small. It also means there are two kinds of law to determine the critical exponent. In this paper, we obtain a blow-up result and get the estimate of the upper bound of the lifespan in critical and sub-critical cases. All of the results support such a conjecture, although for now, the existence part is still open.
1909.08885v3
2019-09-23
Inference of modes for linear stochastic processes
For dynamical systems that can be modelled as asymptotically stable linear systems forced by Gaussian noise, this paper develops methods to infer or estimate their modes from observations in real time. The modes can be real or complex. For a real mode, we wish to infer its damping rate and mode shape. For a complex mode, we wish to infer its frequency, damping rate and (complex) mode shape. Their amplitudes and correlations are encoded in a mode covariance matrix. The work is motivated and illustrated by the problem of detection of oscillations in power flow in AC electrical networks. Suggestions of other applications are given.
1909.10247v2
2019-10-02
Exponential stability for the nonlinear Schrödinger equation with locally distributed damping
In this paper, we study the defocusing nonlinear Schr\"{o}dinger equation with a locally distributed damping on a smooth bounded domain as well as on the whole space and on an exterior domain. We first construct approximate solutions using the theory of monotone operators. We show that approximate solutions decay exponentially fast in the $L^2$-sense by using the multiplier technique and a unique continuation property. Then, we prove the global existence as well as the $L^2$-decay of solutions for the original model by passing to the limit and using a weak lower semicontinuity argument, respectively. The distinctive feature of the paper is the monotonicity approach, which makes the analysis independent from the commonly used Strichartz estimates and allows us to work without artificial smoothing terms inserted into the main equation. We, in addition, implement a precise and efficient algorithm for studying the exponential decay established in the first part of the paper numerically. Our simulations illustrate the efficacy of the proposed control design.
1910.00921v1
2019-10-07
Quantum mechanics at high redshift -- Modelling Damped Lyman-$α$ absorption systems
For around 100 years, hydrogen spectral modelling has been based on Voigt profile fitting. The semi-classical Voigt profile is based on a 2-level atom approximation. Whilst the Voigt profile is excellent for many circumstances, the accuracy is insufficient for very high column density damped Lyman-$\alpha$ absorption systems. We have adapted the quantum-mechanical Kramers-Heisenberg model to include thermal broadening, producing a new profile, the KHT profile. Interactions involving multiple discrete atomic levels and continuum terms, not accounted for in the Voigt model, generate asymmetries in the Lyman line wings. If not modelled, this can lead to significant systematics in parameter estimation when modelling real data. There are important ramifications in particular for measurements of the primordial deuterium abundance. However, the KHT model is complicated. We therefore present a simplified formulation based on Taylor series expansions and look-up tables, quantifying the impact of the approximations made. The KHT profile has been implemented within the widely-used VPFIT code.
1910.02913v2
2019-10-12
Almost Global Solutions to the Three-dimensional Isentropic Inviscid Flows with Damping in Physical Vacuum Around Barenlatt Solutions
For the three-dimensional vacuum free boundary problem with physical singularity that the sound speed is $C^{ {1}/{2}}$-H$\ddot{\rm o}$lder continuous across the vacuum boundary of the compressible Euler equations with damping, without any symmetry assumptions, we prove the almost global existence of smooth solutions when the initial data are small perturbations of the Barenblatt self-similar solutions to the corresponding porous media equations simplified via Darcy's law. It is proved that if the initial perturbation is of the size of $\epsilon$, then the existing time for smooth solutions is at least of the order of $\exp(\epsilon^{-2/3})$. The key issue for the analysis is the slow {\em sub-linear} growth of vacuum boundaries of the order of $t^{1/(3\gamma-1)}$, where $\gamma>1$ is the adiabatic exponent for the gas. This is in sharp contrast to the currently available global-in-time existence theory of expanding solutions to the vacuum free boundary problems with physical singularity of compressible Euler equations for which the expanding rate of vacuum boundaries is linear. The results obtained in this paper is closely related to the open question in multiple dimensions since T.-P. Liu's construction of particular solutions in 1996 .
1910.05516v1
2019-10-15
Nonlocal quantum correlations under amplitude damping decoherence
Different nonlocal quantum correlations of entanglement, steering and Bell nonlocality are defined with the help of local hidden state (LHS) and local hidden variable (LHV) models. Considering their unique roles in quantum information processing, it is of importance to understand the individual nonlocal quantum correlation as well as their relationship. Here, we investigate the effects of amplitude damping decoherence on different nonlocal quantum correlations. In particular, we have theoretically and experimentally shown that the entanglement sudden death phenomenon is distinct from those of steering and Bell nonlocality. In our scenario, we found that all the initial states present sudden death of steering and Bell nonlocality, while only some of the states show entanglement sudden death. These results suggest that the environmental effect can be different for different nonlocal quantum correlations, and thus, it provides distinct operational interpretations of different quantum correlations.
1910.06483v1
2019-10-17
The linearly damped nonlinear Schrödinger equation with localized driving: spatiotemporal decay estimates and the emergence of extreme wave events
We prove spatiotemporal algebraically decaying estimates for the density of the solutions of the linearly damped nonlinear Schr\"odinger equation with localized driving, when supplemented with vanishing boundary conditions. Their derivation is made via a scheme, which incorporates suitable weighted Sobolev spaces and a time-weighted energy method. Numerical simulations examining the dynamics (in the presence of physically relevant examples of driver types and driving amplitude/linear loss regimes), showcase that the suggested decaying rates, are proved relevant in describing the transient dynamics of the solutions, prior their decay: they support the emergence of waveforms possessing an algebraic space-time localization (reminiscent of the Peregrine soliton) as first events of the dynamics, but also effectively capture the space-time asymptotics of the numerical solutions.
1910.08425v2
2019-10-24
Gapless and gapped holographic phonons
We study a holographic model where translations are both spontaneously and explicitly broken, leading to the presence of (pseudo)-phonons in the spectrum. The weak explicit breaking is due to two independent mechanisms: a small source for the condensate itself and additional linearly space-dependent marginal operators. The low energy dynamics of the model is described by Wigner crystal hydrodynamics. In absence of a source for the condensate, the phonons remain gapless, but momentum is relaxed. Turning on a source for the condensate damps and pins the phonons. Finally, we verify that the universal relation between the phonon damping rate, mass and diffusivity reported in arXiv:1812.08118 continues to hold in this model for weak enough explicit breaking.
1910.11330v2
2019-11-06
High spin mixing conductance and spin interface transparency at $Co_2Fe_{0.4}Mn_{0.6}Si$ Heusler alloy and Pt interface
Ferromagnetic materials exhibiting low magnetic damping ($\alpha$) and moderately high saturation magnetization are required from the viewpoints of generation, transmission and detection of spin wave. Since spin-to-charge conversion efficiency is another important parameter, high spin mixing conductance ($g_{r}^{\uparrow \downarrow}$) is the key for efficient spin-to-charge conversion. Full Heusler alloys e.g. $Co_2Fe_{0.4}Mn_{0.6}Si$ (CFMS), which are predicted to be 100$\%$ spin polarized, possess low $\alpha$. However, the $g_{r}^{\uparrow \downarrow}$ at the interface between CFMS and a paramagnet has not fully been understood. Here, we report the investigations of spin pumping and inverse spin Hall effect in $CFMS/Pt$ bilayers. Damping analysis indicates the presence of significant spin pumping at the interface of CFMS and Pt, which is also confirmed by the detection of inverse spin Hall voltage. We show that in CFMS/Pt the $g_{r}^{\uparrow \downarrow}$ (1.77$\times$10$^{20}$m$^{-2}$) and interface transparency (84$\%$) are higher compared to values reported for other ferromagnet/heavy metal systems.
1911.02230v1
2019-11-10
Influence of resonances on the noise performance of SQUID susceptometers
Scanning Superconducting Quantum Interference Device (SQUID) Susceptometry simultaneously images the local magnetic fields and susceptibilities above a sample with sub-micron spatial resolution. Further development of this technique requires a thorough understanding of the current, voltage, and flux characteristics of scanning SQUID susceptometers. These sensors often have striking anomalies in their current-voltage characteristics, which we believe to be due to electromagnetic resonances. The effect of these resonances on the performance of these SQUIDs is unknown. To explore the origin and impact of the resonances, we have developed a model that qualitatively reproduces the experimentally-determined current-voltage characteristics of our scanning SQUID susceptometers. We use this model to calculate the noise characteristics of SQUIDs of different designs. We find that the calculated ultimate flux noise is better in susceptometers with damping resistors that diminish the resonances than susceptometers without damping resistors. Such calculations will enable the optimization of the signal-to-noise characteristics of scanning SQUID susceptometers.
1911.03836v2
2019-11-13
Impact of the crystal orientation on spin-orbit torques in Fe/Pd bilayers
Spin-orbit torques in ferromagnetic (FM)/non-magnetic (NM) heterostructures offer more energy-efficient means to realize spin-logic devices; however, their strengths are determined by the heterostructure interface. This work examines crystal orientation impact on the spin-orbit torque efficiency in different Fe/Pd bilayer systems. Spin torque ferromagnetic measurements evidence that the damping-like torque efficiency is higher in epitaxial than in polycrystalline bilayer structures while the field-like torque is negligible in all bilayer structures. The strength of the damping-like torque decreases with deterioration of the bilayer epitaxial quality. The present finding provides fresh insight for the enhancement of spin-orbit torques in magnetic heterostructures.
1911.05487v1
2019-12-02
Boundary input-to-state stabilization of a damped Euler-Bernoulli beam in the presence of a state-delay
This paper is concerned with the point torque boundary feedback stabilization of a damped Euler-Bernoulli beam model in the presence of a time-varying state-delay. First, a finite-dimensional truncated model is derived by spectral reduction. Then, for a given stabilizing state-feedback of the delay-free truncated model, an LMI-based sufficient condition on the maximum amplitude of the state-delay is employed to guarantee the stability of the closed-loop state-delayed truncated model. Second, we assess the exponential stability of the resulting closed-loop infinite-dimensional system under the assumption that the number of modes of the original infinite-dimensional system captured by the truncated model has been selected large enough. Finally, we consider in our control design the possible presence of a distributed perturbation, as well as additive boundary perturbations in the control inputs. In this case, we derive for the closed-loop system an exponential input-to-state estimate with fading memory of the distributed and boundary disturbances.
1912.01117v1
2019-12-03
The noise fluxes produced by the degree of first-order temporal coherence in a single mode class-A laser amplifier
The noise feature of a single mode class-A laser is investigated in the presence (amplifier) and absence (free-running) of an input signal. The Maxwell-Bloch equations of motion have been solved after adding the cavity Langevin force to calculate fluctuations that imposed to the atomic population inversion and the amplitude and phase of cavity electric field. The correlation function of these fluctuations is then used to derive the spontaneous emission, amplitude, and phase noise fluxes in the below and above-threshold states. The bandwidth of noise fluxes is not only adjusted by the amplitude and frequency detuning of input signal, but also by the laser pumping and cavity damping rates. On the other hand, the degree of first-order temporal coherence (DFOTC) is turned out as the correlation function of the amplitude fluctuation so that its Fourier transform led to the amplitude noise flux. The coherence time plays a dual role in order that it is equal to the damping rate invers of DFOTC and at the same time has an uncertainty relation with the bandwidth of amplitude noise flux. Finally, the flux conservation requires a balance between the input pumping noise flux and the output amplitude and spontaneous emission noise fluxes.
1912.01485v1
2019-12-05
A Fast Implementation for the Canonical Polyadic Decomposition
A new implementation of the canonical polyadic decomposition (CPD) is presented. It features lower computational complexity and memory usage than the available state of art implementations available. The CPD of tensors is a challenging problem which has been approached in several manners. Alternating least squares algorithms were used for a long time, but they convergence properties are limited. Nonlinear least squares (NLS) algorithms - more precisely, damped Gauss-Newton (dGN) algorithms - are much better in this sense, but they require inverting large Hessians, and for this reason there is just a few implementations using this approach. In this paper, we propose a fast dGN implementation to compute the CPD. In this paper, we make the case to always compress the tensor, and propose a fast damped Gauss-Newton implementation to compute the canonical polyadic decomposition.
1912.02366v1
2019-12-05
Damping of spinful excitons in LaCoO$_3$ by thermal fluctuations: Theory and experiment
We present Co $L_3$-edge resonant inelastic x-ray scattering (RIXS) of bulk LaCoO$_3$ across the thermally-induced spin-state crossover around 100~K. Owing to a high energy resolution of 25~meV, we observe unambiguously the dispersion of the intermediate-spin (IS) excitations in the low temperature regime. Approaching the intermediate temperature regime, the IS excitations are damped and the bandwidth is reduced. The observed behavior can be well described by a model of mobile IS excitons with strong attractive interaction, which we solve using dynamical mean-field theory for hard-core bosons. Our results provide a detailed mechanism of how high-spin (HS) and IS excitations interact to establish the physical properties of cobaltite perovskites.
1912.02564v3
2019-12-09
High Frequency Sound in a Unitary Fermi Gas
We present an experimental and theoretical study of the phonon mode in a unitary Fermi gas. Using two-photon Bragg spectroscopy, we measure excitation spectra at a momentum of approximately half the Fermi momentum, both above and below the superfluid critical temperature $T_\mathrm{c}$. Below $T_\mathrm{c}$, the dominant excitation is the Bogoliubov-Anderson (BA) phonon mode, driven by gradients in the phase of the superfluid order parameter. The temperature dependence of the BA phonon is consistent with a theoretical model based on the quasiparticle random phase approximation in which the dominant damping mechanism is via collisions with thermally excited quasiparticles. As the temperature is increased above $T_\mathrm{c}$, the phonon evolves into a strongly damped collisional mode, accompanied by an abrupt increase in spectral width. Our study reveals strong similarities between sound propagation in the unitary Fermi gas and liquid helium.
1912.03830v1
2019-12-10
Stability of traveling waves in a driven Frenkel-Kontorova model
In this work we revisit a classical problem of traveling waves in a damped Frenkel-Kontorova lattice driven by a constant external force. We compute these solutions as fixed points of a nonlinear map and obtain the corresponding kinetic relation between the driving force and the velocity of the wave for different values of the damping coefficient. We show that the kinetic curve can become non-monotone at small velocities, due to resonances with linear modes, and also at large velocities where the kinetic relation becomes multivalued. Exploring the spectral stability of the obtained waveforms, we identify, at the level of numerical accuracy of our computations, a precise criterion for instability of the traveling wave solutions: monotonically decreasing portions of the kinetic curve always bear an unstable eigendirection. We discuss why the validity of this criterion in the {\it dissipative} setting is a rather remarkable feature offering connections to the Hamiltonian variant of the model and of lattice traveling waves more generally. Our stability results are corroborated by direct numerical simulations which also reveal the possible outcomes of dynamical instabilities.
1912.05052v2
2019-12-11
Quasinormal Modes of Charged Fields in Reissner-Nordstrom Backgrounds by Borel-Pade Summation of Bender-Wu Series
We extend recent work of Hatsuda on the computation of quasinormal mode frequencies via analytic continuation of bound state energies and Borel-Pade resummation of the Bender-Wu perturbation series to the case of charged fields in the background of Reissner-Nordstrom black holes. We compare the quasinormal mode frequencies obtained in this manner to calculations using Leaver's method of continued fractions, and find good agreement for damped modes (DMs) with imaginary part remaining finite in the extremal limit. We also present numerical evidence that the frequencies of certain zero-damped modes (ZDMs) with imaginary part tending to zero in the extremal limit can be computed when constructing the Bender-Wu expansion about a peak of the potential inside the outer horizon of the black hole.
1912.05553v2
2019-12-19
On twin peak quasi-periodic oscillations resulting from the interaction between discoseismic modes and turbulence in accretion discs around black holes
Given the peculiar and (in spite of many efforts) unexplained quasi-periodic oscillation (QPO) twin peak phenomena in accretion disc PSD observations, the present exploratory analytical article tries to inquire deeper into the relationship between discoseismic modes and the underlying driving turbulence in order to assess its importance. We employ a toy model in the form of a Gaussian white noise driven damped harmonic oscillator with stochastic frequency. This oscillator represents the discoseismic mode. (Stochastic damping was also considered, but interestingly found to be less relevant for the case at hand.) In the context of this model, we find that turbulence interacts with disc oscillations in interesting ways. In particular, the stochastic part in the oscillator frequency behaves as a separate driving agent. This gives rise to 3:2 twin peaks for some values of the physical parameters, which we find. We conclude with the suggestion that the study of turbulence be brought to the forefront of disc oscillation dynamics, as opposed to being a mere background feature. This change of perspective carries immediate observable consequences, such as considerably shifting the values of the (discoseismic) oscillator frequencies.
1912.09527v1
2019-12-28
Non-linear damping of superimposed primordial oscillations on the matter power spectrum in galaxy surveys
Galaxy surveys are an important probe for superimposed oscillations on the primordial power spectrum of curvature perturbations, which are predicted in several theoretical models of inflation and its alternatives. In order to exploit the full cosmological information in galaxy surveys it is necessary to study the matter power spectrum to fully non-linear scales. We therefore study the non-linear clustering in models with superimposed linear and logarithmic oscillations to the primordial power spectrum by running high-resolution dark-matter-only N-body simulations. We fit a Gaussian envelope for the non-linear damping of superimposed oscillations in the matter power spectrum to the results of the N-body simulations for $k \lesssim 0.6\ h/$Mpc at $0 \leq z \leq 5$ with an accuracy below the percent. We finally use this fitting formula to forecast the capabilities of future galaxy surveys, such as Euclid and Subaru, to probe primordial oscillation down to non-linear scales alone and in combination with the information contained in CMB anisotropies.
1912.12499v3
2020-01-04
Finite Difference/Galerkin Finite Element Simulation of the Semi-Linear Wave Equation with Scale-Invariant Damping and Mass and Power Non-Linearity
This study is concern with the numerical solution of the initial boundary value problem (IBVP) for the semilinear scale-invariant wave equation with damping and mass and power non-linearity. Numerical results of the aforementioned IBVP is obtained by using standart Galerkin finite element method (GFEM) for the spatial variable and the temporal variable is discretized with the finite difference method (FDM). The FDM is also used for the discretization of the spatial variable for the accuracy of the numerical results. The obtained numerical results with different numerical schemes are observed compatible. Numerical simulation of the considered problem is given for the different initial conditions.
2001.01075v2
2020-01-05
Quantifying quantum non-Markovianity based on quantum coherence via skew information
Based on the nonincreasing property of quantum coherence via skew information under incoherent completely positive and trace-preserving maps, we propose a non-Markovianity measure for open quantum processes. As applications, by applying the proposed measure to some typical noisy channels, we find that it is equivalent to the three previous measures of non-Markovianity for phase damping and amplitude damping channels, i.e., the measures based on the quantum trace distance, dynamical divisibility, and quantum mutual information. For the random unitary channel, it is equivalent to the non-Markovianity measure based on $l_1$ norm of coherence for a class of output states and it is incompletely equivalent to the measure based on dynamical divisibility. We also use the modified Tsallis relative $\alpha$ entropy of coherence to detect the non-Markovianity of dynamics of quantum open systems, the results show that the modified Tsallis relative $\alpha$ entropy of coherence are more comfortable than the original Tsallis relative $\alpha$ entropy of coherence for small $\alpha$.
2001.01261v1
2020-01-07
von Neumann entropy and the entropy production of a damped harmonic oscillator
In this paper we analyze the entropy and entropy production of a non-isolated quantum system described within the quantum Brownian motion framework. This is a very general and paradigmatic framework for describing non-isolated quantum systems and can be used in any kind of coupling regime. We start by considering the application of von Neumann entropy to an arbitrarily damped quantum system making use of its reduced density operator. We argue that this application is formally valid and develop a path integral method to evaluate that quantity analytically. We apply this technique to a harmonic oscillator in contact with a heat bath and obtain an exact form for its entropy. Then we study the entropy production of this system and enlighten important characteristics of its thermodynamical behavior on the pure quantum realm and also address their transition to the classical limit.
2001.02261v1
2020-01-09
Photon correlation measurements of stochastic limit cycles emerging from high-$Q$ nonlinear silicon photonic crystal microcavities
We performed measurements of photon correlation [$g^{(2)}(\tau)$] in driven nonlinear high-$Q$ silicon (Si) photonic crystal (PhC) microcavities. The measured $g^{(2)}(\tau)$ exhibits a damped oscillatory behavior when input pump power exceeds a critical value. From comparison between experiments and simulations, we attribute the measured oscillation of $g^{(2)}(\tau)$ to self-pulsing (a limit cycle) emerging from an interplay between photon, carrier, and thermal dynamics. Namely, the oscillation frequency of $g^{(2)}(\tau)$ corresponds to the oscillation period of the limit cycle, while its finite coherence (damping) time originates from the stochastic nature of the limit cycle. From the standpoint of phase reduction theory, we interpret the measured coherence time of $g^{(2)}(\tau)$ as the coherence (diffusion) time of a generalized phase of the limit cycle. Furthermore, we show that an increase in laser input power enhances the coherence time of $g^{(2)}(\tau)$ up to the order of microseconds, which could be a demonstration of the stabilization of a stochastic limit cycle through pumping.
2001.02838v2
2020-01-12
Linear programming bounds for quantum amplitude damping codes
Given that approximate quantum error-correcting (AQEC) codes have a potentially better performance than perfect quantum error correction codes, it is pertinent to quantify their performance. While quantum weight enumerators establish some of the best upper bounds on the minimum distance of quantum error-correcting codes, these bounds do not directly apply to AQEC codes. Herein, we introduce quantum weight enumerators for amplitude damping (AD) errors and work within the framework of approximate quantum error correction. In particular, we introduce an auxiliary exact weight enumerator that is intrinsic to a code space and moreover, we establish a linear relationship between the quantum weight enumerators for AD errors and this auxiliary exact weight enumerator. This allows us to establish a linear program that is infeasible only when AQEC AD codes with corresponding parameters do not exist. To illustrate our linear program, we numerically rule out the existence of three-qubit AD codes that are capable of correcting an arbitrary AD error.
2001.03976v1
2020-01-22
Small data blow-up for the wave equation with a time-dependent scale invariant damping and a cubic convolution for slowly decaying initial data
In the present paper, we study the Cauchy problem for the wave equation with a time-dependent scale invariant damping, i.e.$\frac{2}{1+t}\partial_t v$ and a cubic convolution $(|x|^{-\gamma}*v^2)v$ with $\gamma\in (0,n)$, where $v=v(x,t)$ is an unknown function on $\mathbb{R}^n\times[0,T)$. Our aim of the present paper is to prove a small data blow-up result and show an upper estimate of lifespan of the problem for slowly decaying positive initial data $(v(x,0),\partial_t v(x,0))$ such as $\partial_t v(x,0)=O(|x|^{-(1+\nu)})$ as $|x|\rightarrow\infty$. Here $\nu$ belongs to the scaling supercritical case $\nu<\frac{n-\gamma}{2}$. Our main new contribution is to estimate the convolution term in high spatial dimensions, i.e. $n\ge 4$. This paper is the first blow-up result to treat wave equations with the cubic convolution in high spatial dimensions ($n\ge 4$).
2001.07985v1
2020-01-22
Testing a Quantum Error-Correcting Code on Various Platforms
Quantum error correction plays an important role in fault-tolerant quantum information processing. It is usually difficult to experimentally realize quantum error correction, as it requires multiple qubits and quantum gates with high fidelity. Here we propose a simple quantum error-correcting code for the detected amplitude damping channel. The code requires only two qubits. We implement the encoding, the channel, and the recovery on an optical platform, the IBM Q System, and a nuclear magnetic resonance system. For all of these systems, the error correction advantage appears when the damping rate exceeds some threshold. We compare the features of these quantum information processing systems used and demonstrate the advantage of quantum error correction on current quantum computing platforms.
2001.07998v1
2020-01-22
Dynamic state reconstruction of quantum systems subject to pure decoherence
The article introduces efficient quantum state tomography schemes for qutrits and entangled qubits subject to pure decoherence. We implement the dynamic state reconstruction method for open systems sent through phase-damping channels which was proposed in: Open Syst. Inf. Dyn. 23, 1650019 (2016). In the current article we prove that two distinct observables measured at four different time instants suffice to reconstruct the initial density matrix of a qutrit with evolution given by a phase-damping channel. Furthermore, we generalize the approach in order to determine the optimal criteria for quantum tomography of entangled qubits. Finally, we prove two universal theorems concerning the minimal number of distinct observables required for quantum tomography of qudits. We believe that dynamic state reconstruction schemes bring significant advancement and novelty to quantum tomography since they allow to reduce the number of distinct measurements required to solve the problem, which is important from the experimental point of view.
2001.08167v1
2020-01-28
Rate of Estimation for the Stationary Distribution of Stochastic Damping Hamiltonian Systems with Continuous Observations
We study the problem of the non-parametric estimation for the density $\pi$ of the stationary distribution of a stochastic two-dimensional damping Hamiltonian system $(Z_t)_{t\in[0,T]}=(X_t,Y_t)_{t \in [0,T]}$. From the continuous observation of the sampling path on $[0,T]$, we study the rate of estimation for $\pi(x_0,y_0)$ as $T \to \infty$. We show that kernel based estimators can achieve the rate $T^{-v}$ for some explicit exponent $v \in (0,1/2)$. One finding is that the rate of estimation depends on the smoothness of $\pi$ and is completely different with the rate appearing in the standard i.i.d.\ setting or in the case of two-dimensional non degenerate diffusion processes. Especially, this rate depends also on $y_0$. Moreover, we obtain a minimax lower bound on the $L^2$-risk for pointwise estimation, with the same rate $T^{-v}$, up to $\log(T)$ terms.
2001.10423v1
2020-01-28
Image polaritons in boron nitride for extreme polariton confinement with low losses
Polaritons in two-dimensional materials provide extreme light confinement that is difficult to achieve with metal plasmonics. However, such tight confinement inevitably increases optical losses through various damping channels. Here we demonstrate that hyperbolic phonon polaritons in hexagonal boron nitride can overcome this fundamental trade-off. Among two observed polariton modes, featuring a symmetric and antisymmetric charge distribution, the latter exhibits lower optical losses and tighter polariton confinement. Far-field excitation and detection of this high-momenta mode becomes possible with our resonator design that can boost the coupling efficiency via virtual polariton modes with image charges that we dub image polaritons. Using these image polaritons, we experimentally observe a record-high effective index of up to 132 and quality factors as high as 501. Further, our phenomenological theory suggests an important role of hyperbolic surface scattering in the damping process of hyperbolic phonon polaritons.
2001.10583v2
2020-02-06
Fractional derivative order determination from harmonic oscillator damping factor
This article analysis differential equations which represents damped and fractional oscillators. First, it is shown that prior to using physical quantities in fractional calculus, it is imperative that they are turned dimensionless. Afterwards, approximated expressions that relate the two equations parameters for the case that the fractional order is close to an integer number are presented. Following, a numerical regression is made using power series expansion, and, also from fractional calculus, the fact that both equations cannot be equivalent is concluded. In the end, from the numerical regression data, the analytical approximated expressions that relate the two equations' parameters are refined.
2002.02479v1
2020-02-11
A numerical damped oscillator approach to constrained Schrödinger equations
This article explains and illustrates the use of a set of coupled dynamical equations, second order in a fictitious time, which converges to solutions of stationary Schr\"{o}dinger equations with additional constraints. We include three qualitative different numerical examples: the radial Schr\"{o}dinger equation for the hydrogen atom; the two-dimensional harmonic oscillator with degenerate excited states; and finally a non-linear Schr\"{o}dinger equation for rotating states. The presented method is intuitive, with analogies in classical mechanics for damped oscillators, and easy to implement, either in own coding, or with software for dynamical systems. Hence, we find it suitable to introduce it in a continuation course in quantum mechanics or generally in applied mathematics courses which contain computational parts.
2002.04400v2
2020-02-12
Fast computation of optimal damping parameters for linear vibrational systems
We formulate the quadratic eigenvalue problem underlying the mathematical model of a linear vibrational system as an eigenvalue problem of a diagonal-plus-low-rank matrix $A$. The eigenvector matrix of $A$ has a Cauchy-like structure. Optimal viscosities are those for which $trace(X)$ is minimal, where $X$ is the solution of the Lyapunov equation $AX+XA^{*}=GG^{*}$. Here $G$ is a low-rank matrix which depends on the eigenfrequencies that need to be damped. After initial eigenvalue decomposition of linearized problem which requires $O(n^3)$ operations, our algorithm computes optimal viscosities for each choice of external dampers in $O(n^2)$ operations, provided that the number of dampers is small. Hence, the subsequent optimization is order of magnitude faster than in the standard approach which solves Lyapunov equation in each step, thus requiring $O(n^3)$ operations. Our algorithm is based on $O(n^2)$ eigensolver for complex symmetric diagonal-plus-rank-one matrices and fast $O(n^2)$ multiplication of linked Cauchy-like matrices.
2002.04917v2
2020-02-13
Low-loss two-dimensional plasmon modes in antimonene
The effects of spin-orbit (SOC) and electron-phonon coupling on the collective excitation of doped monolayer Sb$_2$ are investigated using density functional and many-body perturbation theories. The spin-orbit coupling is exclusively important for the monolayer Sb$_2$ and it leads to the reconstruction of the electronic band structure. In particular, plasmon modes of monolayer Sb$_2$ are quite sensitive to the SOC and are characterized by very low damping rates owing to small electron-phonon scatterings. Our results show plasmons in antimonene are significantly less damped compared to monolayer graphene when plasmon energies are $\hbar \omega> 0.2$ eV due to smaller plasmon-phonon coupling in the former material.
2002.05302v1
2020-02-13
Quantization of the damped harmonic oscillator based on a modified Bateman Lagrangian
An approach to quantization of the damped harmonic oscillator (DHO) is developed on the basis of a modified Bateman Lagrangian (MBL); thereby some quantum mechanical aspects of the DHO are clarified. We treat the energy operator for the DHO, in addition to the Hamiltonian operator that is determined from the MBL and corresponds to the total energy of the system. It is demonstrated that the energy eigenvalues of the DHO exponentially decrease with time and that transitions between the energy eigenstates occur in accordance with the Schr\"{o}dinger equation. Also, it is pointed out that a new critical parameter discriminates different behaviours of transition probabilities.
2002.05435v1
2020-02-17
Charge Transfer Through Redox Molecular Junctions in Non-Equilibrated Solvents
Molecular conduction operating in dielectric solvent environments are often described using kinetic rates based on Marcus theory of electron transfer at a molecule-metal electrode interface. However, the successive nature of charge transfer in such system implies that the solvent does not necessarily reach equilibrium in such process. Here we generalize the theory to account for solvent nonequilibrium and consider a molecular junction consisting of an electronic donor-acceptor system coupled to two metallic electrodes and placed in a polarizable solvent. We determine the nonequilbrium distribution of the solvent by solving diffusion equations in the strong- and weak-friction limits and calculate the charge current and its fluctuating behavior. In extreme limits: the absence of the solvent or fast solvent relaxation, the charge transfer statistics is Poissonian, while it becomes correlated by the dynamic solvent in between these limits. A Kramers-like turnover of the nonequilibrium current as a function of the solvent damping is found. Finally, we propose a way to tune the solvent-induced damping using geometrical control of the solvent dielectric response in nanostructured solvent channels.
2002.06932v1
2020-02-19
Diagnostics of plasma ionisation using torsional Alfén waves
Using the recently observed torsional Alfv\'en waves in solar prominences, we determine the ionisation state of the plasma by taking into account that Alfv\'en waves propagate in a partially ionised prominence plasma. We derive the evolutionary equation of waves and compare the analytical solutions to observations to determine the number density of neutrals. Using a single fluid plasma approximation, where the wave damping is provided by the Cowling resistivity, we study the temporal evolution of waves. By comparing the solution of equations with observational data (period, amplitude, propagation speed), we determined the value of the Cowling resistivity that led us to draw a conclusion on the amount of neutrals in the partially ionised plasma, a quantity that cannot be measured directly or indirectly. Our results show that damped torsional Alfv\'en waves are an ideal diagnostic tool for the ionisation state of the plasma. Using a simple model, we find that at the observational temperature of torsional Alfv\'en waves, the number of neutrals is of the order of $5\times 10^{10}$ cm$^{-3}$.
2002.08441v1
2020-03-01
Optimal Oscillation Damping Control of cable-Suspended Aerial Manipulator with a Single IMU Sensor
This paper presents a design of oscillation damping control for the cable-Suspended Aerial Manipulator (SAM). The SAM is modeled as a double pendulum, and it can generate a body wrench as a control action. The main challenge is the fact that there is only one onboard IMU sensor which does not provide full information on the system state. To overcome this difficulty, we design a controller motivated by a simplified SAM model. The proposed controller is very simple yet robust to model uncertainties. Moreover, we propose a gain tuning rule by formulating the proposed controller in the form of output feedback linear quadratic regulation problem. Consequently, it is possible to quickly dampen oscillations with minimal energy consumption. The proposed approach is validated through simulations and experiments.
2003.00472v1
2020-03-06
Accelerating the Convergence of Higher-Order Coupled Cluster Methods II: Coupled Cluster $Λ$ Equations and Dynamic Damping
The method of sub-iteration, which was previously applied to the higher-order coupled cluster amplitude equations, is extended to the case of the coupled cluster $\Lambda$ equations. The sub-iteration procedure for the $\Lambda$ equations is found to be highly similar to that for the amplitude equations, and to exhibit a similar improvement in rate of convergence relative to extrapolation of all $\hat{T}$ or $\hat{\Lambda}$ amplitudes using DIIS. A method of dynamic damping is also presented which is found to effectively recover rapid convergence in the case of oscillatory behavior in the amplitude or $\Lambda$ equations. Together, these techniques allow for the convergence of both the amplitude and $\Lambda$ equations necessary for the calculation of analytic gradients and properties of higher-order coupled cluster methods without the high memory or disk I/O cost of full DIIS extrapolation.
2003.03455v1
2020-03-09
Forces between Silica Particles in Isopropanol Solutions of 1:1 Electrolytes
Interactions between silica surfaces across isopropanol solutions are measured with colloidal probe technique based on atomic force microscope. In particular, the influence of 1:1 electrolytes on the interactions between silica particles is investigated. A plethora of different forces are found in these systems. Namely, van der Waals, double-layer, attractive non-DLVO, repulsive solvation, and damped oscillatory interactions are observed. The measured decay length of the double-layer repulsion is substantially larger than Debye lengths calculated from nominal salt concentrations. These deviations are caused by pronounced ion pairing in alcohol solutions. At separation below 10 nm, additional attractive and repulsive non-DLVO forces are observed. The former are possibly caused by charge heterogeneities induced by strong ion adsorption, whereas the latter originate from structuring of isopropanol molecules close to the surface. Finally, at increased concentrations the transition from monotonic to damped oscillatory interactions is uncovered.
2003.04058v2
2020-03-13
Energy localization and transfer in autoresonant weakly dissipative anharmonic chains
In this work, we develop an analytical framework to explain the influence of dissipation and detuning parameters on the emergence and stability of autoresonance in a strongly nonlinear weakly damped chain subjected to harmonic forcing with a slowly-varying frequency. Using the asymptotic procedures, we construct the evolutionary equations, which describe the behavior of the array under the condition of 1:1 resonance and then approximately compute the slow amplitudes and phases as well as the duration of autoresonance. It is shown that, in contrast to autoresonance in a non-dissipative chain with unbounded growth of energy, the energy in a weakly damped array being initially at rest is growing only in a bounded time interval up to an instant of simultaneous escape from resonance of all autoresonant oscillators. Analytical conditions of the emergence and stability of autoresonance are confirmed by numerical simulations.
2003.06346v1