The autocorrelation function for spectral determinants of quantum graphs

Abstract

The paper considers the spectral determinant of quantum graph families with chaotic classical limit and no symmetries. The secular coefficients of the spectral determinant are found to follow distributions with zero mean and variance approaching a constant in the limit of large network size. This constant is in general different from the random matrix result and depends on the classical limit. A closed expression for this system dependent constant is given here explicitly in terms of the spectrum of an underlying Markov process.

10 pages, 2 figures

References in corpus (1)

• Unitary stochastic matrix ensembles and spectral statistics

Cited by in corpus (4)

• Quantum Graphs: Applications to Quantum Chaos and Universal Spectral Statistics
• Finite pseudo orbit expansions for spectral quantities of quantum graphs
• A sub-determinant approach for pseudo-orbit expansions of spectral determinants in quantum maps and quantum graphs
• Periodic orbit evaluation of a spectral statistic of quantum graphs without the semiclassical limit