Heat conduction in a one-dimensional gas of elastically colliding particles of unequal masses

We study the nonequlibrium state of heat conduction in a one-dimensional system of hard point particles of unequal masses interacting through elastic collisions. A BBGKY-type formulation is presented and some exact results are obtained from it. Extensive numerical simulations for the two-mass problem indicate that even for arbitrarily small mass differences, a nontrivial steady state is obtained. This state exhibits local thermal equilibrium and has a temperature profile in accordance with the predictions of kinetic theory. The temperature jumps typically seen in such studies are shown to be finite-size effects. The thermal conductivity appears to have a very slow divergence with system size, different from that seen in most other systems.Comment: 5 pages, 4 figures, Accepted for publication in Phys. Rev. Let

Non-equilibrium Green's function formalism and the problem of bound states

The non-equilibrium Green's function formalism for infinitely extended reservoirs coupled to a finite system can be derived by solving the equations of motion for a tight-binding Hamiltonian. While this approach gives the correct density for the continuum states, we find that it does not lead, in the absence of any additional mechanisms for equilibration, to a unique expression for the density matrix of any bound states which may be present. Introducing some auxiliary reservoirs which are very weakly coupled to the system leads to a density matrix which is unique in the equilibrium situation, but which depends on the details of the auxiliary reservoirs in the non-equilibrium case.Comment: Revtex4, 32 pages including 5 figures; some corrections made, this is the version published in Phys Rev

Heat transport in harmonic lattices

We work out the non-equilibrium steady state properties of a harmonic lattice which is connected to heat reservoirs at different temperatures. The heat reservoirs are themselves modeled as harmonic systems. Our approach is to write quantum Langevin equations for the system and solve these to obtain steady state properties such as currents and other second moments involving the position and momentum operators. The resulting expressions will be seen to be similar in form to results obtained for electronic transport using the non-equilibrium Green's function formalism. As an application of the formalism we discuss heat conduction in a harmonic chain connected to self-consistent reservoirs. We obtain a temperature dependent thermal conductivity which, in the high-temperature classical limit, reproduces the exact result on this model obtained recently by Bonetto, Lebowitz and Lukkarinen.Comment: One misprint and one error have been corrected; 22 pages, 2 figure

Waiting for rare entropic fluctuations

Non-equilibrium fluctuations of various stochastic variables, such as work and entropy production, have been widely discussed recently in the context of large deviations, cumulants and fluctuation relations. Typically, one looks at the distribution of these observables, at large fixed time. To characterize the precise stochastic nature of the process, we here address the distribution in the time domain. In particular, we focus on the first passage time distribution (FPTD) of entropy production, in several realistic models. We find that the fluctuation relation symmetry plays a crucial role in getting the typical asymptotic behavior. Similarities and differences to the simple random walk picture are discussed. For a driven particle in the ring geometry, the mean residence time is connected to the particle current and the steady state distribution, and it leads to a fluctuation relation-like symmetry in terms of the FPTD.Comment: 5+7 pages, 3 figure

Work distribution functions in polymer stretching experiments

We compute the distribution of the work done in stretching a Gaussian polymer, made of N monomers, at a finite rate. For a one-dimensional polymer undergoing Rouse dynamics, the work distribution is a Gaussian and we explicitly compute the mean and width. The two cases where the polymer is stretched, either by constraining its end or by constraining the force on it, are examined. We discuss connections to Jarzynski's equality and the fluctuation theorems.Comment: 5 pages, 2 figure

Landauer formula for phonon heat conduction: relation between energy transmittance and transmission coefficient

The heat current across a quantum harmonic system connected to reservoirs at different temperatures is given by the Landauer formula, in terms of an integral over phonon frequencies \omega, of the energy transmittance T(\omega). There are several different ways to derive this formula, for example using the Keldysh approach or the Langevin equation approach. The energy transmittance T({\omega}) is usually expressed in terms of nonequilibrium phonon Green's function and it is expected that it is related to the transmission coefficient {\tau}({\omega}) of plane waves across the system. In this paper, for a one-dimensional set-up of a finite harmonic chain connected to reservoirs which are also semi-infinite harmonic chains, we present a simple and direct demonstration of the relation between T({\omega}) and {\tau}({\omega}). Our approach is easily extendable to the case where both system and reservoirs are in higher dimensions and have arbitrary geometries, in which case the meaning of {\tau} and its relation to T are more non-trivial.Comment: 17 pages, 1 figur