Relations Between Quantum and Classical Spectral Determinants (Zeta-Functions)

Details Relations Between Quantum and Classical Spectral Determinants (Zeta-Functions) Relations Between Quantum and Classical Spectral Determinants (Zeta-Functions)

1996-02-25

arxiv.org/abs/cond-mat/9602131v1

Physics

Condensed Matter

4 pages, latex, no figures

Scientific paper

We demonstrate that beyond the universal regime correlators of quantum spectral determinants $\Delta(\epsilon)=\det (\epsilon-\hat{H})$ of chaotic systems, defined through an averaging over a wide energy interval, are determined by the underlying classical dynamics through the spectral determinant $1/Z(z)=\det (z- {\cal L})$, where $e^{-{\cal L}t}$ is the Perron-Frobenius operator. Application of these results to the Riemann zeta function, allows us to conjecture new relations satisfied by this function.

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