Weak Dissipation Research Articles

Photon statistics on the extreme entanglement.

The effects of photon bunching and antibunching correspond to the classical and quantum features of the electromagnetic field, respectively. No direct evidence suggests whether these effects can be potentially related to quantum entanglement. Here we design a cavity quantum electrodynamics model with two atoms trapped in to demonstrate the connections between the steady-state photon statistics and the two-atom entanglement. It is found that within the weak dissipations and to some good approximation, the local maximal two-atom entanglements perfectly correspond to not only the quantum feature of the electromagnetic field—the optimal photon antibunching, but also the classical feature—the optimal photon bunching. We also analyze the influence of strong dissipations and pure dephasing. An intuitive physical understanding is also given finally.

Riverine skin temperature response to subsurface processes in low wind speeds

AbstractBoth surface and subsurface processes modulate the surface thermal skin and as such the skin temperature may serve as an indicator for coastal, estuarine, and alluvial processes. Infrared (IR) imagery offers the unique tool to survey such systems, allowing not only to assess temperature variability of the thermal boundary layer, but also to derive surface flow fields through digital particle image velocimetry, optical flow techniques, or spectral methods. In this study, IR time‐series imagery taken from a boat moored in the Hudson River estuary is used to determine surface flow, turbulent kinetic energy dissipation rate, and characteristic temperature and velocity length scales. These are linked to subsurface measurements provided by in situ instruments. Under the low wind conditions and weak stratification, surface currents and dissipation rate are found to reflect subsurface mean flow (r2 = 0.89) and turbulence (r2 = 0.75). For relatively low dissipation rates, better correlations are obtained by computing dissipation rates directly from wavenumber spectra rather than when having to assume the validity of the Taylor hypothesis. Furthermore, the subsurface dissipation rate scales with the surface length scales (L) and mean flow (U) using (r2 = 0.9). The surface length scale derived from the thermal fields is found to have a strong linear relationship (r2 = 0.88) to water depth (D) with (D/L) ∼ 13. Such a relation may prove useful for remote bathymetric surveys when no waves are present.

Oscillations of a vertically stratified dissipative atmosphere. I. Solution above source

A method of construction of solution for acoustic-gravity waves (AGW) above a wave source, taking dissipation throughout the atmosphere into account (dissipative solution above source, DSAS), is proposed. The method is to combine three solutions for three parts of the atmosphere: an analytical solution for the upper isothermal part and numerical solutions for the real non-isothermal dissipative atmosphere in the middle part and for the real non-isothermal small dissipation atmosphere in the lower one. In this paper the method has been carried out for the atmosphere with thermal conductivity but without viscosity. The heights of strong dissipation and the total absorption index in the regions of weak and average dissipation are found. For internal gravity waves the results of test calculations for an isothermal atmosphere and calculations for a real non-isothermal atmosphere are shown in graphical form. An algorithm and appropriate code to calculate DSAS, taking dissipation due to finite thermal conductivity into account throughout the atmosphere, are developed. The results of test DSAS calculations for an everywhere isothermal atmosphere are given. The calculation results for DSAS for the real non-isothermal atmosphere are also presented. A method for construction of the 2×2 Green's matrix fully taking dissipation into account and allowing us to find disturbance from some source of AGW in the atmosphere is proposed.

Effects of Inertia on the Steady-Shear Rheology of Disordered Solids.

We study the finite-shear-rate rheology of disordered solids by means of molecular dynamics simulations in two dimensions. By systematically varying the damping strength ζ in the low-temperature limit, we identify two well-defined flow regimes, separated by a thin (temperature-dependent) crossover region. In the overdamped regime, the athermal rheology is governed by the competition between elastic forces and viscous forces, whose ratio gives the Weissenberg number Wi∝ζγ[over ˙]; the macroscopic stress Σ follows the frequently encountered Herschel-Bulkley law Σ=Σ_{0}+ksqrt[Wi], with yield stress Σ_{0}>0. In the underdamped (inertial) regime, dramatic changes in the rheology are observed for low damping: the flow curve becomes nonmonotonic. This change is not caused by longer-lived correlations in the particle dynamics at lower damping; instead, for weak dissipation, the sample heats up considerably due to, and in proportion to, the driving. By thermostating more or less underdamped systems, we are able to link quantitatively the rheology to the kinetic temperature and the shear rate, rescaled with Einstein's vibration frequency.

Energy decay of solutions for a variable-coefficient viscoelastic wave equation with a weak nonlinear dissipation

In this paper, we study decay properties of the solutions for a variable-coefficient viscoelastic wave equation with a weak nonlinear dissipative term. The method we used are piecewise multiplier methods and geometric analysis.

Weakly dissipative dust-ion acoustic wave modulation

The modulational instability of dust-ion acoustic (DIA) waves in an unmagnetized dusty plasma is investigated in the presence of weak dissipations arising due to the low rates (compared to the ion oscillation frequency) of ionization recombination and ion loss. Based on the multiple space and time scales perturbation, a new modified nonlinear Schrödinger equation governing the evolution of modulated DIA waves is derived with a linear damping term. It is shown that the combined action of all dissipative mechanisms due to collisions between particles reveals the permitted maximum time for the occurrence of the modulational instability. The influence on the modulational instability regions of relevant physical parameters such as ion temperature, dust concentration, ionization, recombination and ion loss is numerically examined. It is also found that the recombination frequency controls the instability growth rate, whereas recombination and ion loss make the instability regions wider.

Well-posedness of the Ostrovsky–Hunter Equation under the combined effects of dissipation and short-wave dispersion

The Ostrovsky–Hunter equation provides a model for small-amplitude long waves in a rotating fluid of finite depth. It is a nonlinear evolution equation. In this paper we study the well-posedness for the Cauchy problem associated with this equation in presence of some weak dissipation effects.

Effect of guide field on three-dimensional electron shear flow instabilities in electron current sheets

We examine, in the limit of electron plasma ${\it\beta}_{e}\ll 1$, the effect of an external guide field and current sheet thickness on the growth rates and nature of three-dimensional (3-D) unstable modes of an electron current sheet driven by electron shear flow. The growth rate of the fastest growing mode drops rapidly with current sheet thickness but increases slowly with the strength of the guide field. The fastest growing mode is tearing type only for thin current sheets (half-thickness ${\approx}d_{e}$, where $d_{e}=c/{\it\omega}_{pe}$ is the electron inertial length) and zero guide field. For finite guide field or thicker current sheets, the fastest growing mode is a non-tearing type. However, growth rates of the fastest 2-D tearing and 3-D non-tearing modes are comparable for thin current sheets ($d_{e}<\text{half thickness}<2\,d_{e}$) and small guide field (of the order of the asymptotic value of the component of magnetic field supporting the electron current sheet). It is shown that the general mode resonance conditions for tearing modes depend on the effective dissipation mechanism. The usual tearing mode resonance condition ($\boldsymbol{k}\boldsymbol{\cdot }\boldsymbol{B}_{0}=0$, $\boldsymbol{k}$ is the wavevector and $\boldsymbol{B}_{0}$ is the equilibrium magnetic field) can be recovered from the general resonance conditions in the limit of weak dissipation. The conditions (relating current sheet thickness, strength of the guide field and wavenumbers) for the non-existence of tearing mode are obtained from the general mode resonance conditions. We discuss the role of electron shear flow instabilities in magnetic reconnection.

Generalized transport coefficients for inelastic Maxwell mixtures under shear flow.

The Boltzmann equation framework for inelastic Maxwell models is considered to determine the transport coefficients associated with the mass, momentum, and heat fluxes of a granular binary mixture in spatially inhomogeneous states close to the simple shear flow. The Boltzmann equation is solved by means of a Chapman-Enskog-type expansion around the (local) shear flow distributions f(r)(0) for each species that retain all the hydrodynamic orders in the shear rate. Due to the anisotropy induced by the shear flow, tensorial quantities are required to describe the transport processes instead of the conventional scalar coefficients. These tensors are given in terms of the solutions of a set of coupled equations, which can be analytically solved as functions of the shear rate a, the coefficients of restitution α(rs), and the parameters of the mixture (masses, diameters, and composition). Since the reference distribution functions f(r)(0) apply for arbitrary values of the shear rate and are not restricted to weak dissipation, the corresponding generalized coefficients turn out to be nonlinear functions of both a and α(rs). The dependence of the relevant elements of the three diffusion tensors on both the shear rate and dissipation is illustrated in the tracer limit case, the results showing that the deviation of the generalized transport coefficients from their forms for vanishing shear rates is in general significant. A comparison with the previous results obtained analytically for inelastic hard spheres by using Grad's moment method is carried out, showing a good agreement over a wide range of values for the coefficients of restitution. Finally, as an application of the theoretical expressions derived here for the transport coefficients, thermal diffusion segregation of an intruder immersed in a granular gas is also studied.

Divergence of Viscosity in Jammed Granular Materials: A Theoretical Approach.

A theory for jammed granular materials is developed with the aid of a nonequilibrium steady-state distribution function. The approximate nonequilibrium steady-state distribution function is explicitly given in the weak dissipation regime by means of the relaxation time. The theory quantitatively agrees with the results of the molecular dynamics simulation on the critical behavior of the viscosity below the jamming point without introducing any fitting parameter.

Continuous-variable entanglement mediated by a thermal oscillator

We discuss the deterministic Gaussian entangling procedure between continuous variables of two directly noninteracting oscillators. The oscillators can only couple to the same mediating oscillator, which is initially at arbitrary noisy state and can be lost after the procedure. Unitary idealization of the procedure can generate large entanglement for any initial thermal noise of the mediator, thanks to the quantum version of the geometric phase. The generation of entanglement may considerably change when the procedure contains a weak dissipation. A robustness of this entangling procedure for weak dissipation is therefore a basic test of feasibility, especially in the limit of noisy mediator. We theoretically confirm the basic robustness of entanglement generation. Moreover, we suggest a nontrivial numerical optimization of the entangling procedure to approach an absolute robustness. For the weak dissipation, the optimization allows complete avoiding of the impact of the mediator noise. The suggested entangling procedure is therefore verified to be sufficiently robust for further development of quantum transducers.

Profile of a low-Mach-number shock in two-fluid plasma theory

Abstract. Magnetic profiles of low-Mach-number collisionless shocks in space plasmas are studied within the two-fluid plasma theory. Particular attention is given to the upstream magnetic oscillations generated at the ramp. By including weak resistive dissipation in the equations of motion for electrons and protons, the dependence of the upstream wave train features on the ratio of the dispersion length to the dissipative length is established quantitatively. The dependence of the oscillation amplitude and spatial damping scale on the shock normal angle θ is found.

Stability of the relativistic Vlasov–Maxwell–Boltzmann system for short range interaction

The Cauchy problem of the relativistic Vlasov–Maxwell–Boltzmann system for short range interaction is investigated. For perturbative initial data with suitable regularity and integrability, we prove the large time stability of solutions to the relativistic Vlasov–Maxwell–Boltzmann system, and also obtain as a byproduct the convergence rates of solutions. For the proof, a new interactive instant energy functional is introduced to capture the the macroscopic dissipation and the very weak electro-magnetic dissipation of the linearized system. A refined time–velocity weighted energy method is also applied to compensate the weaker dissipation of the linearized collision operator in the case of non-hard potential models. The results also extend the case of “hard ball” model considered by Guo and Strain (2012) to the short range interactions.

Weakly dissipative solitons in dense relativistic-degenerate plasma

We investigate the features of weakly nonlinear waves in a collisional dense plasma consisting of ultra-relativistic degenerate electrons and non-relativistic degenerate ions. In weak dissipation limit, the dynamics of low frequency nonlinear ion (solitary) wave is described by solving a damped Korteweg-deVries equation. The analytical and numerical analysis shows the existence of weakly dissipative solitons evolving with time. The characteristics of soliton evolution with plasma number density and slow ion-neutral collision rate are discussed with some detail. The relevance of the study with degenerate plasmas in ultra-dense astrophysical objects, particularly white dwarf stars is also pointed out.

Dephasing and dissipation in qubit thermodynamics.

We analyze the stochastic evolution and dephasing of a qubit within the quantum jump approach. It allows one to treat individual realizations of inelastic processes, and in this way it provides solutions, for instance, to problems in quantum thermodynamics and distributions in statistical mechanics. We demonstrate that dephasing and relaxation of the qubit render the Jarzynski and Crooks fluctuation relations (FRs) of nonequilibrium thermodynamics intact. On the contrary, the standard two-measurement protocol, taking into account only the fluctuations of the internal energy U, leads to deviations in FRs under the same conditions. We relate the average 〈e(-βU)〉 (where β is the inverse temperature) with the qubit's relaxation and dephasing rates in the weak dissipation limit and discuss this relationship for different mechanisms of decoherence.

Efeito de um termo dissipativo no sistema hamiltoniano de ondas de deriva

<p>O presente trabalho analisa o modelo Hamiltoniano de ondas de deriva que descreve o transporte caótico de partículas no confinamento do plasma. Com apenas uma onda de deriva o sistema é integrável e apresenta órbitas regulares. Ao adicionarmos uma segunda onda, o sistema pode ou não ser integrável dependendo da velocidade de fase de cada onda. Com a mesma velocidade de fase o sistema ainda é integrável. Quando as velocidades de fase entre as duas ondas são diferentes, o sistema apresenta comportamento caótico. A este modelo acrescentamos uma pequena dissipação. Na presença de uma fraca dissipação, para certas condições iniciais, observamos órbitas transientes que convergem para atratores periódicos.</p>

Extended Lagrangian formulation of charge-constrained tight-binding molecular dynamics.

The extended Lagrangian Born-Oppenheimer molecular dynamics formalism [Niklasson, Phys. Rev. Lett., 2008, 100, 123004] has been applied to a tight-binding model under the constraint of local charge neutrality to yield microcanonical trajectories with both precise, long-term energy conservation and a reduced number of self-consistent field optimizations at each time step. The extended Lagrangian molecular dynamics formalism restores time reversal symmetry in the propagation of the electronic degrees of freedom, and it enables the efficient and accurate self-consistent optimization of the chemical potential and atomwise potential energy shifts in the on-site elements of the tight-binding Hamiltonian that are required when enforcing local charge neutrality. These capabilities are illustrated with microcanonical molecular dynamics simulations of a small metallic cluster using an sd-valent tight-binding model for titanium. The effects of weak dissipation on the propagation of the auxiliary degrees of freedom for the chemical potential and on-site Hamiltonian matrix elements that is used to counteract the accumulation of numerical noise during trajectories was also investigated.

Dissipative instability in partially ionised prominence plasmas

We investigate the nature of dissipative instability at the boundary (seen here as tangential discontinuity) between the viscous corona and the partially ionised prominence plasma in the incompressible limit. The importance of the partial ionisation is investigated in terms of the ionisation fraction. Matching the solutions for the transversal component of the velocity and total pressure at the interface between the prominence and coronal plasmas, we derive a dispersion relation whose imaginary part describes the evolution of the instability. Results are obtained in the limit of weak dissipation. Using simple analytical methods, we show that dissipative instabilities appear for flow speeds that are lower than the Kelvin-Helmholtz instability threshold. While viscosity tends to destabilise the plasma, the effect of partial ionisation (through the Cowling resistivity) will act towards stabilising the interface. For ionisation degrees closer to a neutral gas the interface will be unstable for larger values of equilibrium flow. The same principle is assumed when studying the appearance of instability at the interface between prominences and dark plumes. The unstable mode appearing in this case has a very small growth rate and dissipative instability cannot explain the appearance of flows in plumes. The present study improves our understanding of the complexity of dynamical processes at the interface of solar prominences and solar corona, and the role partial ionisation can have on the stability of the plasma. Our results clearly show that the problem of partial ionisation introduces new aspects of plasma stability with consequences on the evolution of solar prominences.

Dynamical phase transition in the open Dicke model

The Dicke model with a weak dissipation channel is realized by coupling a Bose-Einstein condensate to an optical cavity with ultranarrow bandwidth. We explore the dynamical critical properties of the Hepp-Lieb-Dicke phase transition by performing quenches across the phase boundary. We observe hysteresis in the transition between a homogeneous phase and a self-organized collective phase with an enclosed loop area showing power-law scaling with respect to the quench time, which suggests an interpretation within a general framework introduced by Kibble and Zurek. The observed hysteretic dynamics is well reproduced by numerically solving the mean-field equation derived from a generalized Dicke Hamiltonian. Our work promotes the understanding of nonequilibrium physics in open many-body systems with infinite range interactions.

Stability and convergence of relaxation schemes to hyperbolic balance laws via a wave operator

This paper deals with relaxation approximations of nonlinear systems of hyperbolic balance laws. We introduce a class of relaxation schemes and establish their stability and convergence to the solution of hyperbolic balance laws before the formation of shocks, provided that we are within the framework of the compensated compactness method. Our analysis treats systems of hyperbolic balance laws with source terms satisfying a special mechanism which induces weak dissipation in the spirit of Dafermos [Hyperbolic systems of balance laws with weak dissipation, J. Hyp. Diff. Equations 3 (2006) 505–527.], as well as hyperbolic balance laws with more general source terms. The rate of convergence of the relaxation system to a solution of the balance laws in the smooth regime is established. Our work follows in spirit the analysis presented by [Ch. Arvanitis, Ch. Makridakis and A. E. Tzavaras, Stability and convergence of a class of finite element schemes for hyperbolic conservation laws, SIAM J. Numer. Anal. 42(4) (2004) 1357–1393]; [S. Jin and X. Xin, The relaxation schemes for systems of conservation laws in arbitrary space dimensions, Comm. Pure Appl. Math. 48 (1995) 235–277] for systems of hyperbolic conservation laws without source terms.