## Introduction to the Keldysh Nonequilibrium Green Function Technique

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#### Abstract

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.

#### References

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

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