Conjectured resonance mechanism underlying quantum enhancement of thermalization in Bose-Hubbard rings

Determine whether quantum enhancement of thermalization in Bose-Hubbard rings with weak inter-site hopping (Mott insulator regime) originates from approximate resonances between groups of energy levels that correspond to the occupancy distribution of the initial multi-mode Glauber coherent state and its permutations across lattice sites.

Background

The paper numerically demonstrates that, in the Mott insulator regime of Bose-Hubbard rings, relaxation to equipartition from nonequilibrium coherent states is significantly faster in the quantum model than in the classical Gross–Pitaevskii lattice. This quantum enhancement of thermalization (QET) is attributed to genuine quantum transport channels akin to tunneling that bypass slow classical chaotic diffusion.

To rule out trivial spectral explanations, the authors show that weak disorder suppresses long-time equilibration yet does not noticeably affect the initial acceleration associated with QET, suggesting that near-degeneracies of individual levels are not responsible. They then propose a conjectural spectral mechanism involving approximate resonances between groups of levels associated with permutations of site occupancies of the initial state.

Clarifying whether such group-level approximate resonances are indeed the mechanism driving QET would connect observed dynamics to a concrete spectral structure and distinguish QET from effects due to accidental near-degeneracies or classical chaotic transport alone.

References

In spectral terms, while QET cannot be attributed to near-degeneracies of individual energy levels, we conjecture that it arises from an approximate resonance between groups of energy levels, namely those that are associated with the occupancy distribution of the initial coherent state and its counterparts obtained through permutations of the occupancies among the lattice sites. Classical transport between these groups of levels is slow for weak hopping, and quantum effects similar to tunneling allow the system to bridge across slowly diffusive phase-space regions.

— Quantum Enhancement of Thermalization  (2410.06039 - Qiao et al., 2024) in Main text, paragraph following Figure 3 (Quantum enhancement of thermalization in the presence of disorder)