Chaos and anomalous transport in a semiclassical Bose-Hubbard chain

TL;DR

This paper investigates chaotic dynamics and anomalous transport in a semiclassical Bose-Hubbard chain, revealing mixed phase space, universal anomalous diffusion, and a crossover to normal diffusion over long times.

Contribution

It demonstrates the presence of mixed phase space and universal anomalous transport in the Bose-Hubbard chain, supported by analytical scaling and Langevin equation analyses.

Findings

Mixed phase space with regular and chaotic dynamics persists in long chains.

Anomalous diffusion with discrete transport exponents occurs in occupation number space.

Crossover from anomalous to normal diffusion at long times.

Abstract

We study chaotic dynamics and anomalous transport in a Bose-Hubbard chain in the semiclassical regime (the limit when the number of particles goes to infinity). We find that the system has mixed phase space with both regular and chaotic dynamics, even for long chains with up to hundred wells. The consequence of the mixed phase space is strongly anomalous diffusion in the space of occupation numbers, with a discrete set of transport exponents. After very long times the system crosses over to the hydrodynamic regime with normal diffusion. Anomalous transport is quite universal, almost completely independent of the parameters of the model (Coulomb interaction, chemical potential): it is mainly determined by the initial distribution of particles along the chain. We corroborate our findings by analytical arguments: scaling analysis for the anomalous regime and the Langevin equation for the normal diffusion regime.