  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.
