Canonical Transformations in Crystals
| Autor: | Sadurní, Emerson |
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| Rok vydání: | 2013 |
| Předmět: | |
| Zdroj: | Journal of Physics: Conference Series 512 (2014) 012013 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1088/1742-6596/512/1/012013 |
| Popis: | The space representations of linear canonical transformations were studied by Moshinsky and Quesne in 1972. For a few decades, the bilinear hamiltonian remained as the only exactly solvable representative for such problems. In this work we show that the Mello-Moshinsky equations can be solved exactly for a class of problems with discrete symmetry, leading to exact propagators for Wannier-Stark ladders in one and two dimensional crystals. We give a detailed study for a particle in a triangular lattice under the influence of a time-dependent electric field. A more general set of Mello-Moshinsky equations for arbitrary lattices is presented. Comment: Presented at the symposium Quantum Theory and Symmetries VIII. 14 pages |
| Databáze: | arXiv |
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