Canonical Transformations in Crystals
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 MelloMoshinsky equations can be solved exactly for a class of problems with discrete symmetry, leading to exact propagators for WannierStark ladders in one and two dimensional crystals. We give a detailed study for a particle in a triangular lattice under the influence of a timedependent electric field. A more general set of MelloMoshinsky equations for arbitrary lattices is presented.
 Publication:

Journal of Physics Conference Series
 Pub Date:
 May 2014
 DOI:
 10.1088/17426596/512/1/012013
 arXiv:
 arXiv:1308.2603
 Bibcode:
 2014JPhCS.512a2013S
 Keywords:

 Quantum Physics;
 Mathematical Physics
 EPrint:
 Presented at the symposium Quantum Theory and Symmetries VIII. 14 pages