pith. machine review for the scientific record. sign in

arxiv: 2604.12316 · v2 · submitted 2026-04-14 · 🪐 quant-ph · cond-mat.stat-mech· nlin.CD

Recognition: unknown

The Quantum Kicked Rotor: A Paradigm of Quantum Chaos. Foundational aspects and new perspectives

Giuliano Benenti , Giulio Casati , Jiangbin Gong , Zhixing Zou
Authors on Pith no claims yet

Pith reviewed 2026-05-10 15:13 UTC · model grok-4.3

classification 🪐 quant-ph cond-mat.stat-mechnlin.CD
keywords quantum chaoskicked rotordynamical localizationquantum resonancesFloquet systemstopological phasesnon-Hermitian dynamics
0
0 comments X

The pith

The kicked rotor acts as a unifying model that captures the transition from classical chaos to key quantum effects like localization and resonances.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper uses the kicked rotor to establish a simple framework for understanding how regular motion turns chaotic in classical systems and how quantum mechanics modifies this through dynamical localization and resonances. It demonstrates that characteristic time scales govern the quantum-classical correspondence and shows how the model extends to experimental setups in atomic physics and emerging quantum technologies. A reader would care because this single system organizes a wide range of phenomena that otherwise require separate treatments in condensed matter and quantum information contexts. The review then moves to recent extensions including near-resonant behavior, topological features, and non-Hermitian dynamics, indicating the model's ongoing utility for new problems.

Core claim

The kicked rotor provides a simple yet powerful model for introducing many of the central concepts of classical and quantum chaos. Despite its apparent simplicity, it exhibits rich dynamical behavior and has found applications across a wide range of fields, including atomic and optical physics, condensed matter physics, and emerging quantum technologies. Foundational ideas include the classical transition to chaos, quantum dynamical localization, quantum resonances, and the role of time scales in quantum-classical correspondence, with experimental realizations making these concrete. Advanced developments cover near-resonant dynamics, topological features, quantum dynamical phases from classs

What carries the argument

The periodically driven kicked rotor, consisting of a rotator subject to instantaneous kicks at fixed intervals, functions as the central mechanism that displays the classical route to chaos and the quantum suppression of diffusion via localization and resonances.

If this is right

  • Classical energy grows diffusively above a critical kick strength while quantum evolution localizes after a characteristic break time.
  • Quantum resonances at rational multiples of the driving period produce ballistic rather than localized spreading.
  • Experimental cold-atom implementations directly map the predicted localization lengths and resonance peaks.
  • Topological invariants appear in the Floquet spectrum of kicked variants, linking to protected edge modes.
  • Non-Hermitian extensions produce distinct dynamical phases whose boundaries are set by classical transport properties.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The model's minimal parameter set suggests it could serve as a testbed for simulating chaos effects in small quantum processors without extra hardware overhead.
  • Near-resonant regimes may connect directly to Floquet engineering techniques used in driven many-body systems.
  • Quantum dynamical phases inferred from classical transport could offer a route to classifying chaos in open systems where Hermitian assumptions fail.

Load-bearing premise

The kicked rotor's specific behaviors and extensions generalize meaningfully to broader quantum chaotic systems and emerging technologies without requiring major case-by-case modifications.

What would settle it

An experimental or numerical observation in a different quantum chaotic system where the break time for localization or the resonance conditions deviate qualitatively from kicked-rotor predictions, even after scaling the drive strength and period, would undermine its status as a general paradigm.

read the original abstract

The kicked rotor provides a simple yet powerful model for introducing many of the central concepts of classical and quantum chaos. Despite its apparent simplicity, it exhibits rich dynamical behavior and has found applications across a wide range of fields, including atomic and optical physics, condensed matter physics, and emerging quantum technologies. This chapter begins by exploring foundational ideas using the kicked rotor as a unifying framework. We first discuss the transition from regular to chaotic motion in the classical system, and then introduce key quantum phenomena such as dynamical localization and quantum resonances. Special attention is devoted to the emergence of characteristic time scales and their role in the quantum-classical correspondence. To make these ideas more concrete, we also provide a brief overview of experimental realizations of the kicked rotor and its variants, illustrating how theoretical concepts are implemented in practice. In the second part of the chapter, we guide the reader toward more recent and advanced developments. Topics include near-resonant dynamics, topological features of kicked systems, the emergence of quantum dynamical phases inferred from classical transport properties, and extensions to non-Hermitian physics. We conclude with a discussion of open problems and future perspectives, outlining directions in which the kicked rotor continues to offer valuable insights.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 3 minor

Summary. The manuscript is a review chapter positioning the quantum kicked rotor as a unifying pedagogical model for classical and quantum chaos. It covers the classical regular-to-chaotic transition, quantum dynamical localization, resonances, emergence of characteristic time scales and quantum-classical correspondence, experimental realizations in atomic/optical systems, followed by advanced topics including near-resonant dynamics, topological features of kicked systems, quantum dynamical phases inferred from classical transport, non-Hermitian extensions, and concludes with open problems and future perspectives.

Significance. If the coverage of literature is accurate and balanced, the review would provide significant pedagogical value by using a single simple model to bridge foundational concepts with recent extensions in quantum chaos. It could serve as a reference for researchers in atomic physics, condensed matter, and quantum technologies, highlighting applications without introducing new quantitative claims. The structured progression from basics to advanced developments is a strength, as is the emphasis on experimental implementations and open directions.

minor comments (3)
  1. [Abstract] The abstract states that the kicked rotor 'exhibits rich dynamical behavior' but does not specify which behaviors are unique to the model versus generic to chaotic systems; a brief clarifying sentence would strengthen the unifying-framework claim.
  2. [Experimental realizations] In the discussion of experimental realizations, the overview of cold-atom implementations would benefit from explicit mention of the role of finite-temperature effects or decoherence sources, as these are central to the quantum-classical correspondence section.
  3. [Non-Hermitian extensions] The section on non-Hermitian extensions should include a short comparison table or explicit mapping showing how the standard kicked-rotor Hamiltonian is modified (e.g., addition of imaginary potentials), to aid readers transitioning from Hermitian cases.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive and accurate summary of our manuscript, as well as for recommending minor revision. The report correctly identifies the pedagogical structure, progression from foundational concepts to advanced topics, and emphasis on experimental realizations. No specific major comments or requested changes were provided in the report.

Circularity Check

0 steps flagged

Review paper summarizing prior literature with no new derivations

full rationale

This is a review article that uses the kicked rotor as a pedagogical unifying framework to summarize established concepts from classical chaos, quantum dynamical localization, resonances, and extensions to topological and non-Hermitian systems. It references prior literature for foundational results and experimental realizations without introducing original quantitative derivations, predictions, or first-principles claims that could reduce to fitted inputs or self-citations by construction. The chapter structure follows standard historical development of the field, with all central ideas drawn from independent external sources rather than internal re-derivations.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

This is a review paper; the abstract introduces no new free parameters, axioms, or invented entities, relying instead on established concepts from prior literature.

pith-pipeline@v0.9.0 · 5523 in / 951 out tokens · 70133 ms · 2026-05-10T15:13:03.494617+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

118 extracted references · 3 canonical work pages · 3 internal anchors

  1. [1]

    Kornfeld, S.V

    I.P. Kornfeld, S.V. Fomin and Y.G. Sinai, Ergodic Theory, Springer-Verlag, New York (1982)

    1982

  2. [2]

    Alekseev and M

    V. Alekseev and M. Yakobson, Symbolic dynamics and hyperbolic dynamic systems, Physics Reports 75 (1981) 290

    1981

  3. [3]

    Ott, Chaos in Dynamical Systems, Cambridge University Press, Cambridge, UK, 2nd ed

    E. Ott, Chaos in Dynamical Systems, Cambridge University Press, Cambridge, UK, 2nd ed. (2002)

    2002

  4. [4]

    Casati, B.V

    G. Casati, B.V. Chirikov and J. Ford, Marginal local instability of quasi-periodic motion, Physics Letters A 77 (1980) 91

    1980

  5. [5]

    Casati, B.V

    G. Casati, B.V. Chirikov, F.M. Izraelev and J. Ford, Stochastic behavior of a quantum pendulum under a periodic perturbation, in Stochastic Behavior in Classical and Quantum Hamiltonian Systems, G. Casati and J. Ford, eds., (Berlin, Heidelberg), pp. 334–352, Springer Berlin Heidelberg, 1979, DOI

    1979

  6. [6]

    Research concerning the theory of nonlinear resonance and stochasticit

    B.V. Chirikov, “Research concerning the theory of nonlinear resonance and stochasticit. ” 1969

    1969

  7. [7]

    Chirikov, A universal instability of many-dimensional oscillator systems, Physics Reports 52 (1979) 263

    B.V. Chirikov, A universal instability of many-dimensional oscillator systems, Physics Reports 52 (1979) 263

    1979

  8. [8]

    Casati, B.V

    G. Casati, B.V. Chirikov and D.L. Shepelyansky, Quantum limitations for chaotic excitation of the hydrogen atom in a monochromatic field, Phys. Rev. Lett. 53 (1984) 2525

    1984

  9. [9]

    Casati, B.V

    G. Casati, B.V. Chirikov, D.L. Shepelyansky and I. Guarneri, New photoelectric ionization peak in the hydrogen atom, Phys. Rev. Lett. 57 (1986) 823

    1986

  10. [10]

    Casati, B.V

    G. Casati, B.V. Chirikov, I. Guarneri and D.L. Shepelyansky, Dynamical stability of quantum ”chaotic” motion in a hydrogen atom, Phys. Rev. Lett. 56 (1986) 2437

    1986

  11. [11]

    Casati, I

    G. Casati, I. Guarneri and D. Shepelyansky, Hydrogen atom in monochromatic field: chaos and dynamical photonic localization, IEEE Journal of Quantum Electronics 24 (1988) 1420

    1988

  12. [12]

    Bayfield, G

    J.E. Bayfield, G. Casati, I. Guarneri and D.W. Sokol, Localization of classically chaotic diffusion for hydrogen atoms in microwave fields, Phys. Rev. Lett. 63 (1989) 364

    1989

  13. [13]

    Borgonovi, G

    F. Borgonovi, G. Casati and B. Li, Diffusion and localization in chaotic billiards, Phys. Rev. Lett. 77 (1996) 4744

    1996

  14. [14]

    Casati and T

    G. Casati and T. Prosen, The quantum mechanics of chaotic billiards, Physica D: Nonlinear Phenomena 131 (1999) 293

    1999

  15. [15]

    Casati and T.c.v

    G. Casati and T.c.v. Prosen, Triangle map: A model of quantum chaos, Phys. Rev. Lett. 85 (2000) 4261

    2000

  16. [16]

    J. Wang, G. Benenti, G. Casati and W.-g. Wang, Quantum chaos and the correspondence principle, Phys. Rev. E 103 (2021) L030201

    2021

  17. [17]

    J. Wang, G. Benenti, G. Casati and W.-g. Wang, Statistical and dynamical properties of the quantum triangle map, Journal of Physics A: Mathematical and Theoretical 55 (2022) 234002

    2022

  18. [18]

    Arnold and A

    V. Arnold and A. A vez, Ergodic Problems of Classical Mechanics, Advanced book classics, Addison-Wesley (1989)

    1989

  19. [19]

    Lichtenberg and M

    A. Lichtenberg and M. Lieberman, Regular and Chaotic Dynamics, Applied Mathematical Sciences, Springer New York (2013)

    2013

  20. [20]

    Greene, A method for determining a stochastic transition, Journal of Mathematical Physics 20 (1979) 1183

    J.M. Greene, A method for determining a stochastic transition, Journal of Mathematical Physics 20 (1979) 1183

    1979

  21. [21]

    Chirikov, Time-dependent quantum systems, in Chaos and Quantum Physics, Les Houches Session LII, Elsevier Science Publishers (1989)

    B.V. Chirikov, Time-dependent quantum systems, in Chaos and Quantum Physics, Les Houches Session LII, Elsevier Science Publishers (1989)

    1989

  22. [22]

    Izrailev, Simple models of quantum chaos: Spectrum and eigenfunctions, Physics Reports 196 (1990) 299

    F.M. Izrailev, Simple models of quantum chaos: Spectrum and eigenfunctions, Physics Reports 196 (1990) 299 . The Quantum Kicked Rotor: A Paradigm of Quantum Chaos. Foundational aspects and new perspectives 33

    1990

  23. [23]

    Izrailev and D.L

    F.M. Izrailev and D.L. Shepelyanski, Quantum resonance for a rotator in a nonlinear periodic field, Theor. Math. Phys. 43 (1980) 553

    1980

  24. [24]

    Guarneri, On the spectrum of the resonant quantum kicked rotor, Annales Henri Poincaré 10 (2009) 1097

    I. Guarneri, On the spectrum of the resonant quantum kicked rotor, Annales Henri Poincaré 10 (2009) 1097

    2009

  25. [25]

    Casati, J

    G. Casati, J. Ford, I. Guarneri and F. Vivaldi, Search for randomness in the kicked quantum rotator, Phys. Rev. A 34 (1986) 1413

    1986

  26. [26]

    Berman and G

    G. Berman and G. Zaslavsky, Condition of stochasticity in quantum nonlinear systems, Physica A: Statistical Mechanics and its Applications 91 (1978) 450

    1978

  27. [27]

    Chirikov, B, F.M

    F. Chirikov, B, F.M. Izrailev and D.L. Shepelyanski, Dynamical stochasticity in classical and quantum mechanics, Sov. Sci. Rev. C2 (1981) 209

    1981

  28. [28]

    Anderson, Absence of diffusion in certain random lattices, Phys

    P.W. Anderson, Absence of diffusion in certain random lattices, Phys. Rev. 109 (1958) 1492

    1958

  29. [29]

    Lee and T.V

    P.A. Lee and T.V. Ramakrishnan, Disordered electronic systems, Rev. Mod. Phys. 57 (1985) 287

    1985

  30. [30]

    Fishman, D.R

    S. Fishman, D.R. Grempel and R.E. Prange, Chaos, quantum recurrences, and anderson localization, Phys. Rev. Lett. 49 (1982) 509

    1982

  31. [31]

    Grempel, R.E

    D.R. Grempel, R.E. Prange and S. Fishman, Quantum dynamics of a nonintegrable system, Phys. Rev. A 29 (1984) 1639

    1984

  32. [32]

    Bayfield and P.M

    J.E. Bayfield and P.M. Koch, Multiphoton ionization of highly excited hydrogen atoms, Phys. Rev. Lett. 33 (1974) 258

    1974

  33. [33]

    ionization

    P. Koch and K. van Leeuwen, The importance of resonances in microwave “ionization” of excited hydrogen atoms, Physics Reports 255 (1995) 289

    1995

  34. [34]

    Leopold and I.C

    J.G. Leopold and I.C. Percival, Microwave ionization and excitation of rydberg atoms, Phys. Rev. Lett. 41 (1978) 944

    1978

  35. [35]

    Jensen, Stochastic ionization of surface-state electrons, Phys

    R.V. Jensen, Stochastic ionization of surface-state electrons, Phys. Rev. Lett. 49 (1982) 1365

    1982

  36. [36]

    Delone, B.P

    N.B. Delone, B.P. Kraĭnov and D.L. Shepelyanskiĭ, Highly-excited atoms in the electromagnetic field, Soviet Physics Uspekhi 26 (1983) 551

    1983

  37. [37]

    Casati, I

    G. Casati, I. Guarneri and D. Shepelyansky, Classical chaos, quantum localization and fluctuations:, Physica A 163 (1990) 205–214

    1990

  38. [38]

    Moore, J.C

    F.L. Moore, J.C. Robinson, C.F. Bharucha, B. Sundaram and M.G. Raizen, Atom optics realization of the quantum δ-kicked rotor, Phys. Rev. Lett. 75 (1995) 4598

    1995

  39. [39]

    Klappauf, W

    B. Klappauf, W. Oskay, D. Steck and M. Raizen, Quantum chaos with cesium atoms: pushing the boundaries, Physica D: Nonlinear Phenomena 131 (1999) 78

    1999

  40. [40]

    Graham, M

    R. Graham, M. Schlautmann and P. Zoller, Dynamical localization of atomic-beam deflection by a modulated standing light wave, Phys. Rev. A 45 (1992) R19

    1992

  41. [41]

    Abrahams, P.W

    E. Abrahams, P.W. Anderson, D.C. Licciardello and T.V. Ramakrishnan, Scaling theory of localization: Absence of quantum diffusion in two dimensions, Phys. Rev. Lett. 42 (1979) 673

    1979

  42. [42]

    Casati, I

    G. Casati, I. Guarneri and D.L. Shepelyansky, Anderson transition in a one-dimensional system with three incommensurate frequencies, Phys. Rev. Lett. 62 (1989) 345

    1989

  43. [43]

    Chabé, G

    J. Chabé, G. Lemarié, B. Grémaud, D. Delande, P. Szriftgiser and J.C. Garreau, Experimental observation of the anderson metal-insulator transition with atomic matter waves, Phys. Rev. Lett. 101 (2008) 255702

    2008

  44. [44]

    Benenti, G

    G. Benenti, G. Casati, D. Rossini and G. Strini, Principles of Quantum Computation and Information (A Comprehensive Textbook), World Scientific Singapore (2019)

    2019

  45. [45]

    Georgeot and D.L

    B. Georgeot and D.L. Shepelyansky, Exponential gain in quantum computing of quantum chaos and localization, Phys. Rev. Lett. 86 (2001) 2890

    2001

  46. [46]

    Benenti, G

    G. Benenti, G. Casati, S. Montangero and D.L. Shepelyansky, Efficient quantum computing of complex dynamics, Phys. Rev. Lett. 87 (2001) 227901

    2001

  47. [47]

    Benenti, G

    G. Benenti, G. Casati, S. Montangero and D.L. Shepelyansky, Dynamical localization simulated on a few-qubit quantum computer, Phys. Rev. A 67 (2003) 052312

    2003

  48. [48]

    Henry, J

    M.K. Henry, J. Emerson, R. Martinez and D.G. Cory, Localization in the quantum sawtooth map emulated on a quantum-information processor, Phys. Rev. A 74 (2006) 062317

    2006

  49. [49]

    Pizzamiglio, S.Y

    A. Pizzamiglio, S.Y. Chang, M. Bondani, S. Montangero, D. Gerace and G. Benenti, Dynamical localization simulated on actual quantum hardware, Entropy 23 (2021)

    2021

  50. [50]

    Fishman, I

    S. Fishman, I. Guarneri and L. Rebuzzini, Stable quantum resonances in atom optics, Phys. Rev. Lett. 89 (2002) 084101

    2002

  51. [51]

    Fishman, I

    S. Fishman, I. Guarneri and L. Rebuzzini, A theory for quantum accelerator modes in atom optics, Journal of Statistical Physics 110 (2003) 911

    2003

  52. [52]

    M. Abb, I. Guarneri and S. Wimberger, Pseudoclassical theory for fidelity of nearly resonant quantum rotors, Phys. Rev. E 80 (2009) 035206

    2009

  53. [53]

    Sadgrove, S

    M. Sadgrove, S. Wimberger, E. Arimondo, P.R. Berman and C.C. Lin, Chapter 7 - a pseudoclassical method for the atom-optics kicked rotor: from theory to experiment and back, in Advances In Atomic, Molecular, and Optical Physics, vol. 60, pp. 315–369, Academic Press (2011), DOI

    2011

  54. [54]

    J. Wang, I. Guarneri, G. Casati and J. Gong, Long-lasting exponential spreading in periodically driven quantum systems, Phys. Rev. Lett. 107 (2011) 234104

    2011

  55. [55]

    Artuso, F

    R. Artuso, F. Borgonovi, I. Guarneri, L. Rebuzzini and G. Casati, Phase diagram in the kicked Harper model, Phys. Rev. Lett. 69 (1992) 3302

    1992

  56. [56]

    Artuso, G

    R. Artuso, G. Casati, F. Borgonovi, L. Rebuzzini and I. Guarneri, Fractal and dynamical properties of the kicked Harper model, Int. J. Mod. Phys. B 08 (1994) 207

    1994

  57. [57]

    Fang and J

    P. Fang and J. Wang, Superballistic wavepacket spreading in double kicked rotors, Sci. China Phys. Mech. 59 (2016) 680011

    2016

  58. [58]

    Rebuzzini, I

    L. Rebuzzini, I. Guarneri and R. Artuso, Spinor dynamics of quantum accelerator modes near higher-order resonances, Phys. Rev. A 79 (2009) 033614

    2009

  59. [59]

    H. Wang, J. Wang, I. Guarneri, G. Casati and J. Gong, Exponential quantum spreading in a class of kicked rotor systems near high-order resonances, Phys. Rev. E 88 (2013) 052919

    2013

  60. [60]

    Zou and J

    Z. Zou and J. Wang, A pseudoclassical theory for the wavepacket dynamics of the kicked rotor model, Sci. China Phys. Mech. 67 (2024) 230511

    2024

  61. [61]

    Zou and J

    Z. Zou and J. Wang, Pseudoclassical dynamics of the kicked top, Entropy 24 (2022)

    2022

  62. [62]

    Z. Zou, J. Gong and W. Chen, Enhancing quantum metrology by quantum resonance dynamics, Phys. Rev. Lett. 134 (2025) 230802

    2025

  63. [63]

    Ho and J

    D.Y.H. Ho and J. Gong, Quantized adiabatic transport in momentum space, Phys. Rev. Lett. 109 (2012) 010601

    2012

  64. [64]

    Zhou and J

    L. Zhou and J. Gong, Floquet topological phases in a spin- 1/2 double kicked rotor, Phys. Rev. A 97 (2018) 063603

    2018

  65. [65]

    Koyama, K

    Y. Koyama, K. Fujimoto, S. Nakajima and Y. Kawaguchi, Designing nontrivial one-dimensional Floquet topological phases using 34 The Quantum Kicked Rotor: A Paradigm of Quantum Chaos. Foundational aspects and new perspectives a spin-1/2 double-kicked rotor, Phys. Rev. Res. 5 (2023) 043167

    2023

  66. [66]

    Wang, D.Y.H

    H. Wang, D.Y.H. Ho, W. Lawton, J. Wang and J. Gong, Kicked-Harper model versus on-resonance double-kicked rotor model: From spectral difference to topological equivalence, Phys. Rev. E 88 (2013) 052920

    2013

  67. [67]

    Roy and F

    R. Roy and F. Harper, Periodic table for Floquet topological insulators, Phys. Rev. B 96 (2017) 155118

    2017

  68. [68]

    Zhou and J

    L. Zhou and J. Pan, Non-hermitian Floquet topological phases in the double-kicked rotor, Phys. Rev. A 100 (2019) 053608

    2019

  69. [69]

    Zhou, Floquet second-order topological phases in momentum space, Nanomaterials 11 (2021)

    L. Zhou, Floquet second-order topological phases in momentum space, Nanomaterials 11 (2021)

    2021

  70. [70]

    García-García and J

    A.M. García-García and J. Wang, Universality in quantum chaos and the one-parameter scaling theory, Phys. Rev. Lett. 100 (2008) 070603

    2008

  71. [71]

    W. Chen, G. Lemarié and J. Gong, Critical dynamics of long-range quantum disordered systems, Phys. Rev. E 108 (2023) 054127

    2023

  72. [72]

    W. Chen, O. Giraud, J. Gong and G. Lemarié, Describing the critical behavior of the anderson transition in infinite dimension by random-matrix ensembles: Logarithmic multifractality and critical localization, Phys. Rev. B 110 (2024) 014210

    2024

  73. [73]

    W. Chen, O. Giraud, J. Gong and G. Lemarié, Quantum logarithmic multifractality, Phys. Rev. Res. 6 (2024) L032024

    2024

  74. [74]

    Edwards and D.J

    J.T. Edwards and D.J. Thouless, Numerical studies of localization in disordered systems, Journal of Physics C: Solid State Physics 5 (1972) 807

    1972

  75. [75]

    García-García and J

    A.M. García-García and J. Wang, Anderson transition in quantum chaos, Phys. Rev. Lett. 94 (2005) 244102

    2005

  76. [76]

    Zaslavsky, Chaos, fractional kinetics, and anomalous transport, Physics Reports 371 (2002) 461

    G.M. Zaslavsky, Chaos, fractional kinetics, and anomalous transport, Physics Reports 371 (2002) 461

    2002

  77. [77]

    Mirlin, Statistics of energy levels and eigenfunctions in disordered systems, Physics Reports 326 (2000) 259

    A.D. Mirlin, Statistics of energy levels and eigenfunctions in disordered systems, Physics Reports 326 (2000) 259

    2000

  78. [78]

    Chen and C

    Y. Chen and C. Tian, Planck’s quantum-driven integer quantum Hall effect in chaos, Phys. Rev. Lett. 113 (2014) 216802

    2014

  79. [79]

    C. Tian, Y. Chen and J. Wang, Emergence of integer quantum Hall effect from chaos, Phys. Rev. B 93 (2016) 075403

    2016

  80. [80]

    Guarneri, C

    I. Guarneri, C. Tian and J. Wang, Self-duality triggered dynamical transition, Phys. Rev. B 102 (2020) 045433

    2020

Showing first 80 references.