Optimal light cone for macroscopic particle transport in long-range systems: A quantum speed limit approach

TL;DR

This paper establishes fundamental limits on the speed of macroscopic particle transport in long-range quantum systems using a quantum speed limit framework, providing rigorous bounds applicable to generic bosonic models.

Contribution

It introduces a unified approach based on optimal transport theory to bound transport times in long-range bosonic systems, resolving an open problem.

Findings

Minimum transport time is bounded by source-target distance.

Derived an upper bound for boson number probability in target.

Results apply to arbitrary initial states with long-range interactions.

Abstract

Understanding the ultimate rate at which information propagates is a pivotal issue in nonequilibrium physics. Nevertheless, the task of elucidating the propagation speed inherent in quantum bosonic systems presents challenges due to the unbounded nature of their interactions. In this study, we tackle the problem of macroscopic particle transport in a long-range generalization of the lattice Bose-Hubbard model through the lens of the quantum speed limit. By developing a unified approach based on optimal transport theory, we rigorously prove that the minimum time required for macroscopic particle transport is always bounded by the distance between the source and target regions, while retaining its significance even in the thermodynamic limit. Furthermore, we derive an upper bound for the probability of observing a specific number of bosons inside the target region, thereby providing additional insights into the dynamics of particle transport. Our results hold true for arbitrary initial states under both long-range hopping and long-range interactions, thus resolving an open problem of particle transport in generic bosonic systems.