Eigensolutions of the kicked Harper model

2005/11/11 by G. A. Kells, Kells, G. A.
Physics and Astronomy · #FOS: Physical sciences #Quantum Physics (quant-ph) #quant-ph

paper · pdf · doi:10.48550/arxiv.quant-ph/0511108

9 pages, 12 figures

arxiv created 2006/07/14 · arxiv updated 2009/12/01

Abstract

The time-evolution operator for the kicked Harper model is reduced to block matrix form when the effective Planck's constant hbar = 2 pi M/N and M and N are integers. Each block matrix is spanned by an orthonormal set of N "kq" (quasi-position/quasi-momentum) functions. This implies that the system's eigenfunctions or stationary states are necessarily discrete and periodic. The reduction allows, for the first time, an examination of the 2-dimensional structure of the system's quasi-energy spectrum and the study of, with unprecedented accuracy, the system's stationary states.

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