Fractal energy carpets in non-Hermitian Hofstadter quantum mechanics

被引：7
|
作者：
Chernodub, Maxim N. [1 ,2 ,3 ]
Ouvry, Stephane [4 ]
机构：
[1] Univ Tours, CNRS, Lab Math & Phys Theor, UMR 7350, F-37200 Tours, France
[2] Univ Ghent, Dept Phys & Astron, B-9000 Ghent, Belgium
[3] Far Eastern Fed Univ, Soft Matter Phys Lab, Vladivostok 690950, Russia
[4] Univ Paris 11, CNRS, UMR 8626, Lab Phys Theor & Modeles Stat, F-91405 Orsay, France
来源：
PHYSICAL REVIEW E | 2015年 / 92卷 / 04期
关键词：
Energy spectra - Hausdorff dimension - Hermitians - Quantum particles - Quasimomentum - Space-filling curve - Spider web - Square lattices;
D O I：
10.1103/PhysRevE.92.042102
中图分类号：
O35 [流体力学]; O53 [等离子体物理学];
学科分类号：
070204 ; 080103 ; 080704 ;
摘要：
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 quasimomentum 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 web in contrast to the Hofstadter butterfly for unbiased motion.
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页数：12
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