Generalized Master Equation Approach to Time-Dependent Many-Body Transport

We recall theoretical studies on transient transport through interacting mesoscopic systems. It is shown that a generalized master equation (GME) written and solved in terms of many-body states provides the suitable formal framework to capture both the effects of the Coulomb interaction and electron--photon coupling due to a surrounding single-mode cavity. We outline the derivation of this equation within the Nakajima-Zwanzig formalism and point out technical problems related to its numerical implementation for more realistic systems which can neither be described by non-interacting two-level models nor by a steady-state Markov-Lindblad equation. We first solve the GME for a lattice model and discuss the dynamics of many-body states in a two-dimensional nanowire, the dynamical onset of the current-current correlations in electrostatically coupled parallel quantum dots and transient thermoelectric properties. Secondly, we rely on a continuous model to get the Rabi oscillations of the photocurrent through a double-dot etched in a nanowire and embedded in a quantum cavity. A~many-body Markovian version of the GME for cavity-coupled systems is also presented.Comment: 39 pages, 13 figure

Stepwise introduction of model complexity in a generalized master equation approach to time-dependent transport

We demonstrate that with a stepwise introduction of complexity to a model of an electron system embedded in a photonic cavity and a carefully controlled stepwise truncation of the ensuing many-body space it is possible to describe the time-dependent transport of electrons through the system with a non-Markovian generalized quantum master equation. We show how this approach retains effects of an external magnetic field and the geometry of an anisotropic electronic system. The Coulomb interaction between the electrons and the full electromagnetic coupling between the electrons and the photons are treated in a non-perturbative way using "exact numerical diagonalization".Comment: RevTeX, 14 pages with included eps figures, replaced to mend scaling in figure axes for time "t" and current "J

Coulomb interaction and transient charging of excited states in open nanosystems

We obtain and analyze the effect of electron-electron Coulomb interaction on the time dependent current flowing through a mesoscopic system connected to biased semi-infinite leads. We assume the contact is gradually switched on in time and we calculate the time dependent reduced density operator of the sample using the generalized master equation. The many-electron states (MES) of the isolated sample are derived with the exact diagonalization method. The chemical potentials of the two leads create a bias window which determines which MES are relevant to the charging and discharging of the sample and to the currents, during the transient or steady states. We discuss the contribution of the MES with fixed number of electrons N and we find that in the transient regime there are excited states more active than the ground state even for N=1. This is a dynamical signature of the Coulomb blockade phenomenon. We discuss numerical results for three sample models: short 1D chain, 2D lattice, and 2D parabolic quantum wire.Comment: 12 pages, 12 figure

A correlated-polaron electronic propagator: open electronic dynamics beyond the Born-Oppenheimer approximation

In this work we develop a theory of correlated many-electron dynamics dressed by the presence of a finite-temperature harmonic bath. The theory is based on the ab-initio Hamiltonian, and thus well-defined apart from any phenomenological choice of collective basis states or electronic coupling model. The equation-of-motion includes some bath effects non-perturbatively, and can be used to simulate line- shapes beyond the Markovian approximation and open electronic dynamics which are subjects of renewed recent interest. Energy conversion and transport depend critically on the ratio of electron-electron coupling to bath-electron coupling, which is a fitted parameter if a phenomenological basis of many-electron states is used to develop an electronic equation of motion. Since the present work doesn't appeal to any such basis, it avoids this ambiguity. The new theory produces a level of detail beyond the adiabatic Born-Oppenheimer states, but with cost scaling like the Born-Oppenheimer approach. While developing this model we have also applied the time-convolutionless perturbation theory to correlated molecular excitations for the first time. Resonant response properties are given by the formalism without phenomenological parameters. Example propagations with a developmental code are given demonstrating the treatment of electron-correlation in absorption spectra, vibronic structure, and decay in an open system.Comment: 25 pages 7 figure

Geometrical effects and signal delay in time-dependent transport at the nanoscale

The nonstationary and steady-state transport through a mesoscopic sample connected to particle reservoirs via time-dependent barriers is investigated within the reduced density operator method. The generalized Master equation is solved via the Crank-Nicolson algorithm by taking into account the memory kernel which embodies the non-Markovian effects that are commonly disregarded. We propose a physically reasonable model for the lead-sample coupling which takes into account the match between the energy of the incident electrons and the levels of the isolated sample, as well as their overlap at the contacts. Using a tight-binding description of the system we investigate the effects induced in the transient current by the spectral structure of the sample and by the localization properties of its eigenfunctions. In strong magnetic fields the transient currents propagate along edge states. The behavior of populations and coherences is discussed, as well as their connection to the tunneling processes that are relevant for transport.Comment: 26 pages, 13 figures. To appear in New Journal of Physic

Density functional calculations of nanoscale conductance

Density functional calculations for the electronic conductance of single molecules are now common. We examine the methodology from a rigorous point of view, discussing where it can be expected to work, and where it should fail. When molecules are weakly coupled to leads, local and gradient-corrected approximations fail, as the Kohn-Sham levels are misaligned. In the weak bias regime, XC corrections to the current are missed by the standard methodology. For finite bias, a new methodology for performing calculations can be rigorously derived using an extension of time-dependent current density functional theory from the Schroedinger equation to a Master equation.Comment: topical review, 28 pages, updated version with some revision

A self-consistent quantum master equation approach to molecular transport

We propose a self-consistent generalized quantum master equation (GQME) to describe electron transport through molecular junctions. In a previous study [M.Esposito and M.Galperin. Phys. Rev. B 79, 205303 (2009)], we derived a time-nonlocal GQME to cure the lack of broadening effects in Redfield theory. To do so, the free evolution used in the Born-Markov approximation to close the Redfield equation was replaced by a standard Redfield evolution. In the present paper, we propose a backward Redfield evolution leading to a time-local GQME which allows for a self-consistent procedure of the GQME generator. This approach is approximate but properly reproduces the nonequilibrium steady state density matrix and the currents of an exactly solvable model. The approach is less accurate for higher moments such as the noise.Comment: 9 pages, 4 figure

Density-operator approaches to transport through interacting quantum dots: Simplifications in fourth-order perturbation theory

Various theoretical methods address transport effects in quantum dots beyond single-electron tunneling while accounting for the strong interactions in such systems. In this paper we report a detailed comparison between three prominent approaches to quantum transport: the fourth-order Bloch-Redfield quantum master equation (BR), the real-time diagrammatic technique (RT), and the scattering rate approach based on the T-matrix (TM). Central to the BR and RT is the generalized master equation for the reduced density matrix. We demonstrate the exact equivalence of these two techniques. By accounting for coherences (nondiagonal elements of the density matrix) between nonsecular states, we show how contributions to the transport kernels can be grouped in a physically meaningful way. This not only significantly reduces the numerical cost of evaluating the kernels but also yields expressions similar to those obtained in the TM approach, allowing for a detailed comparison. However, in the TM approach an ad hoc regularization procedure is required to cure spurious divergences in the expressions for the transition rates in the stationary (zero-frequency) limit. We show that these problems derive from incomplete cancellation of reducible contributions and do not occur in the BR and RT techniques, resulting in well-behaved expressions in the latter two cases. Additionally, we show that a standard regularization procedure of the TM rates employed in the literature does not correctly reproduce the BR and RT expressions. All the results apply to general quantum dot models and we present explicit rules for the simplified calculation of the zero-frequency kernels. Although we focus on fourth-order perturbation theory only, the results and implications generalize to higher orders. We illustrate our findings for the single impurity Anderson model with finite Coulomb interaction in a magnetic field.Comment: 29 pages, 12 figures; revised published versio

Fluctuations and Noise: A General Model with Applications

A wide variety of dissipative and fluctuation problems involving a quantum system in a heat bath can be described by the independent-oscillator (IO) model Hamiltonian. Using Heisenberg equations of motion, this leads to a generalized quantum Langevin equation (QLE) for the quantum system involving two quantities which encapsulate the properties of the heat bath. Applications include: atomic energy shifts in a blackbody radiation heat bath; solution of the problem of runaway solutions in QED; electrical circuits (resistively shunted Josephson barrier, microscopic tunnel junction, etc.); conductivity calculations (since the QLE gives a natural separation between dissipative and fluctuation forces); dissipative quantum tunneling; noise effects in gravitational wave detectors; anomalous diffusion; strongly driven quantum systems; decoherence phenomena; analysis of Unruh radiation and entropy for a dissipative system.Comment: Presented at the SPIE International Symposium on Fluctuations and Noise in Photonics and Quantum Optics (Austin, May 2005