Wannier–Stark resonances in optical and semiconductor superlattices

In this work, we discuss the resonance states of a quantum particle in a periodic potential plus a static force. Originally, this problem was formulated for a crystal electron subject to a static electric field and it is nowadays known as the Wannier–Stark problem. We describe a novel approach to th...

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Bibliographic Details
Published inPhysics reports Vol. 366; no. 3; pp. 103 - 182
Main Authors Glück, Markus, R. Kolovsky, Andrey, Korsch, Hans Jürgen
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.08.2002
Subjects
Optical lattices
Quantum chaos
Resonance statistics
Semiconductor superlattices
Wannier–Stark resonances
Optical lattices
03.65.−w
Resonance statistics
Semiconductor superlattices
73.20.Dx
Quantum chaos
05.45.+b
32.80.Pj
Wannier–Stark resonances
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Summary:In this work, we discuss the resonance states of a quantum particle in a periodic potential plus a static force. Originally, this problem was formulated for a crystal electron subject to a static electric field and it is nowadays known as the Wannier–Stark problem. We describe a novel approach to the Wannier–Stark problem developed in recent years. This approach allows to compute the complex energy spectrum of a Wannier–Stark system as the poles of a rigorously constructed scattering matrix and solves the Wannier–Stark problem without any approximation. The suggested method is very efficient from the numerical point of view and has proven to be a powerful analytic tool for Wannier–Stark resonances appearing in different physical systems such as optical lattices or semiconductor superlattices.
ISSN:0370-1573
1873-6270
DOI:10.1016/S0370-1573(02)00142-4