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Article Dans Une Revue Physical Review E : Statistical, Nonlinear, and Soft Matter Physics Année : 2015

Fractal energy carpets in non-Hermitian Hofstadter quantum mechanics

Résumé

We study the non-Hermitian Hofstadter dynamics of a quantum particle with biased motion on a square lattice in the background of a magnetic field. We show that in quasi-momentum space the energy spectrum is an overlap of infinitely many inequivalent fractals. The energy levels in each fractal are space-filling curves with Hausdorff dimension 2. The band structure of the spectrum is similar to a fractal spider net in contrast to the Hofstadter butterfly for unbiased motion.

Dates et versions

hal-01143350 , version 1 (17-04-2015)

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Citer

Maxim N. Chernodub, Stéphane Ouvry. Fractal energy carpets in non-Hermitian Hofstadter quantum mechanics. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, 2015, 92 (042102), pp.12. ⟨10.1103/PhysRevE.92.042102⟩. ⟨hal-01143350⟩
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