Finite size effects and equilibration in Bose-Hubbard chains with central well dephasing

TL;DR

This study explores how finite size and dephasing affect equilibration, entanglement, and dynamics in Bose-Hubbard chains, revealing size-dependent effects and differences caused by phase diffusion.

Contribution

It demonstrates that initial quantum states influence dynamics, and that larger chains do not fully equilibrate, with phase diffusion altering evolution and entanglement signatures.

Findings

Chains with more than three wells do not reach full equilibrium.

Edge effects become significant in larger chains.

Phase diffusion qualitatively changes the evolution and entanglement indicators.

Abstract

We investigate Bose-Hubbard chains in a central depleted well configuration, with dephasing in the middle well. We look at equilibration of populations, pseudo-entropy, and entanglement measures. Using stochastic integration in the truncated Wigner representation, we find that the initial quantum states of the occupied wells has an influence on the subsequent dynamics, and that with more than three wells, the chains do not reach a full equilibrium, with edge effects becoming important, and the time to reach the steady state becoming longer. The evolutions with and without phase diffusion are qualitatively different. We find no convincing evidence of entanglement in the final states with phase diffusion. Although at least one accepted measure indicates the presence of mode entanglement, we are easily able to show that it can give ambiguous predictions.