The Breakdown of Classical Mechanics

John Stringer

Rodrigo Muñoz-Vega, Alberto García-Quiroz, Ernesto López-Chávez +1 more

First, the properties of a classical model of spontaneous symmetry breakdown are analyzed. Then, the pros and cons of some pedagogical non-relativistic quantum-mechanical models, also used to illustrate spontaneous symmetry breakdown, are discussed. Finally, a simple quantum-mechanical toy model (a spinor on the line, with a spin-dependent interaction) is presented, that exhibits the spontaneous breaking of an internal symmetry.

Thomas Strohm

G.C. Stey

Shane P. Kelly, Eddy Timmermans, Shan-Wen Tsai

By developing a semiclassical analysis based on the eigenstate thermalization hypothesis, we determine the long time behavior of a large spin evolving with a nonlinear Hamiltonian. Despite integrable classical dynamics, we find the eigenstate thermalization hypothesis for the diagonal matrix elements of observables is satisfied in the majority of eigenstates, and thermalization of long time averaged observables is generic. The exception is an unusual mechanism for the breakdown of thermalization based on an unstable fixed point in the classical dynamics. Using the semiclassical analysis, we derive how the equilibrium values of observables encode properties of the initial state. This analysis shows an unusual memory effect in which the remembered initial state property is not conserved in the integrable classical dynamics. We conclude with a discussion of relevant experiments and the potential generality of this mechanism for long time memory and the breakdown of thermalization.