Dynamical properties of a particle in a time-dependent double-well potential. (English) Zbl 1047.37059

Summary: Some chaotic properties of a classical particle interacting with a time-dependent double-square-well potential are studied. The dynamics of the system is characterized using a two-dimensional nonlinear area-preserving map. Scaling arguments are used to study the chaotic sea in the low-energy domain. It is shown that the distributions of successive reflections and of corresponding successive reflection times obey power laws with the same exponent. If one or both wells move randomly, the particle experiences the phenomenon of Fermi acceleration in the sense that it has unlimited energy growth.


37N20 Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics)
81Q50 Quantum chaos
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