Nonlinear Sciences – Chaotic Dynamics
Scientific paper
2002-03-14
Nonlinear Sciences
Chaotic Dynamics
10 pages, 2 figures
Scientific paper
10.1088/0305-4470/35/29/304
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.
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