Fractal position spectrum for a class of oscillators
Quantum Physics
2015-09-29 v2 Mathematical Physics
math.MP
Abstract
We show that the position operator for a class of -deformed oscillators has a fractal spectrum, homeomorphic to the Cantor set, via a unitary transformation to Harper's model. The class corresponds to a choice of ergodic operators for the deformation function. Hofstadter's butterfly is plotted by direct diagonalization of a position operator with an originally vanishing diagonal. This is equivalent to a one-dimensional hamiltonian without potential.
Keywords
Cite
@article{arxiv.1504.06330,
title = {Fractal position spectrum for a class of oscillators},
author = {E. Sadurní and E. Rivera-Mociños},
journal= {arXiv preprint arXiv:1504.06330},
year = {2015}
}
Comments
9 pages, 2 figures