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29 March 2024
 
  » arxiv » cond-mat/0310429

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The Ehrenfest Oscillations in The Level Statistics of Chaotic Quantum Dots
Chushun Tian ; Anatoly I. Larkin ;
Date 17 Oct 2003
Subject Mesoscopic Systems and Quantum Hall Effect | cond-mat.mes-hall
AbstractWe study a crossover from classical to quantum picture in the electron energy statistics in a system with broken time-reversal symmetry. The perturbative and nonperturbative parts of the two level correlation function, $R(omega)$ are analyzed. We find that in the intermediate region, $Deltallomegasim t_E^{-1}ll t_{erg}^{-1}$, where $t_E$ and $t_{erg}$ are the Ehrenfest and ergodic times, respectively, $R(omega)$ consists of a series of oscillations with the periods depending on $t_E$, deviating from the universal Wigner-Dyson statistics. These Ehrenfest oscillations have the period dependence as $t_E^{-1}$ in the perturbative part. [For systems with time-reversal symmetry, this oscillation in the perturbative part of $R(omega)$ was studied in an earlier work (I. L. Aleiner and A. I. Larkin, Phys. Rev. E {f 55}, R1243 (1997))]. In the nonperturbative part they have the period dependence as $(Delta^{-1}+alpha t_E)^{-1}$ with $alpha$ a universal numerical factor. The amplitude of the leading order Ehrenfest oscillation in the nonperturbative part is larger than that of the perturbative part.
Source arXiv, cond-mat/0310429
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