Full counting statistics, fluctuation relations, and linear response properties in a one-dimensional Kitaev chain.

Abstract

We analytically calculate the cumulant generating function of energy and particle transport in an open one-dimensional Kitaev chain at finite temperature by utilizing the Keldysh technique. The joint distribution of particle and energy currents satisfies different fluctuation relations in different regions of the parameter space as a result of U(1) symmetry breaking and energy conservation. Furthermore, we investigate the linear response behavior of the Kitaev chain within the framework of three-terminal systems, deriving the expressions for the Seebeck coefficient and thermal conductance. Notably, we observe a pronounced peak in the thermal conductance near the phase transition point, in agreement with previous predictions. Additionally, we prove that the peak value saturates at half of the thermal conductance quantum for finite-length chains at the zero temperature limit.