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Quantization of a free particle interacting linearly with a harmonic oscillator

Mainiero, Thomas and Porter, Mason A. (2007) Quantization of a free particle interacting linearly with a harmonic oscillator. Chaos, 17 (4). Art. No. 043130. ISSN 1054-1500.

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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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Additional Information:©2007 American Institute of Physics. (Received 13 February 2007; accepted 1 November 2007; published online 28 December 2007) We thank Stephan De Bièvre, Jens Marklof, Jerry Marsden, Alex McCauley, Kevin Mitchell, Paul Parris, Alex Silvius, and Turgay Uzer for useful discussions concerning this research. We also thank Alex Barnett, Mark Dykman, Joachim Stolze, and two anonymous referees for providing numerous critical comments and suggestions regarding this manuscript. T.M. acknowledges support from Caltech’s Summer Undergraduate Research Fellowship (SURF) Program and the Richter Memorial Funds. M.A.P. acknowledges support from the Gordon and Betty Moore Foundation through Caltech’s Center for the Physics of Information where he held a postdoctoral position during this research).
Subject Keywords:chaos, eigenvalues and eigenfunctions, energy level crossing, harmonic oscillators
Issue or Number:4
Record Number:CaltechAUTHORS:MAIcha07b
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:9424
Deposited By: Archive Administrator
Deposited On:30 Dec 2007
Last Modified:03 Oct 2019 00:00

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