Nonequilibrium dynamics of a stochastic model of anomalous heat transport (original) (raw)

Nonequilibrium dynamics of a stochastic model of anomalous heat transport: numerical analysis

Journal of Physics A Mathematical and Theoretical

We study heat transport in a chain of harmonic oscillators with random elastic collisions between nearest-neighbours. The equations of motion of the covariance matrix are numerically solved for free and fixed boundary conditions. In the thermodynamic limit, the shape of the temperature profile and the value of the stationary heat flux depend on the choice of boundary conditions. For free boundary conditions, they also depend on the coupling strength with the heat baths. Moreover, we find a strong violation of local equilibrium at the chain edges that determine two boundary layers of size sqrtN\sqrt{N}sqrtN (where NNN is the chain length), that are characterized by a different scaling behaviour from the bulk. Finally, we investigate the relaxation towards the stationary state, finding two long time scales: the first corresponds to the relaxation of the hydrodynamic modes; the second is a manifestation of the finiteness of the system. Comment: Submitted to Journal of Physics A, Mathematical a...

A stochastic model of anomalous heat transport: analytical solution of the steady state

Journal of Physics A Mathematical and Theoretical

We consider a one-dimensional harmonic crystal with conservative noise, in contact with two stochastic Langevin heat baths at different temperatures. The noise term consists of collisions between neighbouring oscillators that exchange their momenta, with a rate γ. The stationary equations for the covariance matrix are exactly solved in the thermodynamic limit (N → ∞). In particular, we derive an analytical expression for the temperature profile, which turns out to be independent of γ. Moreover, we obtain an exact expression for the leading term of the energy current, which scales as . Our theoretical results are finally found to be consistent with the numerical solutions of the covariance matrix for finite N.

Normal heat conductivity in chains with noisy, time-dependent, quadratic Hamiltonians

arXiv preprint cond-mat/0505346, 2005

We present a model for conductivity and energy diffusion in a linear chain described by a quadratic Hamiltonian with Gaussian noise. We show that when the correlation matrix is diagonal, the noiseaveraged Liouville-von Neumann equation governing the time-evolution of the system reduces to the Lindblad equation with Hermitian Lindblad operators. We show that the noise-averaged density matrix for the system expectation values of the energy density and the number density satisfy discrete versions of the heat and diffusion ...

Steady state fluctuations of the dissipated heat for a quantum stochastic model

Reviews in Mathematical Physics, 2006

We introduce a quantum stochastic dynamics for heat conduction. A multilevel subsystem is coupled to reservoirs at different temperatures. Energy quanta are detected in the reservoirs allowing the study of steady state fluctuations of the entropy dissipation. Our main result states a symmetry in its large deviation rate function.

Large Deviations for a Stochastic Model of Heat Flow

Journal of Statistical Physics, 2005

We investigate a one dimensional chain of 2N harmonic oscillators in which neighboring sites have their energies redistributed randomly. The sites −N and N are in contact with thermal reservoirs at different temperature τ − and τ + . Kipnis, Marchioro, and Presutti [18] proved that this model satisfies Fourier's law and that in the hydrodynamical scaling limit, when N → ∞, the stationary state has a linear energy density profileθ(u), u ∈ [−1, 1]. We derive the large deviation function S(θ(u)) for the probability of finding, in the stationary state, a profile θ(u) different fromθ(u). The function S(θ) has striking similarities to, but also large differences from, the corresponding one of the symmetric exclusion process. Like the latter it is nonlocal and satisfies a variational equation. Unlike the latter it is not convex and the Gaussian normal fluctuations are enhanced rather than suppressed compared to the local equilibrium state. We also briefly discuss more general model and find the features common in these two and other models whose S(θ) is known.

Non-Isothermal Fluctuation-Dissipation Relations and Brownian Thermometry

The classical theory of Brownian motion rests on fundamental laws of statistical mechanics, such as the equipartition theorem and the fluctuation-dissipation theorem, which are not applicable in non-isothermal situations. We derive the generalized fluctuation-dissipation relations and Langevin equations governing such non-isothermal Brownian motion, including explicit results for the frequency-dependent noise temperature and Brownian thermometry far from equilibrium.

Stochastic effects in a thermochemical system with Newtonian heat exchange

Physical Review E, 2001

We develop a mesoscopic description of stochastic effects in the Newtonian heat exchange between a diluted gas system and a thermostat. We explicitly study the homogeneous Semenov model involving a thermochemical reaction and neglecting consumption of reactants. The master equation includes a transition rate for the thermal transfer process, which is derived on the basis of the statistics for inelastic collisions between gas particles and walls of the thermostat. The main assumption is that the perturbation of the Maxwellian particle velocity distribution can be neglected. The transition function for the thermal process admits a continuous spectrum of temperature changes, and consequently, the master equation has a complicated integro-differential form. We perform Monte Carlo simulations based on this equation to study the stochastic effects in the Semenov system in the explosive regime. The dispersion of ignition times is calculated as a function of system size. For sufficiently small systems, the probability distribution of temperature displays transient bimodality during the ignition period. The results of the stochastic description are successfully compared with those of direct simulations of microscopic particle dynamics.

A stochastic force model for the ballistic-diffusive transition of heat conduction

Physica Scripta, 2020

We theoretically study the heat conduction in a harmonic chain with a stochastic force field, in contact with two Langevin thermal baths at different temperatures. In particular, we investigate the interplay between the thermal baths properties and the size of the system. To this aim, we introduce a stochastic force field, which is simple enough to be energy-conserving for each particle of the chain, but sufficiently aleatory to induce the ballistic to diffusive transition in the conductive behavior of the chain. When this stochastic force field is absent, we observe a ballistic behavior strongly dependent on the characteristic collision frequency of the thermal baths for any size of the system. On the other hand, when the stochastic force field is activated, the diffusive behavior is established and the effect of the thermal baths is removed in the thermodynamic limit.

On the Physical Origin of Long-Ranged Fluctuations in Fluids in Thermal Nonequilibrium States

Journal of Statistical Physics, 2000

Thermodynamic fluctuations in systems that are in nonequilibrium steady states are always spatially long ranged, in contrast to fluctuations in thermodynamic equilibrium. In the present paper we consider a fluid subjected to a stationary temperature gradient. Two different physical mechanisms have been identified by which the temperature gradient causes long-ranged fluctuations. One cause is the presence of couplings between fluctuating fields. Secondly, spatial variation of the strength of random forces, resulting from the local version of the fluctuation-dissipation theorem, has also been shown to generate long-ranged fluctuations. We evaluate the contributions to the long-ranged temperature fluctuations due to both mechanisms. While the inhomogeneously correlated Langevin noise does lead to long-ranged fluctuations, in practice, they turn out to be negligible as compared to nonequilibrium temperature fluctuations resulting from the coupling between temperature and velocity fluctuations.