Cumulant generating function formula of heat transfer in ballistic system with lead-lead coupling

TL;DR

This paper derives an exact formula for the cumulant generating function of heat transfer in a lead-lead system with coupling, valid in transient and steady states, and verifies fluctuation symmetry properties.

Contribution

It provides a novel exact formula for heat transfer cumulant generating function considering lead-lead coupling using NEGF, applicable in all time regimes.

Findings

Exact cumulant generating function derived for heat transfer

Verification of Gallavotti-Cohen fluctuation symmetry

Discussion on the impact of Hamiltonian repartitioning

Abstract

Based on two-time observation protocol, we consider heat transfer in a given time interval $t_{M}$ in lead-junction-lead system taking coupling between the leads into account. In view of the two-time observation, consistency conditions are carefully verified in our specific family of quantum histories. Furthermore, its implication is briefly explored. Then using nonequilibrium Green's function (NEGF) method, we obtain an exact formula for the cumulant generating function for heat transfer between the two leads valid in both transient and steady-state regimes. Also, a compact formula for the cumulant generating function in the long-time limit is derived, for which the Gallavotti-Cohen (GC) fluctuation symmetry is explicitly verified. In addition, a brief discussion of Di Ventra's trick regarding whether the effect of the repartitioning procedure of the total Hamiltonian on nonequilibium steady-state current fluctuation exists is given. All kinds of properties of nonequilibrium current fluctuations such as the fluctuation theorem in different time regimes could be readily given according to these exact formulas.