Quasiclassical analysis of Bloch oscillations in non-Hermitian tight-binding lattices

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Title: Quasiclassical analysis of Bloch oscillations in non-Hermitian tight-binding lattices
Authors: Graefe, EM
Korsch, HJ
Rush, A
Item Type: Journal Article
Abstract: Many features of Bloch oscillations in one-dimensional quantum lattices with a static force can be described by quasiclassical considerations for example by means of the acceleration theorem, at least for Hermitian systems. Here the quasiclassical approach is extended to non-Hermitian lattices, which are of increasing interest. The analysis is based on a generalised non-Hermitian phase space dynamics developed recently. Applications to a single-band tight-binding system demonstrate that many features of the quantum dynamics can be understood from this classical description qualitatively and even quantitatively. Two non-Hermitian and PT-symmetric examples are studied, a Hatano–Nelson lattice with real coupling constants and a system with purely imaginary couplings, both for initially localised states in space or in momentum. It is shown that the time-evolution of the norm of the wave packet and the expectation values of position and momentum can be described in a classical picture.
Issue Date: 11-Jul-2016
Date of Acceptance: 3-Jun-2016
URI: http://hdl.handle.net/10044/1/33382
DOI: http://dx.doi.og/10.1088/1367-2630/18/7/075009
ISSN: 1367-2630
Publisher: IOP Publishing
Journal / Book Title: New Journal of Physics
Volume: 18
Copyright Statement: Original content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
Sponsor/Funder: The Royal Society
Funder's Grant Number: UF130339
Keywords: quant-ph
Fluids & Plasmas
Physical Sciences
Article Number: 075009
Appears in Collections:Mathematics
Applied Mathematics and Mathematical Physics
Faculty of Natural Sciences

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