scholarly journals Driven Liouville–von Neumann Equation for Quantum Transport and Multiple-Probe Green’s Functions

2019 ◽  
Author(s):  
Francisco Ramírez ◽  
Daniel Dundas ◽  
Cristián G. Sánchez ◽  
Damian A. Scherlis ◽  
Tchavdar N. Todorov
Keyword(s):  
Quantum Transport ◽  
Green's Functions ◽  
Green’S Functions ◽  
Von Neumann ◽  
Von Neumann Equation ◽  
Multiple Probe

Nonequilibrium Green’s Functions

2018 ◽  
Author(s):  
Klaus Morawetz
Keyword(s):  
Green’S Function ◽  
Quantum Transport ◽  
Green's Function ◽  
Green's Functions ◽  
Green’S Functions ◽  
Equation Of Motion ◽  
Diagrammatic Technique ◽  
Initial Correlations ◽  
Nonequilibrium Green’S Functions ◽  
Nonequilibrium Green's Functions

The method of the equation of motion is used to derive the Martin–Schwinger hierarchy for the nonequilibrium Green’s functions. The formal closure of the hierarchy is reached by using the selfenergy which provides a recipe for how to construct selfenergies from approximations of the two-particle Green’s function. The Langreth–Wilkins rules for a diagrammatic technique are shown to be equivalent to the weakening of initial correlations. The quantum transport equations are derived in the general form of Kadanoff and Baym equations. The information contained in the Green’s function is discussed. In equilibrium this leads to the Matsubara diagrammatic technique.

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