Abstract
The role of quantum interference phenomena is examined for strongly localized, non-interacting electrons. We compute, both numerically and analytically, the probability distribution for tunneling between sites separated a distance t, by summing all forward scattering paths. We find a probability distribution that is approximately log-normal; its mean proportional to t, and its variance growing as t 2ω, with ω depending on the dimension d. Since the mean and variance are independent, two parameters are necessary to describe the tunneling probability. We also study the response of the system to a magnetic field B, with and without spin-orbit (SO) scattering. Without SO a magnetic field leads to an increase in the localization length scaling as B 1/2. With SO, there is still a positive magnetoconductance (initially scaling as B 2 t 3), but no change in the localization length. The universal characteristics of the probability distribution can be probed by examining its moments. These moments describe the world lines of n attracting bosons in d - 1 dimensions- a well known many body problem! Various results for this simple problem are then used to provide analytical information on the distribution for tunneling in strong localization.
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© 1992 Springer Science+Business Media New York
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Kardar, M., Medina, E. (1992). Quantum Interference Phenomena in Strong Localization. In: Ainsworth, T.L., Campbell, C.E., Clements, B.E., Krotscheck, E. (eds) Recent Progress in Many-Body Theories. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-3466-2_10
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DOI: https://doi.org/10.1007/978-1-4615-3466-2_10
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