Nonlinear Sciences – Chaotic Dynamics
Scientific paper
1999-05-18
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.
Boose Dominique
Main Joerg
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