Phonon transport across a two-dimensional region with time-varying spring constants

Abstract

We model the flow of phonons in a semi-infinite two-dimensional system where the spring constants in the central region are changing in time. Since phonons are carriers of energy, their flow corresponds to the flow of heat in the system. We derive an expression for the heat current by determining how the quantized Hamiltonian changes in time via the use of Heisenberg’s equation of motion. We then express the final form of the current using two-time nonequilibrium Green’s functions.