Distributions of Transition Matrix Elements in Classically Mixed Quantum Systems

Details Distributions of Transition Matrix Elements in Classically Mixed Quantum Systems Distributions of Transition Matrix Elements in Classically Mixed Quantum Systems

1999-05-18

arxiv.org/abs/chao-dyn/9905029v1

Phys. Rev. E 60 (1999) 2831

Nonlinear Sciences

Chaotic Dynamics

14 pages, 10 figures, REVTEX, submitted to Phys. Rev. E

Scientific paper

10.1103/PhysRevE.60.2831

The quantitative contributions of a mixed phase-space to the mean characterizing the distribution of diagonal transition matrix elements and to the variance characterizing the distributions of non-diagonal transition matrix elements are studied. It is shown that the mean can be expressed as the sum of suitably weighted classical averages along an ergodic trajectory and along the stable periodic orbits. Similarly, it is shown that the values of the variance are well reproduced by the sum of the suitably weighted Fourier transforms of classical autocorrelation functions along an ergodic trajectory and along the stable periodic orbits. The illustrative numerical computations are done in the framework of the Hydrogen atom in a strong magnetic field, for three different values of the scaled energy.

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