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
  • [21] Non-hermitian quantum mechanics in non-commutative space
    Giri, Pulak Ranjan
    Roy, P.
    EUROPEAN PHYSICAL JOURNAL C, 2009, 60 (01): : 157 - 161
  • [22] Emergent parallel transport and curvature in Hermitian and non-Hermitian quantum mechanics
    Ju, Chia-Yi
    Miranowicz, Adam
    Chen, Yueh-Nan
    Chen, Guang-Yin
    Nori, Franco
    QUANTUM, 2024, 8 : 1 - 20
  • [23] Gaussian eigenstate pinning in non-Hermitian quantum mechanics
    Zeng, Qi-Bo
    Lu, Rong
    PHYSICAL REVIEW A, 2023, 107 (06)
  • [24] Non-hermitian techniques of canonical transformations in quantum mechanics
    Phys Rev A, 2 (982):
  • [25] Non-Hermitian quantum mechanics in the context of the Lindblad equation
    Selsto, Solve
    XXVII INTERNATIONAL CONFERENCE ON PHOTONIC, ELECTRONIC AND ATOMIC COLLISIONS (ICPEAC 2011), PTS 1-15, 2012, 388
  • [26] Non-Hermitian Hamiltonians with Real Spectrum in Quantum Mechanics
    J. da Providência
    N. Bebiano
    J. P. da Providência
    Brazilian Journal of Physics, 2011, 41 : 78 - 85
  • [27] Non-Hermitian Quantum Mechanics with Minimal Length Uncertainty
    Jana, T. K.
    Roy, P.
    SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS, 2009, 5
  • [28] On Unitarity of the Scattering Operator in Non-Hermitian Quantum Mechanics
    Novikov, R. G.
    Taimanov, I. A.
    ANNALES HENRI POINCARE, 2024, 25 (08): : 3899 - 3909
  • [29] Non-Hermitian quantum mechanics and localization in physical systems
    Hatano, N
    QUANTUM COHERENCE AND DECOHERENCE, 1999, : 319 - 322
  • [30] Entanglement and Purification Transitions in Non-Hermitian Quantum Mechanics
    Gopalakrishnan, Sarang
    Gullans, Michael J.
    PHYSICAL REVIEW LETTERS, 2021, 126 (17)
12345