Spectral form factor of hyperbolic systems: leading off-diagonal approximation
نویسنده
چکیده
The spectral fluctuations of a quantum Hamiltonian system with time-reversal symmetry are studied in the semiclassical limit by using periodic-orbit theory. It is found that, if long periodic orbits are hyperbolic and uniformly distributed in phase space, the spectral form factor K(τ) agrees with the GOE prediction of random-matrix theory up to second order included in the time τ measured in units of the Heisenberg time (leading off-diagonal approximation). Our approach is based on the mechanism of periodic-orbit correlations discovered recently by Sieber and Richter [1]. By reformulating the theory of these authors in phase space, their result on the free motion on a Riemann surface with constant negative curvature is extended to general Hamiltonian hyperbolic systems with two degrees of freedom. PACS numbers: 05.45.Mt, 03.65.Sq
منابع مشابه
Leading off-diagonal approximation for the spectral form factor for uniformly hyperbolic systems
We consider the semiclassical approximation to the spectral form factor K(τ) for twodimensional uniformly hyperbolic systems, and derive the first off-diagonal correction for small τ . The result agrees with the τ -term of the form factor for the GOE random matrix ensemble. PACS numbers: 03.65.Sq Semiclassical theories and applications. 05.45.Mt Semiclassical chaos (“quantum chaos”). 1 E-mail: ...
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