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arXiv · 1504.06330

Fractal position spectrum for a class of oscillators

E. Sadurní·E. Rivera-Mociños
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Abstract

We show that the position operator for a class of $f$-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.

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E. Sadurní, E. Rivera-Mociños. 2015-04-23. Fractal position spectrum for a class of oscillators. https://doi.org/10.1088/1751-8113/48/40/405301

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