Anomalous transport in long-ranged open quantum systems

TL;DR

This paper investigates how long-range hopping and dephasing noise influence charge transport in a 1D fermionic system, revealing anomalous super-diffusive behavior for certain decay exponents and deriving fractional diffusion equations.

Contribution

It provides the first analytical demonstration of anomalous transport in long-range open quantum systems with dephasing, linking long-range interactions to fractional diffusion.

Findings

Super-diffusive transport observed for 1<α<1.5

Conventional diffusive behavior for α>1.5

Derivation of fractional diffusion equations from multiple-scale analysis

Abstract

We consider a one-dimensional fermionic lattice system with long-ranged power-law decaying hopping with exponent $\alpha$. The system is further subjected to dephasing noise in the bulk. We investigate two variants of the problem: (i) an open quantum system where the setup is further subjected to boundary reservoirs enabling the scenario of a non-equilibrium steady state charge transport, and (ii) time dynamics of an initially localized single particle excitation in the absence of boundary reservoirs. In both variants, anomalous super-diffusive behavior is observed for $1< \alpha< 1.5$, and for $\alpha> 1.5$ the setup is effectively short-ranged and exhibits conventional diffusive transport. Our findings are supported by analytical calculations based on the multiple-scale analysis technique that leads to the emergence of a fractional diffusion equation for the density profile. Our study unravels an interesting interplay between long-range interaction and dephasing mechanism that could result in the emergence of unconventional behaviour in open quantum systems.