Role of the on-site pinning potential in establishing quasi-steady-state conditions of heat transport in finite quantum systems

TL;DR

This study investigates how an on-site pinning potential influences the establishment of steady-state heat transport in finite quantum harmonic chains, revealing that a nonzero potential is essential for steady-state formation.

Contribution

It demonstrates that a nonzero on-site pinning potential is crucial for achieving steady-state heat current in finite quantum systems, supported by analytical and numerical analysis.

Findings

Steady-state current forms only with nonzero on-site potential.

Recurrent phenomena occur without on-site potential.

Analytical expressions clarify the role of on-site potential.

Abstract

We study the transport of energy in a finite linear harmonic chain by solving the Heisenberg equation of motion, as well as by using nonequilibrium Green's functions to verify our results. The initial state of the system consists of two separate and finite linear chains that are in their respective equilibriums at different temperatures. The chains are then abruptly attached to form a composite chain. The time evolution of the current from just after switch-on to the transient regime and then to later times is determined numerically. We expect the current to approach a steady-state value at later times. Surprisingly, this is possible only if a nonzero quadratic on-site pinning potential is applied to each particle in the chain. If there is no on-site potential a recurrent phenomenon appears when the time scale is longer than the traveling time of sound to make a round trip from the midpoint to a chain edge and then back. Analytic expressions for the transient and steady-state currents are derived to further elucidate the role of the on-site potential.