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Power Spectrum of Long Eigenlevel Sequences in Quantum Chaotic Systems

Riser, Roman; Osipov, Vladimir Al LU and Kanzieper, Eugene (2017) In Physical Review Letters 118(20).
Abstract

We present a nonperturbative analysis of the power spectrum of energy level fluctuations in fully chaotic quantum structures. Focusing on systems with broken time-reversal symmetry, we employ a finite-N random matrix theory to derive an exact multidimensional integral representation of the power spectrum. The N→ limit of the exact solution furnishes the main result of this study - a universal, parameter-free prediction for the power spectrum expressed in terms of a fifth Painlevé transcendent. Extensive numerics lends further support to our theory which, as discussed at length, invalidates a traditional assumption that the power spectrum is merely determined by the spectral form factor of a quantum system.

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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Physical Review Letters
volume
118
issue
20
publisher
American Physical Society
external identifiers
  • scopus:85019929842
  • wos:000401460100004
ISSN
0031-9007
DOI
10.1103/PhysRevLett.118.204101
language
English
LU publication?
yes
id
26528729-bcd4-4c36-9829-3d582f1b9179
date added to LUP
2017-06-14 14:33:56
date last changed
2017-09-18 11:41:15
@article{26528729-bcd4-4c36-9829-3d582f1b9179,
  abstract     = {<p>We present a nonperturbative analysis of the power spectrum of energy level fluctuations in fully chaotic quantum structures. Focusing on systems with broken time-reversal symmetry, we employ a finite-N random matrix theory to derive an exact multidimensional integral representation of the power spectrum. The N→ limit of the exact solution furnishes the main result of this study - a universal, parameter-free prediction for the power spectrum expressed in terms of a fifth Painlevé transcendent. Extensive numerics lends further support to our theory which, as discussed at length, invalidates a traditional assumption that the power spectrum is merely determined by the spectral form factor of a quantum system.</p>},
  articleno    = {204101},
  author       = {Riser, Roman and Osipov, Vladimir Al and Kanzieper, Eugene},
  issn         = {0031-9007},
  language     = {eng},
  month        = {05},
  number       = {20},
  publisher    = {American Physical Society},
  series       = {Physical Review Letters},
  title        = {Power Spectrum of Long Eigenlevel Sequences in Quantum Chaotic Systems},
  url          = {http://dx.doi.org/10.1103/PhysRevLett.118.204101},
  volume       = {118},
  year         = {2017},
}