Introduction to the Keldysh Nonequilibrium Green Function Technique

By A. P. Jauho



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Keldysh nonequilibrium Green function technique is used very widely to describe transport phenomena in mesoscopic systems. The technique is somewhat subtle, and a rigorous treatment would require much more than we have at our disposal, see, for example, the text-bookk by Haug and Jauho [1]. The goal of these lectures is to give a rough idea of how the technique works, and illustrate it with a few simple examples. Our main applicaton is to calculate the current through a resonant-tunnelling diod; this calculation can be done in a number of different ways, such as the Landauer-Buttiker formalism, or by a Master Equation approach, and our hope is that studying this exactly solvable problem by different methods will give insight to the different formalisms.


  1. H. Haug and A.P. Jauho, Quantum Kinetics in Transport and Optics of Semiconductors, Springer, Berlin, 1996, ISBN: 3540616020

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  • A. P. Jauho (2006), "Introduction to the Keldysh Nonequilibrium Green Function Technique,"

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