Semiclassical universality of parametric spectral correlations

Abstract

We consider quantum systems with a chaotic classical limit that depend on an external parameter, and study correlations between the spectra at different parameter values. In particular, we consider the parametric spectral form factor $K(\tau ,x)$ which depends on a scaled parameter difference $x$. For parameter variations that do not change the symmetry of the system we show by using semiclassical periodic orbit expansions that the small $\tau$ expansion of the form factor agrees with Random Matrix Theory for systems with and without time reversal symmetry.

18 pages, no figures

References in corpus (3)

• Semiclassical Foundation of Universality in Quantum Chaos
• Periodic-Orbit Theory of Universality in Quantum Chaos
• Semiclassical Theory of Chaotic Conductors

Cited by in corpus (9)

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• The density of states of chaotic Andreev billiards
• Quantum Corrections to Fidelity Decay in Chaotic Systems
• Semiclassical expansion of parametric correlation functions of the quantum time delay
• Semiclassics for chaotic systems with tunnel barriers
• Semiclassical Theory for Universality in Quantum Chaos with Symmetry Crossover
• Semiclassical Approach to Parametric Spectral Correlation with Spin 1/2
• The semiclassical continuity equation for open chaotic systems
• Chaotic Transport in the Symmetry Crossover Regime with a Spin-orbit Interaction