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Landauer, Kubo, and microcanonical approaches to quantum transport and noise: A comparison and implications for cold-atom dynamics

  • Author(s): Chien, CC
  • Di Ventra, M
  • Zwolak, M
  • et al.
Abstract

We compare the Landauer, Kubo, and microcanonical [J. Phys.: Condens. Matter 16, 8025 (2005)JCOMEL0953-898410.1088/0953-8984/16/45/024] approaches to quantum transport for the average current, the entanglement entropy, and the semiclassical full-counting statistics (FCS). Our focus is on the applicability of these approaches to isolated quantum systems such as ultracold atoms in engineered optical potentials. For two lattices connected by a junction, we find that the current and particle number fluctuations from the microcanonical approach compare well with the values predicted by the Landauer formalism and FCS assuming a binomial distribution. However, we demonstrate that well-defined reservoirs (i.e., particles in Fermi-Dirac distributions) are not present for a substantial duration of the quasi-steady state. Thus, on the one hand, the Landauer assumption of reservoirs and/or inelastic effects is not necessary for establishing a quasi-steady state. Maintaining such a state indefinitely requires an infinite system, and in this limit well-defined Fermi-Dirac distributions can occur. On the other hand, as we show, the existence of a finite speed of particle propagation preserves the quasi-steady state irrespective of the existence of well-defined reservoirs. This indicates that global observables in finite systems may be substantially different from those predicted by an uncritical application of the Landauer formalism, with its underlying thermodynamic limit. Therefore, the microcanonical formalism which is designed for closed, finite-size quantum systems seems more suitable for studying particle dynamics in ultracold atoms. Our results highlight both the connection and differences with more traditional approaches to calculating transport properties in condensed matter systems, and will help guide the way to their simulations in cold-atom systems. © 2014 American Physical Society.

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