Long-time tail in an electric conduction system

The long-time behavior of the velocity autocorrelation function in a classical two-dimensional electric conduction system is studied by the molecular dynamics simulation. In equilibrium, the effect of coexistence of many-body interactions and a random potential is investigated. A crossover from a positive tail proportional to $t^{-1}$, to a negative tail proportional to $-t^{-2}$ is observed as the strength of the random potential increases. In nonequilibrium, the positive tail is enhanced whereas the negative tail appears at earlier times as an electric field increases.Comment: 8 pages, 3 figures, submitted to Prog. Theor. Phys. Suppl. as a Proceedings of the 50th Anniversary of the Alder transitio

A perturbative method for nonequilibrium steady state of open quantum systems

We develop a method of calculating the nonequilibrium steady state (NESS) of an open quantum system that is weakly coupled to reservoirs in different equilibrium states. We describe the system using a Redfield-type quantum master equation (QME). We decompose the Redfield QME into a Lindblad-type QME and the remaining part $\mathcal{R}$. Regarding the steady state of the Lindblad QME as the unperturbed solution, we perform a perturbative calculation with respect to $\mathcal{R}$ to obtain the NESS of the Redfield QME. The NESS thus determined is exact up to the first order in the system-reservoir coupling strength (pump/loss rate), which is the same as the order of validity of the QME. An advantage of the proposed method in numerical computation is its applicability to systems larger than those in methods of directly solving the original Redfield QME. We apply the method to a noninteracting fermion system to obtain an analytical expression of the NESS density matrix. We also numerically demonstrate the method in a nonequilibrium quantum spin chain.Comment: 15 pages, 3 figures. To appear in J. Phys. Soc. Jp

Geometrical Excess Entropy Production in Nonequilibrium Quantum Systems

For open systems described by the quantum Markovian master equation, we study a possible extension of the Clausius equality to quasistatic operations between nonequilibrium steady states (NESSs). We investigate the excess heat divided by temperature (i.e., excess entropy production) which is transferred into the system during the operations. We derive a geometrical expression for the excess entropy production, which is analogous to the Berry phase in unitary evolution. Our result implies that in general one cannot define a scalar potential whose difference coincides with the excess entropy production in a thermodynamic process, and that a vector potential plays a crucial role in the thermodynamics for NESSs. In the weakly nonequilibrium regime, we show that the geometrical expression reduces to the extended Clausius equality derived by Saito and Tasaki (J. Stat. Phys. {\bf 145}, 1275 (2011)). As an example, we investigate a spinless electron system in quantum dots. We find that one can define a scalar potential when the parameters of only one of the reservoirs are modified in a non-interacting system, but this is no longer the case for an interacting system.Comment: 28 pages, 3 figures. 'Remark on the fluctuation theorem' has been revised in ver. 2. Brief Summary has been added in Sec. 1 in ver.