2001/11/30 by M. Glueck, Markus Glück, A. R. Kolovsky +1 · 5 citations
Physics and Astronomy · #Laser-Matter Interactions and Applications #Quantum chaos and dynamical systems #Spectroscopy and Quantum Chemical Studies #quant-ph
paper · pdf · doi:10.1016/s0370-1573(02)00142-4
published as Phys. Rep. 366 (2002) 103 · 94 pages, 41 figures, typos corrected, references added
arxiv created 2002/03/18 · openalex publication_date 2002/08/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.