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.
引用
收藏
页数：12
相关论文
共 50 条
  • [1] Relativistic non-Hermitian quantum mechanics
    Jones-Smith, Katherine
    Mathur, Harsh
    [J]. PHYSICAL REVIEW D, 2014, 89 (12):
  • [2] Pseudospectra in non-Hermitian quantum mechanics
    Krejcirik, D.
    Siegl, P.
    Tater, M.
    Viola, J.
    [J]. JOURNAL OF MATHEMATICAL PHYSICS, 2015, 56 (10)
  • [3] Non-Hermitian noncommutative quantum mechanics
    J. F. G. dos Santos
    F. S. Luiz
    O. S. Duarte
    M. H. Y. Moussa
    [J]. The European Physical Journal Plus, 134
  • [4] Editorial: Non-Hermitian quantum mechanics
    Hatano, Naomichi
    [J]. PROGRESS OF THEORETICAL AND EXPERIMENTAL PHYSICS, 2020, 2020 (12):
  • [5] Non-Hermitian noncommutative quantum mechanics
    dos Santos, J. F. G.
    Luiz, F. S.
    Duarte, O. S.
    Moussa, M. H. Y.
    [J]. EUROPEAN PHYSICAL JOURNAL PLUS, 2019, 134 (07):
  • [6] The area distribution of two-dimensional random walks and non-Hermitian Hofstadter quantum mechanics
    Matveenko, Sergey
    Ouvry, Stephane
    [J]. JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2014, 47 (18)
  • [7] Localization, Resonance, and Non-Hermitian Quantum Mechanics
    Hatano, Naomichi
    [J]. JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, 2003, 72
  • [8] Statistical mechanics for non-Hermitian quantum systems
    Cao, Kui
    Kou, Su-Peng
    [J]. PHYSICAL REVIEW RESEARCH, 2023, 5 (03):
  • [9] CONFORMAL ANOMALY IN NON-HERMITIAN QUANTUM MECHANICS
    Giri, Pulak Ranjan
    [J]. INTERNATIONAL JOURNAL OF MODERN PHYSICS A, 2010, 25 (01): : 155 - 161
  • [10] QUANTUM-MECHANICS WITH A NON-HERMITIAN HAMILTONIAN
    GRIGORENKO, AN
    [J]. PHYSICS LETTERS A, 1993, 172 (05) : 350 - 354
12345