Theoretical studies on quantum pump and excess entropy production: Quantum master equation approach

Abstract

In this thesis, we considered quantum systems coupled to several baths. We supposed that the system state is governed by the quantum master equation (QME). We investigated the quantum pump and the excess entropy production. In the first half of the thesis, we investigated the quantum pump using the full counting statistics with quantum master equation (FCS-QME) approach. In the latter part of the thesis, we investigated the excess entropy production. The average entropy production is composed of the time integral of the instantaneous steady entropy production rate and the excess entropy production. We define average entropy production rate using the average energy and particle currents, which are calculated by using the full counting statistics with QME. The excess entropy production is given by a line integral in the control parameter space and its integrand is called the Berry-Sinitsyn-Nemenman (BSN) vector. In the weakly nonequilibrium regime, we show that BSN vector is described by $\ln \rho_0^{(-1)}$ and $\rho_0$ where $\rho_0$ is the instantaneous steady state of the QME and $\rho_0^{(-1)}$ is that of the QME which is given by reversing the sign of the Lamb shift term. In general, the potential dose not exist. The origins of the non-existence of the potential are a quantum effect (the Lamb shift) and the breaking of the time-reversal symmetry. The non-existence of the potential means that the excess entropy essentially depends on the path of the modulation. If the system Hamiltonian is non-degenerate or the Lamb shift term is negligible, the excess entropy production approximately reduces to the difference between the von Neumann entropies of the system. We pointed out that the expression of the entropy production obtained in the classical Markov jump process is different from our result and showed that these are approximately equivalent only in the weakly nonequilibrium regime.