Thermalization and its Breakdown for a Large Nonlinear Spin

Understand

By developing a semi-classical 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 a novel mechanism for the breakdown of thermalization based on an unstable fixed point in the classical dynamics.
• Using the semi-classical analysis we derive how the equilibrium values of observables encode properties of the initial state.