Energy Transport in the Integrable System in Contact with Various Types of Phonon Reservoirs

TL;DR

This paper investigates how the spectral densities of heat reservoirs influence energy transport in a quantum harmonic chain, revealing that reservoir types affect temperature and energy profiles, especially when reservoirs differ.

Contribution

It derives a master equation for a quantum harmonic chain coupled to various spectral density reservoirs and analyzes how these affect energy transport and temperature profiles.

Findings

Temperature profile is independent of reservoir types when reservoirs are identical.

Energy profile near the ends depends on reservoir spectral densities when they differ.

Finite coupling causes wide variation in temperature profiles depending on spectral densities.

Abstract

We study how energy transport in an integrable system is affected by the spectral densities of heat reservoirs. The model investigated here is the quantum harmonic chain whose both ends are in contact with two heat reservoirs at different temperatures. The master equation for the reduced density matrix is derived on the assumption that the reservoirs are composed of an infinite number of independent harmonic oscillators. We evaluate temperature profile and energy flux in the stationary state for the master equation and discuss how they depend on the types of spectral densities. When we attach the reservoirs of the same type of spectral density, we find that the temperature profile is independent of the types. On the other hand, when the two reservoirs have different types of spectral densities, the energy profile near the ends of the chain depends on the types. When the coupling is finite, the temperature profile near the ends shows wide variation of behavior dependent on spectral densities and temperatures of reservoirs. This dependence is discussed with the Fokker-Planck equations obtained in the classical limit.