Nonequilibrium Green function method

Lake, R. and Datta, S. (1992) Nonequilibrium greens-function method applied to double-barrier resonanttunneling diodes. Phys. Rev. B, 45, 6670-6685. 

By using the nonequilibrium Green function method with gradient expression as well as the generalized Kadanoff-Baym Ansatz [24], we construct the KSBEs as follows ... 

We use the nonequilibrium Green function (NGF) method, as introduced in Section III. The current in the left (i = L) or right (i = R) contact to the molecule is described by the expression... 

We applied the Liouville-von Neumann (LvN) method, a canonical method, to nonequilibrium quantum phase transitions. The essential idea of the LvN method is first to solve the LvN equation and then to find exact wave functionals of time-dependent quantum systems. The LvN method has several advantages that it can easily incorporate thermal theory in terms of density operators and that it can also be extended to thermofield dynamics (TFD) by using the time-dependent creation and annihilation operators, invariant operators. Combined with the oscillator representation, the LvN method provides the Fock space of a Hartree-Fock type quadratic part of the Hamiltonian, and further allows to improve wave functionals systematically either by the Green function or perturbation technique. In this sense the LvN method goes beyond the Hartree-Fock approximation. 

The effect of thermal pion fluctuations on the specific heat and the neutrino emissivity of neutron stars was discussed in [27, 28] together with other in-medium effects, see also reviews [29, 30], Neutron pair breaking and formation (PBF) neutrino process on the neutral current was studied in [31, 32] for the hadron matter. Also ref. [32] added the proton PBF process in the hadron matter and correlation processes, and ref. [33] included quark PBF processes in quark matter. PBF processes were studied by two different methods with the help of Bogolubov transformation for the fermion wave function [31, 33] and within Schwinger-Kadanoff-Baym-Keldysh formalism for nonequilibrium normal and anomalous fermion Green functions [32, 28, 29],... 

For such nonequilibrium processes, the direct mapping of the electron propagator methods to calculations of electric current becomes inapplicable because of the time-dependent nature of electric current in both phenomena. A time-dependent problem requires the further development of the theory of Green s functions to electron dynamics in which e-e correlation effects are taken into account. Such methodology already exists in physics in which many-body ideas have been developed for time-dependent problems. This theory is based on nonequilibrium Green s or Keldysh functions [2,5, 6, 40-46]. 

In this work, we present a brief introduction to the nonequilibrium Green s function method and discuss two important examples in which nonequli-brium Green s functions can be employed (1) electric current calculations in molecular tunneling devices and (2) in quantum dot-sensitized solar cells. 

The applications of nonequilibrium Green s functions to the calculations of different molecular devices show the importance of electron correlation effects. The electron propagator method is able to explain experimental data and predict new electronic devices. 

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