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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 | Abstract: | We 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 | Services: | Forum | Review | PDF | Favorites |
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