Spectral statistics of Hamiltonian matrices in tridiagonal form

R. A. Molina , A.P. Zuker (1) , A. Relaño , J. Retamosa

1 IReS - Institut de Recherches Subatomiques

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.

Mots clés: statistical models (nuclear); matrix algebra

Domaines: Physique Nucléaire Théorique [nucl-th]

R. A. Molina, A.P. Zuker, A. Relaño, J. Retamosa. Spectral statistics of Hamiltonian matrices in tridiagonal form. Physical Review C, 2005, 71, 064317 (5 p.). ⟨10.1103/PhysRevC.71.064317⟩. ⟨in2p3-00024568⟩