Periodic-orbit theory of level correlations

S Heusler; S Muller; A Altland; P Braun; F Haake

doi:10.1103/PhysRevLett.98.044103

Periodic-orbit theory of level correlations

S Heusler, S Muller, A Altland, P Braun, F Haake

Research output: Contribution to journal › Article (Academic Journal) › peer-review

118 Citations (Scopus)

Abstract

We present a semiclassical explanation of the so-called Bohigas-Giannoni-Schmit conjecture which asserts universality of spectral fluctuations in chaotic dynamics. We work with a generating function whose semiclassical limit is determined by quadruplets of sets of periodic orbits. The asymptotic expansions of both the nonoscillatory and the oscillatory part of the universal spectral correlator are obtained. Borel summation of the series reproduces the exact correlator of random-matrix theory.

Translated title of the contribution	Periodic-orbit theory of level correlations
Original language	English
Article number	Article no. 044103
Pages (from-to)	1 - 4
Number of pages	4
Journal	Physical Review Letters
Volume	98 (4)
DOIs	https://doi.org/10.1103/PhysRevLett.98.044103
Publication status	Published - Jan 2007

Bibliographical note

Publisher: American Physical Soc

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abstract = "We present a semiclassical explanation of the so-called Bohigas-Giannoni-Schmit conjecture which asserts universality of spectral fluctuations in chaotic dynamics. We work with a generating function whose semiclassical limit is determined by quadruplets of sets of periodic orbits. The asymptotic expansions of both the nonoscillatory and the oscillatory part of the universal spectral correlator are obtained. Borel summation of the series reproduces the exact correlator of random-matrix theory.",

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AU - Muller, S

AU - Altland, A

AU - Braun, P

AU - Haake, F

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N2 - We present a semiclassical explanation of the so-called Bohigas-Giannoni-Schmit conjecture which asserts universality of spectral fluctuations in chaotic dynamics. We work with a generating function whose semiclassical limit is determined by quadruplets of sets of periodic orbits. The asymptotic expansions of both the nonoscillatory and the oscillatory part of the universal spectral correlator are obtained. Borel summation of the series reproduces the exact correlator of random-matrix theory.

AB - We present a semiclassical explanation of the so-called Bohigas-Giannoni-Schmit conjecture which asserts universality of spectral fluctuations in chaotic dynamics. We work with a generating function whose semiclassical limit is determined by quadruplets of sets of periodic orbits. The asymptotic expansions of both the nonoscillatory and the oscillatory part of the universal spectral correlator are obtained. Borel summation of the series reproduces the exact correlator of random-matrix theory.

U2 - 10.1103/PhysRevLett.98.044103

DO - 10.1103/PhysRevLett.98.044103

M3 - Article (Academic Journal)

C2 - 17358777

VL - 98 (4)

SP - 1

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JO - Physical Review Letters

JF - Physical Review Letters

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