[hal-00494026, v1] A partition-free approach to transient and steady -state charge currents

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A partition-free approach to transient and steady-state charge currents1 2 3Horia D. Cornean , C´eline Gianesello , Valentin ZagrebnovAbstractWe construct a non-equilibrium steady state and calculate the corresponding current for amesoscopic Fermi system in the partition-free setting. To this end we study a small samplecoupled to a ﬁnite number of semi-inﬁnite leads. Initially, the whole system of quasi-freefermions is in a grand canonical equilibriumstate. At t = 0 we turnon a potential bias on theleads and let the system evolve. We study how the charge current behaves in time and howit stabilizes itself around a steady state value, which is given by a Landauer-type formula.1 IntroductionAt the present time one can essentially distinguish two diﬀerent ways of constructing non equilib-rium steady states (NESS) for composed systems.Theﬁrstmethodconsistsofpreparingapartitioned initialstateforthe totalsystemcontainingseveral sub-systems, each of which being in a diﬀerent state of thermal equilibrium, and then putthem into contact with each other at t = 0, and let the coupled total system evolve in time untilit reaches a steady state. In the mathematical physics community this method goes back to D.Ruelle [30], [31]. It was seriously promoted during the recent years through numerous papers, seee.g. [29, 1, 16, 31, 28, 5] and references therein. One can allow the carriers to interact in thesample [15], and the theory still works. Note that even if one ...

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