Semiclassical spectral correlator in quasi one-dimensional systems

Details Semiclassical spectral correlator in quasi one-dimensional systems Semiclassical spectral correlator in quasi one-dimensional systems

2008-06-12

arxiv.org/abs/0806.2066v1

J. Phys. A: Math. Theor. 41, 395101 (2008)

Nonlinear Sciences

Chaotic Dynamics

10 pages, no figures

Scientific paper

10.1088/1751-8113/41/39/395101

We investigate the spectral statistics of chaotic quasi one dimensional systems such as long wires. To do so we represent the spectral correlation function $R(\epsilon)$ through derivatives of a generating function and semiclassically approximate the latter in terms of periodic orbits. In contrast to previous work we obtain both non-oscillatory and oscillatory contributions to the correlation function. Both types of contributions are evaluated to leading order in $1/\epsilon$ for systems with and without time-reversal invariance. Our results agree with expressions from the theory of disordered systems.

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