Relaxation timescales versus interaction range in long-range quantum systems

Determine the dependence of relaxation time scales on the interaction range exponent α in long-range interacting quantum systems following a quantum quench, in regimes where relaxation is described by generalized Gibbs ensembles under the eigenstate thermalization hypothesis or quantum ergodic theory.

Background

The paper investigates non-equilibrium dynamics in one-dimensional Bose and fermion gases with long-range interactions decaying as 1/rα, focusing on quenches from strongly repulsive to strongly attractive regimes. It analyzes relaxation via many-body entropies and observes violent fragmentation, Fock-space delocalization, and apparent classical-gas behavior.

While the authors characterize relaxation behavior across a broad range of α values and quench strengths, they highlight a general uncertainty about how relaxation times depend on the interaction range. This question is framed within the context of relaxation processes understood through generalized Gibbs ensembles and the eigenstate thermalization hypothesis.

References

Theoretical concepts like the quantum ergodic theory or the eigenstate thermalization hypothesis (ETH) infer possible relaxation processes described through generalized Gibbs ensembles. However, it is unclear on what time scale this occurs depending on the interaction range.

— Unbounded entropy production and violent fragmentation for repulsive-to-attractive interaction quench in long-range interacting systems  (2405.14928 - Molignini et al., 2024) in Section 5, Understanding of relaxation process

Finally, the approach to compact support raises a dynamical question: how do the particle-exchange and structural-relaxation times grow as the tails are suppressed? Determining their dependence on tail strength, density, and particle number would connect the few-particle clustering results to the many-body liquid and clarify the order of the long-time, thermodynamic, and compact-support limits. A quantitative relation between these timescales, the small Laplacian eigenvalues, and the rare large-momentum events would further connect the equilibrium statistics to the mechanisms of melting.

— Statistical mechanics of classical fractons on a line  (2609.25999 - Sadki et al., 22 Sep 2026) in Section Summary and future directions