## Nonequilibrium stationary states of noninteracting electrons in a one-dimensional lattice.(English)Zbl 0994.82049

Summary: Nonequilibrium stationary states of a one-dimensional quantum conductor placed between two reservoirs are investigated. Applying the theory of $$C^*$$-algebra, as $$t\to+\infty$$, 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 $$t\to-\infty$$ limit of the initial state. The consistency between the dynamical reversibility and the irreversibility of the evolution of states is discussed as well.

### MSC:

 82C10 Quantum dynamics and nonequilibrium statistical mechanics (general) 46L60 Applications of selfadjoint operator algebras to physics 82C20 Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs in time-dependent statistical mechanics
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### References:

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