Analytic approach to the (an)harmonic crystal chains with self-consistent stochastic reservoirs

Abstract

We consider the harmonic and anharmonic chains of oscillators with self-consistent stochastic reservoirs and derive an integral representation (à la Feynman-Kac) for the correlations, in particular, for the heat flow. For the harmonic chain, we give a new proof that its thermal conductivity is finite in the steady state. Based on this integral representation for the correlations and a perturbative analysis, the approach is quite general and can be extended to more intricate systems.

Length dependence of heat conduction in (an)harmonic chains with asymmetries or long range interparticle interactions

“…For several models, for example, harmonic and also anharmonic chains with self-consistent reservoirs and nearest neighbor interactions, after intricate computations [19,20,18] we find that the heat flow between the sites j and j + 1 is given by…”

“…small J). The generality of the approach used to derive such expression [19,20,18] allows us to extend it to systems with interactions beyond nearest neighbor sites. More comments and details are presented in Ref.…”

Increasing thermal rectification: Effects of long-range interactions

“…For the particular case of a chain with nearest neighbor interparticle interaction, several works have been devoted to the problem. For systems with harmonic potentials and self-consistent reservoirs, it is proved [13,17] that…”

“…The approach and the integral formalism used to derive such results [17,18] allow us to write a similar expression for F j,ℓ in the case of an interparticle potential with interaction beyond next-neighbor sites, and so, we also have…”

“…For example, for the homogeneous harmonic chain with self-consistent reservoirs and weak nearest neighbor interaction (|J j,j+1 | small), it is proved in Refs. [17,18] that…”