Theory of localization and resonance phenomena in the quantum kicked rotor

Tian, Chushun; Altland, Alexander

doi:10.1088/1367-2630/12/4/043043

Cited by 32 publications

(65 citation statements)

References 49 publications

(128 reference statements)

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“…Then, the homotopy group for the mappings from the n 1 into target space is the same as (13). This implies the absence of a topological term in the effective field theory.…”

Section: Effective Field Theorymentioning

confidence: 99%

“…This is a key step, which makes subsequent derivation completely different from that of the effective field theory for the conventional QKR 13,21 . In deriving Eqs.…”

Section: Separation Of Fast and Slow Modesmentioning

confidence: 99%

“…The quadratic action thereby obtained has a rotationally invariant generalization which describes fluctuations around any Q(n 1 ) (see Ref. 13 for details). The result is…”

Section: Effective Field Theorymentioning

confidence: 99%

“…(i) For (generic) irrational values of h e /(4π), the rotor's energy growth is bounded for periodic QKR, i.e., when the driving force is strictly periodic. This is the celebrated dynamical localization 9 -an analog of Anderson localization in quasi one-dimensional (1D) disordered systems 12,13 . For quasiperiodic QKR, richer phenomena arise.…”

Section: Introductionmentioning

confidence: 99%

“…Correspondingly, the system simulates a quantum metal. The insulating phases, however, are conceptually different from conventional rotor insulators 4,[9][10][11][12][13][14] . That is, we find that each of them is characterized by a hidden quantum number, denoted as σ * H , which is of topological nature.…”

Section: Introductionmentioning

confidence: 99%

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Emergence of integer quantum Hall effect from chaos

Tian¹,

Chen²,

Wang³

2016

Phys. Rev. B

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We present an analytic microscopic theory showing that in a large class of spin-1 2 quasiperiodic quantum kicked rotors, a dynamical analog of the integer quantum Hall effect (IQHE) emerges from an intrinsic chaotic structure. Specifically, the inverse of the Planck's quantum (he) and the rotor's energy growth rate mimic the 'filling fraction' and the 'longitudinal conductivity' in conventional IQHE, respectively, and a hidden quantum number is found to mimic the 'quantized Hall conductivity'. We show that for an infinite discrete set of critical values of he, the long-time energy growth rate is universal and of order of unity ('metallic' phase), but otherwise vanishes ('insulating' phase). Moreover, the rotor insulating phases are topological, each of which is characterized by a hidden quantum number. This number exhibits universal behavior for small he, i.e., it jumps by unity whenever he decreases, passing through each critical value. This intriguing phenomenon is not triggered by the like of Landau band filling, well-known to be the mechanism for conventional IQHE, and far beyond the canonical Thouless-Kohmoto-Nightingale-Nijs paradigm for quantum Hall transitions. Instead, this dynamical phenomenon is of strong chaos origin; it does not occur when the dynamics is (partially) regular. More precisely, we find that, for the first time, a topological object, similar to the topological theta angle in quantum chromodynamics, emerges from strongly chaotic motion at microscopic scales, and its renormalization gives the hidden quantum number. Our analytic results are confirmed by numerical simulations. Our findings indicate that rich topological quantum phenomena can emerge from chaos and might point to a new direction of study in the interdisciplinary area straddling chaotic dynamics and condensed matter physics. This work is a substantial extension of a short paper published earlier by two of us [Y. Chen and C. Tian, Phys. Rev. Lett. 113, 216802 (2014)].

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“…Then, the homotopy group for the mappings from the n 1 into target space is the same as (13). This implies the absence of a topological term in the effective field theory.…”

Section: Effective Field Theorymentioning

confidence: 99%

“…This is a key step, which makes subsequent derivation completely different from that of the effective field theory for the conventional QKR 13,21 . In deriving Eqs.…”

Section: Separation Of Fast and Slow Modesmentioning

confidence: 99%

“…The quadratic action thereby obtained has a rotationally invariant generalization which describes fluctuations around any Q(n 1 ) (see Ref. 13 for details). The result is…”

Section: Effective Field Theorymentioning

confidence: 99%