Singularity in classical and quantum Kepler Problem with Weak Anisotropy

Details Singularity in classical and quantum Kepler Problem with Weak Anisotropy Singularity in classical and quantum Kepler Problem with Weak Anisotropy

2001-10-23

arxiv.org/abs/nlin/0110042v1

Nonlinear Sciences

Chaotic Dynamics

6 pages, 2 figures, 1 table

Scientific paper

10.1016/S0375-9601(02)00778-8

Anisotropic Kepler problem is investigated by perturbation method in both classical and quantum mechanics. In classical mechanics, due to the singularity of the potential, global diffusion in phase space occurs at an arbitrarily small perturbation parameter. In quantum mechanics, the singularity induces a large transition amplitude between quasi degenerate eigen states, which generically decays as $\hbar$ in the semi-classical limit.

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