Green's functions in condensed matter physics: basics

Quantum Condensed Matter Physics: Lecture 18

Theoretical physicist Dr Andrew Mitchell presents an advanced undergraduate / introductory Master's level lecture course on Quantum Condensed Matter Physics at University College Dublin. This is a complete and self-contained set of lectures, in which the theory is built up from scratch, and requires only a knowledge of basic quantum mechanics.

In this lecture I introduce the theory of Green's functions in condensed matter physics. I describe carefully from scratch the basic definitions in terms of time-dependent correlation functions (single-particle propagators), and show how these can be computed using the usual machinery of statistical mechanics. The Keldysh and retarded Green's functions in both time and frequency domain are introduced and explicitly calculated for a single quantum orbital. The fluctuation-dissipation theorem is derived, and the spectral (Lehmann) representation given. Finally we consider double-time Green's functions in a system with a time-dependent Hamiltonian. We look at the example of a Quantum Quench in detail. Subtleties to do with convergence of Fourier integrals and analytic continuation of complex functions to the real axis are discussed.

Navigate through the lectures of this course in order using the playlist:
   • Quantum condensed matter physics lect...  

Recommended course textbook: "Many-body quantum theory in condensed matter physics" by Bruss and Flensberg