Thermalization in closed quantum systems: semiclassical approach

Thermalization in closed quantum systems can be explained either by means of the eigenstate thermalization hypothesis or the concept of canonical typicality. Both concepts are based on quantum mechanical formalism such as spectral properties of the eigenstates or entanglement between subsystems respectively. Here we study the onset of thermalization of Bose particles in a two-band double well potential using the truncated Wigner approximation. This allows us to use the familiar classical formalism to explain quantum thermalization in this system. In particular, we demonstrate that sampling of an initial quantum state plays the role of a statistical mechanical ensemble, while subsequent chaotic classical evolution turns the initial quantum state into the thermal state.