Quantum phase-space analysis of equilibration in multi-well Bose-Hubbard systems

We examine the quantum dynamics and thermalisation of two, three and four-well Bose-Hubbard models using stochastic integration in the truncated Wigner phase-space representation. For the two-well model, we compare our results with those obtained by exact methods. We find that all three systems will thermalise, with the details depending on both the classical initial conditions and the initial quantum statistics. We construct an effective single-particle reduced density matrix for each of the systems, using the expectation values of operator moments, and use this to calculate an effective entropy. Knowing the expected maximum values of this entropy for each system, we are able to quantify the different approaches to equilibrium.