Spectral statistics of Hamiltonian matrices in tridiagonal form

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When a matrix is reduced to Lanczos tridiagonal form, its matrix elements can be divided into an analytic smooth mean value and a fluctuating part. The next-neighbor spacing distribution P(s) and the spectral rigidity Delta _(3) are shown to be universal functions of the average value of the fluctuating part. It is explained why the behavior of these quantities suggested by random matrix theory is valid in far more general cases.
©2005 The American Physical Society. We thank Oriol Bohigas for enlightening discussions. This work is supported in part by Spanish government grants BFM2000-0600 and FTN2000-0963-C02. R. A. Molina acknowledges financial support from the European Unions Human Potential Program (contract no. HPRN-CT-200000144).
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