A many-body approach to transport in quantum systems: From the transient regime to the stationary state

• URL: http://arxiv.org/abs/2201.02646v2
• Date: Fri, 22 Apr 2022 13:09:18 GMT
• Title: A many-body approach to transport in quantum systems: From the transient regime to the stationary state
• Authors: M. Ridley, N. W. Talarico, D. Karlsson, N. Lo Gullo, and R. Tuovinen
• Abstract summary: We review one of the most versatile theoretical approaches to the study of time-dependent correlated quantum transport in nano-systems. Within this formalism, one can treat, on the same formulae, inter-particle interactions, external drives and/or footings, and coupling to baths with a continuum set of degrees of freedom.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We review one of the most versatile theoretical approaches to the study of time-dependent correlated quantum transport in nano-systems: the non-equilibrium Green's function (NEGF) formalism. Within this formalism, one can treat, on the same footing, inter-particle interactions, external drives and/or perturbations, and coupling to baths with a (piece-wise) continuum set of degrees of freedom. After a historical overview on the theory of transport in quantum systems, we present a modern introduction of the NEGF approach to quantum transport. We discuss the inclusion of inter-particle interactions using diagrammatic techniques, and the use of the so-called embedding and inbedding techniques which take the bath couplings into account non-perturbatively. In various limits, such as the non-interacting limit and the steady-state limit, we then show how the NEGF formalism elegantly reduces to well-known formulae in quantum transport as special cases. We then discuss non-equilibrium transport in general, for both particle and energy currents. Under the presence of a time-dependent drive - encompassing pump-probe scenarios as well as driven quantum systems - we discuss the transient as well as asymptotic behavior, and also how to use NEGF to infer information on the out-of-equilibrium system. As illustrative examples, we consider model systems general enough to pave the way to realistic systems. These examples encompass one- and two-dimensional electronic systems, systems with electron-phonon couplings, topological superconductors, and optically responsive molecular junctions where electron-photon couplings are relevant.

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