Quantization of a Free Particle Interacting Linearly with a Harmonic Oscillator

Details Quantization of a Free Particle Interacting Linearly with a Harmonic Oscillator Quantization of a Free Particle Interacting Linearly with a Harmonic Oscillator

2007-02-14

arxiv.org/abs/nlin/0702025v3

Nonlinear Sciences

Chaotic Dynamics

12 pages, 10 figures; version with higher-quality figures available at http://www.its.caltech.edu/~mason/papers/; version 3: t

Scientific paper

10.1063/1.2819060

We investigate the quantization of a free particle coupled linearly to a harmonic oscillator. This system, whose classical counterpart has clearly separated regular and chaotic regions, provides an ideal framework for studying the quantization of mixed systems. We identify key signatures of the classically chaotic and regular portions in the quantum system by constructing Husimi distributions and investigating avoided level crossings of eigenvalues as functions of the strength and range of the interaction between the system's two components. We show, in particular, that the Husimi structure becomes mixed and delocalized as the classical dynamics becomes more chaotic.

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