Equation of motion for nonequilibrium Green functions

Niu, C.; Lin, D. L.; Lin, Tie

doi:10.1088/0953-8984/11/6/015

Cited by 56 publications

(47 citation statements)

References 29 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…For a ballistic system, such equation closes, so a complete, exact solution is possible. However, there are some subtleties (on the boundary conditions/initial conditions) as to how these equations can be solved [39]. The approach taken here is to express the unknown Green's function with what we know, e.g., decoupled equilibrium Green's functions discussed in earlier sections.…”

Section: Equation Of Motion On Contourmentioning

confidence: 99%

Nonequilibrium Green’s function method for quantum thermal transport

et al. 2013

View full text Add to dashboard Cite

This review deals with the nonequilibrium Green's function (NEGF) method applied to the problems of energy transport due to atomic vibrations (phonons), primarily for small junction systems. We present a pedagogical introduction to the subject, deriving some of the well-known results such as the Laudauer-like formula for heat current in ballistic systems. The main aim of the review is to build the machinery of the method so that it can be applied to other situations, which are not directly treated here. In addition to the above, we consider a number of applications of NEGF, not in routine model system calculations, but in a few new aspects showing the power and usefulness of the formalism. In particular, we discuss the problems of multiple leads, coupled left-right-lead system, and system without a center. We also apply the method to the problem of full counting statistics. In the case of nonlinear systems, we make general comments on the thermal expansion effect, phonon relaxation time, and a certain class of mean-field approximations. Lastly, we examine the relationship between NEGF, reduced density matrix, and master equation approaches to thermal transport.

show abstract

Section: Equation Of Motion On Contourmentioning

confidence: 99%

Nonequilibrium Green’s function method for quantum thermal transport

et al. 2013

View full text Add to dashboard Cite

show abstract

“…Multi-level systems were started to be considered only recently [210,211]. Besides, there are some difficulties in building the lesser GF in the nonequilibrium case (at finite bias voltages) by means of the EOM method [212,213,214].…”

Section: General Nanoscale Quantum Transport Theorymentioning

confidence: 99%

Green Function Techniques in the Treatment of Quantum Transport at the Molecular Scale

Ryndyk

Gutiérrez²,

Song

2009

Springer Series in Chemical Physics

View full text Add to dashboard Cite

The theoretical investigation of charge (and spin) transport at nanometer length scales requires the use of advanced and powerful techniques able to deal with the dynamical properties of the relevant physical systems, to explicitly include out-of-equilibrium situations typical for electrical/heat transport as well as to take into account interaction effects in a systematic way. Equilibrium Green function techniques and their extension to non-equilibrium situations via the Keldysh formalism build one of the pillars of current state-of-the-art approaches to quantum transport which have been implemented in both model Hamiltonian formulations and first-principle methodologies. In this chapter we offer a tutorial overview of the applications of Green functions to deal with some fundamental aspects of charge transport at the nanoscale, mainly focusing on applications to model Hamiltonian formulations.

show abstract

“…The noninteracting Green's functions can be obtained easily from the equations of motion [49] using H 0 :…”

Section: B Nonequilibrium Perturbation Theorymentioning

confidence: 99%

“…In the atomic limit, it can be easily verified using equations of motion, [49] that the exact retarded Green's function is…”

Section: The Interpolative Perturbative Approach (Ipa)mentioning

confidence: 99%

“…[42][43][44][45] It can be extended naturally to the nonequilibrium case using the Keldysh formalism. [46][47][48][49] In the equilibrium case, the second order approximation has been used for several nanoscopic systems. [12,35,[50][51][52][53] A shortcoming of this method is that it cannot describe the exponential decrease of T K in the Kondo regime as U is increased.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Nonequilibrium magnetotransport through a quantum dot: An interpolative perturbative approach

Aligia

2006

Phys. Rev. B

View full text Add to dashboard Cite

We study the differential conductance, spectral density and magnetization, for a quantum dot coupled to two conducting leads as a function of bias voltage V ds , magnetic field B and temperature T . The system is modeled with the Anderson model solved using a spin dependent interpolative perturbative approximation in the Coulomb repulsion U that conserves the current. For large enough magnetic field, the differential conductance as a function of bias voltage shows split peaks. This splitting is larger than the corresponding splitting in the spectral density of states ρ d (ω), in agreement with experiment.

show abstract

Equation of motion for nonequilibrium Green functions

Cited by 56 publications

References 29 publications

Nonequilibrium Green’s function method for quantum thermal transport

Nonequilibrium Green’s function method for quantum thermal transport

Green Function Techniques in the Treatment of Quantum Transport at the Molecular Scale

Nonequilibrium magnetotransport through a quantum dot: An interpolative perturbative approach

Contact Info

Product

Resources

About