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Quantization of a free particle interacting linearly with a harmonic oscillator
Thomas Mainiero1, Mason A Porter
1Department of Physics, California Institute of Technology, Pasadena, California 91125, USA.
Abstract:
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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