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Quantum Simulation

Canonical Transformations in Crystals

arXiv
Authors: Emerson Sadurní

Year

2013

Paper ID

33259

Status

Preprint

Abstract Read

~2 min

Abstract Words

97

Citations

N/A

Abstract

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.

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  • This paper contributes to the Quantum Simulation research area in the Quantum Articles archive.
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  • The space representations of linear canonical transformations were studied by Moshinsky and Quesne in 1972.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:1308.2603 [2] arXiv https://arxiv.org/abs/1308.2603 [3] Publisher https://arxiv.org/abs/1308.2603

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