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

Nonequilibrium stationary states of a one-dimensional quantum conductor placed between two reservoirs are investigated. Applying the theory of C*-algebra, as t→+∞, any state including the degrees of freedom of reservoirs is shown to weakly evolve to a quasifree stationary state with nonvanishing currents. The stationary state exhibits transports which are consistent 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 results by Sivan–Imry and Bagwell–Orlando in appropriate regimes. As a consequence of the time reversal symmetry, there exists another stationary state with anti-thermodynamical transports, which is the t→−∞ limit of the initial state. The consistency between the dynamical reversibility and the irreversibility of the evolution of states is discussed as well.