Canonical Transformations in Crystals

8th International Symposium on Quantum Theory and Symmetries

Sadurní, E.^1

Instituto de Física, Benemérita Universidad Autónoma de Puebla, Apartado Postal J-48, 72570 Puebla, Mexico^1

关键词: A-particles;    Canonical transformation;    Discrete symmetry;    General sets;    Time-dependent electric field;    Triangular lattice;    Two-dimensional crystals;    Wannier-Stark ladder;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/512/1/012013/pdf
DOI  :  10.1088/1742-6596/512/1/012013

来源: IOP

【 摘 要 】

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.