Projection operator approach to transport in complex single-particle quantum systems

TL;DR

This paper explores the use of the time-convolutionless projection operator method to analyze transport phenomena in complex, modular quantum systems, providing a systematic perturbation framework for understanding local quantity dynamics.

Contribution

It introduces a lowest order TCL approach for transport in modular quantum systems and extends the projection to include non-Markovian effects for improved accuracy.

Findings

Lowest order TCL effectively models transport in modular quantum systems.

The approach reveals how transport depends on system size and structure.

Extended projection captures non-Markovian influences on transport.

Abstract

We discuss the time-convolutionless (TCL) projection operator approach to transport in closed quantum systems. The projection onto local densities of quantities such as energy, magnetization, particle number, etc. yields the reduced dynamics of the respective quantities in terms of a systematic perturbation expansion. In particular, the lowest order contribution of this expansion is used as a strategy for the analysis of transport in "modular" quantum systems corresponding to quasi one-dimensional structures which consist of identical or similar many-level subunits. Such modular quantum systems are demonstrated to represent many physical situations and several examples of complex single-particle models are analyzed in detail. For these quantum systems lowest order TCL is shown to represent an efficient tool which also allows to investigate the dependence of transport on the considered length scale. To estimate the range of validity of the obtained equations of motion we extend the standard projection to include additional degrees of freedom which model non-Markovian effects of higher orders.