Regularity versus randomness in matrix-element distributions in quantum nonintegrable Hamiltonian systems
- 1 January 1989
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review A
- Vol. 39 (1) , 282-295
- https://doi.org/10.1103/physreva.39.282
Abstract
The relationship between matrix-element correlations and level-spacing properties is analyzed for typical Hamiltonian systems by introducing both global and local statistical measures. Two-dimensional two-point correlation functions and higher-order traces for Hamiltonian matrices are introduced for abstracting global properties of matrix-element distributions. The global behavior of correlation patterns for Hamiltonian matrices is shown to be markedly different from that for δ-correlated random matrices, which suggests that the Wigner-type spacing characteristic is not a property specific of the standard random matrix but a property of a more general class of nonrandom matrices. A technique of site randomization for matrix elements is introduced for exploring the local property of matrix-element correlations. It is demonstrated that level-spacing distributions for a class of statistically most-realizable matrix element configurations, constructed by a local site randomization from a given Hamiltonian matrix, generally do not coincide with that for a matrix-element configuration of the original Hamiltonian matrix itself.Keywords
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