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

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 nonequilibrium 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.

Energy dynamics, heat production and heat–work conversion with qubits: toward the development of quantum machines

“…Experimentally, the latter is determined as the linear coefficient of ⟨F ϕ ⟩ as a function of θ. Given the curvature, the Chern number is calculated from equation (68). The comparison between theory and experiment is excellent.…”

“…with P(t) = ∑ ℓ P ℓ (t). While the definition of work is easily connected with the usual definition for a quasi-static process as in equation ( 2), the definition of heat in the time-domain has been the subject of several discussions in the context of electron systems strongly coupled to fermionic reservoirs [60][61][62][63][64][65][66][67][68] and, more recently, also in the context of two-level systems [69]. In particular, there is no full consensus on how to properly account for the energy stored in the contact terms H cont of equation (1).…”

Energy dynamics, heat production and heat-work conversion with qubits: towards the development of quantum machines

“…While the definition of work is easily connected with the usual definition for a quasi-static process as in Eq. ( 2), the definition of heat in the time-domain has been the subject of several discussions in the context of electron systems strongly coupled to fermionic reservoirs [57,58,59,60,61,62,169,64,65] and, more recently, also in the context of two-level systems [66]. In particular, there is no full consensus on how to properly account for the energy stored in the contact terms H cont of Eq.…”

Doping and gap-size dependence of high-harmonic generation in graphene : Importance of consistent formulation of light-matter coupling

“…The last term indicates the contribution from the correlations originating from electron-electron interactions, electronphonon interactions and impurities, although these are absent in our Hamiltonian (1). ∂ t ρ(t)| corr can be directly evaluated by explicitly including these terms in the Hamiltonian and using the diagrammatic expansions [52][53][54][55] . However, the direct microscopic evaluation of ∂ t ρ(t)| corr is computationally expensive, and instead the correlation effects are often taken into account phenomenologically through the relaxation time approximation [see Sec.…”

“…However, in real materials, electron-electron interactions, electron-phonon interactions, and disorders give rise to relaxation and dephasing of excited carriers. These effects can be taken into account by explicitly including these terms in the Hamiltonian and solve the problem using proper methods such as the nonequilibrium Green's function method [52][53][54][55] . However, such treatment is expensive and, instead, the relaxation and dephasing terms are often taken into account phenomenologically through the relaxation time approximation.…”