Effective Equilibrium Description of Nonequilibrium Quantum Transport I: Fundamentals and Methodology
arXiv:1004.5591 · doi:10.1016/j.aop.2011.07.001
Abstract
The theoretical description of strongly correlated quantum systems out of equilibrium presents several challenges and a number of open questions persist. In this paper we focus on nonlinear electronic transport through a quantum dot maintained at finite bias using a concept introduced by Hershfield [Phys. Rev. Lett. 70, 2134 (1993)] whereby one can express such nonequilibrium quantum impurity models in terms of the system's Lippmann-Schwinger operators. These scattering operators allow one to reformulate the nonequilibrium problem as an effective equilibrium problem associated with a modified Hamiltonian, thus facilitating the implementation of equilibrium many-body techniques. We provide an alternative derivation of the effective Hamiltonian of Hershfield using the concept of an "open system". Furthermore, we demonstrate the equivalence between observables computed using the Schwinger-Keldysh framework and the effective equilibrium approach. For the study of transport, the non-equilibrium spectral function of the dot is identified as the quantity of principal interest and we derive general expressions for the current (the Meir-Wingreen formula) and the charge occupation of the dot. We introduce a finite temperature formalism which is used as a tool for computing real time Green's functions. In a companion paper we elucidate a generic scheme for perturbative calculations of interacting models, with particular reference to the Anderson model.
Part I and Part II have been combined in arXiv:1101.1526. Final version to be published in Annals of Physics
References in corpus (28)
- Continuous-time Monte Carlo methods for quantum impurity models
- Observation of the two-channel Kondo effect
- Diagrammatic Monte Carlo simulation of non-equilibrium systems
- On steady-state currents through nano-devices: a scattering-states numerical renormalization group approach to open quantum systems
- Real-time simulations of nonequilibrium transport in the single-impurity Anderson model
- Twofold advance in the theoretical understanding of far-from-equilibrium properties of interacting nanostructures
- A perturbative nonequilibrium renormalization group method for dissipative quantum mechanics: Real-time RG in frequency space (RTRG-FS)
- Weak-coupling quantum Monte Carlo calculations on the Keldysh contour: theory and application to the current-voltage characteristics of the Anderson model
- Transient dynamics of the Anderson impurity model out of equilibrium
- Bosonization of one dimensional fermions out of equilibrium
- Noisy Kondo impurities
- Universal Resistances of the Quantum RC circuit
- Imaginary-time formulation of steady-state nonequilibrium: application to strongly correlated transport
- Theory of non-equilibrium transport in the SU(N) Kondo regime
- Relaxation vs decoherence: Spin and current dynamics in the anisotropic Kondo model at finite bias and magnetic field
- New method for studying steady states in quantum impurity problems: The interacting resonant level model
- Functional renormalization group study of the interacting resonant level model in and out of equilibrium
- Splitting of the Kondo resonance in anisotropic magnetic impurities on surfaces
- Current noise through a Kondo quantum dot in a SU(N) Fermi liquid state
- Comparison between scattering-states numerical renormalization group and the Kadanoff-Baym-Keldysh approach to quantum transport: Crossover from weak to strong correlations
- Shot Noise in SU(N) Quantum Dot Kondo Effects
- Anderson impurity model in nonequilibrium: analytical results versus quantum Monte Carlo data
- Phonon-assisted tunneling and two-channel Kondo physics in molecular junctions
- Imaginary-time formulation of steady-state nonequilibrium in quantum dot models
- Transport through a Kondo quantum dot: Functional RG approach
- Full counting statistics of spin transfer through ultrasmall quantum dots
- Superconducting Tunneling Spectroscopy of a Carbon Nanotube Quantum Dot
- Failure of mean-field approach in out-of-equilibrium Anderson model
Cited by in corpus (23)
- Numerically Exact Long Time Magnetization Dynamics at the Nonequilibrium Kondo Crossover of the Anderson Impurity Model
- Decoherence and lead induced inter-dot coupling in nonequilibrium electron transport through interacting quantum dots: A hierarchical quantum master equation approach
- Auxiliary master equation approach to non-equilibrium correlated impurities
- Non-perturbative stochastic method for driven spin-boson model
- Driven dissipative dynamics and topology of quantum impurity systems
- Tunable Hybrid Quantum Electrodynamics from Non-Linear Electron Transport
- Full Counting Statistics in the Resonant-Level Model
- How to construct the proper gauge-invariant density matrix in steady-state nonequilibrium: Applications to spin-transfer and spin-orbit torques
- Theory of Entropy Production in Quantum Many-Body Systems
- Steady-state spectra, current and stability diagram of a quantum dot: a non-equilibrium Variational Cluster Approach
- Nonequilibrium density matrix for quantum transport: Hershfield approach as a McLennan-Zubarev form of the statistical operator
- Strongly-Correlated Thermoelectric Transport beyond Linear Response
- Imaginary-time quantum many-body theory out of equilibrium I: Formal equivalence to Keldysh real-time theory and calculation of static properties
- Nonequilibrium thermodynamics of interacting tunneling transport: variational grand potential, density-functional formulation, and nature of steady-state forces
- Nonequilibrium density matrix for simultaneous heat and charge steady-state transport in quantum open systems
- Nonequilibrium distribution functions for quantum transport: universality and approximation for the steady state regime
- Impurity model for non-equilibrium steady states
- Non-equilibrium quantum transport through a dissipative resonant level
- Non-equilibrium charge susceptibility and dynamical conductance: Identification of scattering processes in quantum transport
- Exact interacting Green's function for the Anderson impurity at high bias voltages
- Nonlinear Fermi-liquid transport through a quantum dot in asymmetric tunnel junctions
- Quantum Recurrences in a One-Dimensional Gas of Impenetrable Bosons
- Reconciling Kubo and Keldysh Approaches to Fermi-Sea-Dependent Nonequilibrium Observables: Application to Spin Hall Current and Spin-Orbit Torque in Spintronics