A metaphor for adiabatic evolution to symmetry

Abstract

In this paper we study a Hamiltonian system with a spatially asymmetric potential. We are interested in the eects on the dynamics when the potential becomes symmetric slowly in time. We focus on a highly simplied non-trivial model problem (a metaphor) to be able to pursue explicit calculations as far as possible. Using the techniques of averaging and adiabatic invariants, we are able to study all bounded solutions, which reveals signicant asymmetric dynamics even when the asymmetric contributions to the potential have become negligibly small.