Abstract
The ensemble average of noninteracting particles in a nonlinear oscillator system is investigated. Depending on the initial phase-space distribution, the nonlinearity-induced dephasing mechanism can lead to temporal decays of the average particle position that can be quite different from the standard exponential decay. In fact, the approach to the equilibrium can be Gaussian or even nonmonotonic in time. In the long-time limit, it is possible to construct a single differential equation for the time evolution of the average position. Unlike the infinite set of coupled nonlinear differential equations derived from the standard approach based on the Liouville equation, this equation can be even linear. We also show that the predicted dephasing mechanisms have their direct counterpart in the corresponding dynamics of quantum mechanical wave packets.
- Received 3 November 2021
- Revised 7 March 2022
- Accepted 28 April 2022
DOI:https://doi.org/10.1103/PhysRevA.105.052209
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