Periodic-orbit theory of universality in quantum chaos

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

doi:10.1103/PhysRevE.72.046207

Periodic-orbit theory of universality in quantum chaos

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

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

170 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 universality in quantum chaos
Original language	English
Article number	Article no 044103
Pages (from-to)	1 - 30
Number of pages	30
Journal	Physical Review Letters
Volume	98 (4)
DOIs	https://doi.org/10.1103/PhysRevE.72.046207
Publication status	Published - Jan 2005

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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.",

author = "S Muller and S Heusler and P Braun and F Haake and F Haake and A Altland",

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AU - Muller, S

AU - Heusler, S

AU - Braun, P

AU - Haake, F

AU - Altland, A

N1 - Publisher: American Physical Soc

PY - 2005/1

Y1 - 2005/1

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/PhysRevE.72.046207

DO - 10.1103/PhysRevE.72.046207

M3 - Article (Academic Journal)

SN - 1079-7114

VL - 98 (4)

SP - 1

EP - 30

JO - Physical Review Letters

JF - Physical Review Letters

M1 - Article no 044103

ER -

Periodic-orbit theory of universality in quantum chaos

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