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Chinese Physics C

Chaotic Motion of a Nucleon in Mean Field Potential with Octupole Deformation (III) Study of Probability Density Distribution in Space-Temporal Variation of Initial Coherent States and the Strength of Disturbance

Li Jun

Published Jan 1, 2000• 0 citations
OpenAlex

Abstract

Coherent states of two dimensional asymmetrical harmonic oscillator,which prop- agate in additional octupole deformation potentials, are used to investigate the complexity of the density matrix and the sensitivity against the strength of disturbance. It was found that according to the regular, partly chaotic and overall chaotic characteristics of the phase space of the classical system,its quantum analogy bears out corresponding characters, which were associated with the existence of the negative curvature at the potential surface and the magni- tude of the negative curvature.

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Chinese Physics C•Jan 1, 2002•0 citations
Coherent states of two dimensional asymmetrical harmonic oscillator,which prop- agate in additional octupole deformation potentials, are used to investigate the complexity of the density matrix and the sensitivity against the strength of disturbance. It was found that according to the regular, partly chaotic and overall chaotic characteristics of the phase space of the classical system,its quantum analogy bears out corresponding characters, which were associated with the existence of the negative curvature at the potential surface and the magni- tude of the negative curvature.
Coherent states of two dimensional asymmetrical harmonic oscillator, which prop- agate in additional octupole deformation potentials, are used to investigate the characteristics of expectation values and uncertainty measures of canonical variables in space-temporal varia- tions.The quantum chaotic system shows varying behaviors as the corresponding classical chaotic system does. Thus the characteristics of quantum chaos are associated with the geom- atric symmetry of the potential surface, specifically, the existence of the negative curvature and the magnitude of the curvature in the potential surface.
In the two cases that the deformed nuclear system is regular and chaotic, the spatial temporal evolution of the coherent states of a two dimensional harmonic oscillator system as an initial state was analyzed with the Fourier transformation, especially by comparing the Fourier transformation of the width of the wave packet in the whole time stage with that the wave packet approaching to the saturation in the chaotic system. It was found that since a large number of avoided level crossings destroy the regular structure of the state space of the system, the components in the wave packet are no longer coherent and the motion of the wave packet becomes chaotic. Afterwards, the contribution coming from the different components tends to uniform, the influence of the avoided level crossings on the motion of the wave packet is not obvious also
The time evolution of expectation values of the basic dynamic variables in a quantum system under different effective Planck constant were compared with the exact values of the basic dynamic variables in classical system. It is found, for the regular motion, the difference comes from the quantum effect; for the chaotic motion, it comes from the dynamical effect and the destruction of the dynamical system. With these results, a correspondence between the quantum heterogeneity of the phase space and the Lyapunov exponent is made satisfactorily.