Nonequilibrium stationary states of noninteracting electrons in a one-dimensional lattice

Nonequilibrium stationary states of a one-dimensional quantum conductor pla ced between two reservoirs are investigated. Applying the theory of C-*-alg ebra, as t --> +infinity, any state including the degrees of freedom of res ervoirs is shown to weakly evolve to a quasiftee stationary state with nonv anishing currents. The stationary state exhibits transports which are consi stent with nonequilibrium thermodynamics and, in this sense, it has broken time symmetry. Particularly, the electric and energy currents are shown to be expressed by two-probe Landauer-type formulas and they reduce to the res ults by Sivan-Imry and Bagwell-Orlando in appropriate regimes. As a consequ ence of the time reversal symmetry, there exists another stationary state w ith anti-thermodynamical transports, which is the t --> infinity limit of t he initial state. The consistency between the dynamical reversibility and t he irreversibility of the evolution of states is discussed as well. (C) 200 1 Elsevier Science Ltd. All rights reserved.