dorsal/arxiv
View SchemaTwo-dimensional Bloch oscillations: A Lie-algebraic approach
| Authors | S. Mossmann, A. Schulze, D. Witthaut, H. J. Korsch |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0409114 |
| URL | https://arxiv.org/abs/quant-ph/0409114 |
| DOI | 10.1088/0305-4470/38/15/010 |
| Journal | J. Phys. A 38, 3381 (2005) |
Abstract
A Lie-algebraic approach successfully used to describe one-dimensional Bloch oscillations in a tight-binding approximation is extended to two dimensions. This extension has the same algebraic structure as the one-dimensional case while the dynamics shows a much richer behaviour. The Bloch oscillations are discussed using analytical expressions for expectation values and widths of the operators of the algebra. It is shown under which conditions the oscillations survive in two dimensions and the centre of mass of a wave packet shows a Lissajous like motion. In contrast to the one-dimensional case, a wavepacket shows systematic dispersion that depends on the direction of the field and the dispersion relation of the field free system.
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"abstract": "A Lie-algebraic approach successfully used to describe one-dimensional Bloch\noscillations in a tight-binding approximation is extended to two dimensions.\nThis extension has the same algebraic structure as the one-dimensional case\nwhile the dynamics shows a much richer behaviour. The Bloch oscillations are\ndiscussed using analytical expressions for expectation values and widths of the\noperators of the algebra. It is shown under which conditions the oscillations\nsurvive in two dimensions and the centre of mass of a wave packet shows a\nLissajous like motion. In contrast to the one-dimensional case, a wavepacket\nshows systematic dispersion that depends on the direction of the field and the\ndispersion relation of the field free system.",
"arxiv_id": "quant-ph/0409114",
"authors": [
"S. Mossmann",
"A. Schulze",
"D. Witthaut",
"H. J. Korsch"
],
"categories": [
"quant-ph"
],
"doi": "10.1088/0305-4470/38/15/010",
"journal_ref": "J. Phys. A 38, 3381 (2005)",
"title": "Two-dimensional Bloch oscillations: A Lie-algebraic approach",
"url": "https://arxiv.org/abs/quant-ph/0409114"
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