Multiple-path transport in quantum networks

2012/10/31 by Geva Arwas, Doron Cohen
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Quantum and electron transport phenomena #cond-mat.mes-hall #quant-ph #stochastic dynamics and bifurcation

paper · pdf · doi:10.1088/1751-8113/46/16/165101

published as J. Phys. A 46, 165101 (2013) · 13 pages, 5 figures, with much more details, JPA accepted version

arxiv created 2013/03/11 · openalex publication_date 2013/04/03 · arxiv updated 2013/04/05 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We find an exact expression for the current (I) that flows via a tagged bond from a site ("dot") whose potential (u) is varied in time. We show that the analysis reduces to that of calculating time dependent probabilities, as in the stochastic formulation, but with splitting (branching) ratios that are not bounded within [0,1]. Accordingly our result can be regarded as a multiple-path version of the continuity equation. It generalizes results that have been obtained from adiabatic transport theory in the context of quantum "pumping" and "stirring". Our approach allows to address the adiabatic regime, as well as the Slow and Fast non-adiabatic regimes, on equal footing. We emphasize aspects that go beyond the familiar picture of sequential Landau-Zener crossings, taking into account Wigner-type mixing of the energy levels.

Citations

• Counting statistics in multiple path geometries and the fluctuations of the integrated current in a quantum stirring device
• Full counting statistics of a general quantum mechanical variable
• Evidence for wavelike energy transfer through quantum coherence in photosynthetic systems
• Quantum stirring in low-dimensional devices
• Quantum pumping in closed systems, adiabatic transport, and the Kubo formula
• Directed Flow in Nonadiabatic Stochastic Pumps
• Quantal phase factors accompanying adiabatic changes
• A Topological Look at the Quantum Hall Effect