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

@article{Mainiero2007QuantizationOA,
  title={Quantization of a free particle interacting linearly with a harmonic oscillator.},
  author={Tom Mainiero and Mason A. Porter},
  journal={Chaos},
  year={2007},
  volume={17 4},
  pages={
          043130
        }
}
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… 
View on PubMed
authors.library.caltech.edu
1 Citations

One Citation

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…

References

SHOWING 1-10 OF 97 REFERENCES

Chaotic dynamics of a free particle interacting linearly with a harmonic oscillator

Classical and quantum chaos for a kicked top

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…

Chaos-revealing multiplicative representation of quantum eigenstates

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…

On the zeros of the Husimi distribution

The basic features of the zeros of the Husimi phase-space density of a quantum eigenstate are discussed. It is demonstrated that some special properties of the harmonic oscillator related to the…

The influence of classical resonances on quantum energy levels

In this paper, we examine the behavior of the quantum energy levels of a coupled oscillator system as the zero‐order frequencies are varied to carry the corresponding classical system through a…
...