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Statistical properties of matrix elements in a Hamilton system between integrability and chaosProsen, Tomaž, 1970-This paper concerns the statistical properties of matrix elements of Hermitianoperators in an eigenbasis of a typical bounded Hamiltonian, which can be classically either ergodic, or integrable, or ... somewhere in between (mixed dynamics). The various types of statistics are addressedČ the (one-)matrix element probability distribution, the correlations among different matrix elements and the so-called cross-correlations of matrix elements belonging to different operators. A sort of n-point correlation function among n matrix elements is defined and calculated (which can reduce to the generalized Feingold-Peres formula for the mean square magnitude of matrix elements in the special case of n = 2) and it is shown that in the semiclassical limit it tends to a microcanonical average over analog expressions involving classical observables. The semiclassical O(h) corrections yield interesting purely classical relations expressing microcanonical averages involving different time Poisson brackets as energy derivatives of microcanonical averages involving only ordinary products. In the classically ergodic case random matrix theory can be applied for modeling of all types of statistics, although the newly defined cross-statistics seem to be behaving nonuniversally at first sight.Source: Annals of physics. - ISSN 0003-4916 (235, 1994, str. 115-164)Type of material - article, component partPublish date - 1994Language - englishCOBISS.SI-ID - 1427044
Author
Prosen, Tomaž, 1970-
Topics
energy-level statistics |
quantum-mechanics |
eigenvector statistics |
analytic boundaries |
transition |
fluctuations |
billiards |
ensemble |
dynamics |
spectra |
energijski nivoji |
kvantna mehanika |
statistika |
prehodi |
fluktuacije |
dinamika |
spektri
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Prosen, Tomaž, 1970- | 12279 |
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