期刊
NEW JOURNAL OF PHYSICS
卷 18, 期 -, 页码 -出版社
IOP PUBLISHING LTD
DOI: 10.1088/1367-2630/18/7/075009
关键词
non-Hermitian quantum mechanics; PT-symmetry; Bloch oscillations; semiclassical analysis
资金
- Royal Society [UF130339]
- Engineering and Physical Sciences Research Council [EP/K502856/1]
- Engineering and Physical Sciences Research Council [1231392] Funding Source: researchfish
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.
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