Quantization of a free particle interacting linearly with a harmonic oscillator.

  title={Quantization of a free particle interacting linearly with a harmonic oscillator.},
  author={Tom Mainiero and Mason A. Porter},
  volume={17 4},
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… 
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Avoided level crossings in the quantization of a mixed regular-chaotic system.

The study of avoided level crossings in the spectra of quantum Hamiltonians whose classical counterparts exhibit mixed regular-chaotic dynamics reveals important information about the quantum



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We discuss a top undergoing constant precession around a magnetic field and suffering a periodic sequence of impulsive nonlinear kicks. The squared angular momentum being a constant of the motion the

Phase space approach to quantum dynamics

Replaces the Schrodinger equation for the time propagation of states of a quantized 2D spherical phase space by the dynamics of a system of N particles lying in phase space. This is done through

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The quantisation of the two-dimensional toric and spherical phase spaces is considered in analytic coherent state representations. Every pure quantum state admits therein a finite multiplicative

Quantum double pendulum: study of an autonomous classically chaotic quantum system.

  • L. Perotti
  • Physics
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2004
Compared with classical and semiclassical results is used to understand the behavior of the energy curves of the levels, to define regimes in terms of the gravity parameter, and to classify the (resonant) interactions among levels by connecting them to various classical phase space structures.

Quantum signatures of chaos

The distinction between level clustering and level repulsion is one of the quantum analogues of the classical distinction between globally regular and predominantly chaotic motion (see Figs. 1, 2,

Classical and Quantum Eigenstates of a Kicked Rotor

We consider the classical kicked rotor as an eigenvalue problem. We formulate the dynamics on a discrete lattice of size N X N and introduce a classical evolution operator. We then modify the

Properties of vibrational energy levels in the quasi periodic and stochastic regimes

Several aspects of the quantal energy spectrum are explored for the Henon–Heiles Hamiltonian system: a striking and initially unexpected continuation of sequences of eigenvalues from the

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In this Letter, the connection between the classical concepts of nonintegrability and chaos and the quantum concept of dynamical symmetry breaking are described and results obtained for a model of two coupled spins are illustrated.

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The authors calculate semiclassical limiting level spacing distributions P(S) for systems whose classical energy surface is divided into a number of separate region in which motion is regular or