Wavefunction localization and its semiclassical description in a 3-dimensional system with mixed classical dynamics

Details Wavefunction localization and its semiclassical description in a 3-dimensional system with mixed classical dynamics Wavefunction localization and its semiclassical description in a 3-dimensional system with mixed classical dynamics

2000-09-04

arxiv.org/abs/nlin/0009010v1

Physica Scripta T90, 146 (2001)

Nonlinear Sciences

Chaotic Dynamics

4 pages, 5 figures, contribution to the Nobel Symposium on Quantum Chaos

Scientific paper

10.1238/Physica.Topical.090a0014

We discuss the localization of wavefunctions along planes containing the shortest periodic orbits in a three-dimensional billiard system with axial symmetry. This model mimicks the self-consistent mean field of a heavy nucleus at deformations that occur characteristically during the fission process [1,2]. Many actinide nuclei become unstable against left-right asymmetric deformations, which results in asymmetric fragment mass distributions. Recently we have shown [3,4] that the onset of this asymmetry can be explained in the semiclassical periodic orbit theory by a few short periodic orbits lying in planes perpendicular to the symmetry axis. Presently we show that these orbits are surrounded by small islands of stability in an otherwise chaotic phase space, and that the wavefunctions of the diabatic quantum states that are most sensitive to the left-right asymmetry have their extrema in the same planes. An EBK quantization of the classical motion near these planes reproduces the exact eigenenergies of the diabatic quantum states surprisingly well.

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