Dynamical behavior and energy dissipation of a classical particle in harmonic-plus-Legendre potential

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Abstract
The dynamical motion of a classical particle in a potential taken as the sum of harmonic oscillator and time-independent or time-dependent multipolar Legendre function was investigated. Starting from various initial conditions, with increasing strength of the Legendre potential, which broke down the rotational invariance of the system, the dynamical behavior of the particle changed from regular to chaotic type. Meanwhile the local curvature of the potential surface may change from positive to zero, and negative sign. This negative curvature was demonstrated to be responsible for the local instability of a trajectory. Only via the mechanism of chaotic particle motion could the time-dependent potential permanently exchange energy with the particle. Contrasting this phenomenon with properties of independent particle model of nucleus with spherical or deformed shape would shed light on the foundation of significant property of the corresponding quantum system and the mechanism of the energy dissipation during nuclear reaction process.
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