Mixing in anharmonic potential well
Abstract
We prove phasespace mixing for solutions to Liouville's equation for integrable systems. Under a natural nonharmonicity condition, we obtain weak convergence of the distribution function with rate ⟨time⟩−1. In one dimension, we also study the case where this condition fails at a certain energy, showing that mixing still holds but with a slower rate. When the condition holds and functions have higher regularity, the rate can be faster.
 Publication:

Journal of Mathematical Physics
 Pub Date:
 July 2022
 DOI:
 10.1063/5.0091016
 arXiv:
 arXiv:2201.07019
 Bibcode:
 2022JMP....63g1502M
 Keywords:

 Mathematical Physics;
 Mathematics  Analysis of PDEs;
 82C70 (Primary) 35Q49;
 82C40 (Secondary)
 EPrint:
 12 pages, 1 figure. v2:additional result in Theorem 1.3, typos corrected