Quantum noise theory for phonon transport through nanostructures
  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. 
Li Wan, Yunmi Huang, and Changcheng Huang
cond-mat.mes-hall cond-mat.stat-mech