Eur. Phys. J. B (2013) 86: 500
https://doi.org/10.1140/epjb/e2013-40907-3

Regular Article

Cumulants of heat transfer across nonlinear quantum systems

¹ Department of Physics and Center for Computational Science and Engineering, National University of Singapore, 117542 Singapore, Republic of Singapore
² Chemistry Department, University of California, Irvine, California 92697-2025, USA
³ NUS Graduate School for Integrative Sciences and Engineering, 117456 Singapore, Republic of Singapore
⁴ Center for Phononics and Thermal Energy Science, School of Physical Science and Engineering, Tongji University, 200092 Shanghai, P.R. China

^a e-mail: g0900726@nus.edu.sg

Received: 10 October 2013
Received in final form: 4 November 2013
Published online: 9 December 2013

Abstract

We consider thermal conduction across a general nonlinear phononic junction. Based on two-time observation protocol and the nonequilibrium Green’s function method, heat transfer in steady-state regimes is studied, and practical formulas for the calculation of the cumulant generating function are obtained. As an application, the general formalism is used to study anharmonic effects on fluctuation of steady-state heat transfer across a single-site junction with a quartic nonlinear on-site pinning potential. An explicit nonlinear modification to the cumulant generating function exact up to the first order is given, in which the Gallavotti-Cohen fluctuation symmetry is found still valid. Numerically a self-consistent procedure is introduced, which works well for strong nonlinearity.