Quantum noise theory for phonon transport through nanostructures

TL;DR

This paper introduces a quantum noise approach using quantum Langevin equations to analyze phonon transport in nanostructures, enabling thermal conductivity calculations without defining local temperatures in non-equilibrium states.

Contribution

The paper develops a novel quantum noise framework for phonon transport that avoids the need for local temperature definitions in non-equilibrium nanostructures.

Findings

Derived a quantum Langevin equation for phonon transport

Calculated thermal conductivity without local temperature assumptions

Studied finite size effects on thermal conductivity

Abstract

We have developed a quantum noise approach to study the phonon transport through nanostructures. The nanostructures acting as phonon channels are attached to two phonon reservoirs. And the temperature drop between the two reservoirs drives the phonon transport through the channels. We have derived a quantum Langevin equation(QLE) to describe the phonon transport with the quantum noise originated from the thermal fluctuation of the reservoirs. Within the Markov approximation, the QLE is used to get the thermal conductivity $\kappa$ of the nanostructures and the finite size effect of the $\kappa$ then is studied. In this study, the advantage of the quantum noise approach lays on the fact that no any local temperature needs to be defined for the nanostructures in its non-equilibrium state.