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Periodic orbit theory and spectral statistics for scaling quantum graphs
Yu. Dabaghian
abstract: The explicit solution to the spectral problem of quantum graphs found
recently in \cite{Anima}, is used to produce the exact periodic orbit theory
description for the probability distributions of spectral statistics, including
the distribution for the nearest neighbor separations, $s_{n}=k_{n}-k_{n-1}$,
and the distribution of the spectral oscillations around the average, $\delta
k_{n}=k_{n}-\bar k_{n}$.
- oai_identifier:
- oai:arXiv.org:quant-ph/0701128
- categories:
- quant-ph
- comments:
- 24 pages, 5 figures
- arxiv_id:
- quant-ph/0701128
- created:
- 2007-01-17
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