Transition from diffusive to ballistic dynamics for a class of finite quantum models

TL;DR

This paper investigates how excitation transport in finite quantum systems transitions between diffusive and ballistic regimes depending on the length scale, using analytical and numerical methods.

Contribution

It demonstrates a scale-dependent transition from diffusive to ballistic transport in finite quantum models using the time-convolutionless projection operator technique and exact diagonalization.

Findings

Transport behavior depends on length scale.

Transition from diffusive to ballistic occurs at small and large scales.

Results verified by numerical solutions of the Schrödinger equation.

Abstract

The transport of excitation probabilities amongst weakly coupled subunits is investigated for a class of finite quantum systems. It is demonstrated that the dynamical behavior of the transported quantity depends on the considered length scale, e. g., the introduced distinction between diffusive and ballistic transport appears to be a scale-dependent concept, especially since a transition from diffusive to ballistic behavior is found in the limit of small as well as in the limit of large length scales. All these results are derived by an application of the time-convolutionless projection operator technique and are verified by the numerical solution of the full time-dependent Schroedinger equation which is obtained by exact diagonalization for a range of model parameters.