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Fractal energy carpets in non-Hermitian Hofstadter quantum mechanics

Abstract : 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.
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https://hal.archives-ouvertes.fr/hal-01143350
Contributor : Maxim Chernodub <>
Submitted on : Friday, April 17, 2015 - 1:47:50 PM
Last modification on : Thursday, March 5, 2020 - 5:33:21 PM

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

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