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

Agam, O.; Andreev, A. V.; Altshuler, B. L.

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

Authors

Agam, O.

Andreev, A. V.

Altshuler, B. L.

Description

We demonstrate that beyond the universal regime correlators of quantum spectral determinants $Δ(ε)=\det (ε-\hat{H})$ 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.
4 pages, latex, no figures