Spontaneous symmetry breaking and superposition of states in systems with dynamic chaos
Keywords:nonlinear dynamics, strange attractor, probability density, chaos, perturbation theory, superposition principle
The article discusses one of the typical problems described by the equations of nonlinear dynamics—forced oscillations in a system with W-potential. It focuses, in particular, on chaotic oscillations in the presence of dissipation. In this case the state of the system is described by a chaotic (strange) attractor and can be characterized by the probability density in the phase space. A partial differential equation for the probability density is presented. It is shown that when the parameters change in the system under consideration, symmetry breaking can occur. In this case the superposition principle for the probability density is valid. It is similar to the superposition principle for the quantum mechanical function in the problem of particle motion in the W-potential field.
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