Non-equilibrium Statistical Mechanics of Anharmonic Crystals with Self-consistent Stochastic Reservoirs

Abstract

We consider a d-dimensional crystal with an arbitrary harmonic interaction and an anharmonic on-site potential, with stochastic Langevin heat bath at each site. We develop an integral formalism for the correlation functions that is suitable for the study of their relaxation (time decay) as well as their behavior in space. Furthermore, in a perturbative analysis, for the one-dimensional system with weak coupling between the sites and small quartic anharmonicity, we investigate the steady state and show that the Fourier's law holds. We also obtain an expression for the thermal conductivity (for arbitrary next-neighbor interactions) and give the temperature profile in the steady state.

References in corpus (9)

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• Fourier law from a chain of coupled anharmonic oscillators under energy conserving noise
• Fourier's law from a chain of coupled planar harmonic oscillators under energy conserving noise
• Perfect Thermal Rectification in a Many-Body Quantum Ising Model
• Wigner entropy production and heat transport in linear quantum lattices
• A perturbative approach for the crystal chains with self-consistent stochastic reservoirs
• Nonequilibrium processes from Generalised Langevin Equations: realistic nanoscale systems connected to two thermal baths
• Thermal rectification in anharmonic chains under an energy-conserving noise
• Thermal Rectification in Classical and Quantum Systems: Searching for Efficient Thermal Diodes
• Nonequilibrium Generalised Langevin Equation for the calculation of heat transport properties in model 1D atomic chains coupled to two 3D thermal baths
• Heat transport along a chain of coupled quantum harmonic oscillators
• Temperature gradient and Fourier's law in gradient-mass harmonic systems
• Heat flow in anharmonic crystals with internal and external stochastic baths: A convergent polymer expansion for a model with discrete time and long range interparticle interaction