Physics – Condensed Matter
Scientific paper
1997-05-10
Physics
Condensed Matter
15 pages(twocolumn format), LaTeX, EPSF, (figures included)
Scientific paper
10.1103/PhysRevE.57.4063
In the present work we study the two-point correlation function $R(\epsilon)$ of the quantum mechanical spectrum of a classically chaotic system. Recently this quantity has been computed for chaotic and for disordered systems using periodic orbit theory and field theory. In this work we present an independent derivation, which is based on periodic orbit theory. The main ingredient in our approach is the use of the spectral zeta function and its autocorrelation function $C(\epsilon)$. The relation between $R(\epsilon)$ and $C(\epsilon)$ is constructed by making use of a probabilistic reasoning similar to that which has been used for the derivation of Hardy -- Littlewood conjecture. We then convert the symmetry properties of the function $C(\epsilon)$ into relations between the so-called diagonal and the off-diagonal parts of $R(\epsilon)$. Our results are valid for generic systems with broken time reversal symmetry, and with non-commensurable periods of the periodic orbits.
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