Levitov, Leonid, 8.514 Strongly Correlated Systems in Condensed Matter Physics, Fall 2003. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed 09 Jul, 2010). License: Creative Commons BY-NC-SA

Strongly Correlated Systems in Condensed Matter Physics

Fall 2003

Quasiparticles and Green's functions in BCS theory. (Image courtesy of Professor Leonid Levitov, from the course materials.)

Course Highlights

This course includes lecture notes, problem sets, and a term paper project.

Course Description

In this course we shall develop theoretical methods suitable for the description of the many-body phenomena, such as Hamiltonian second-quantized operator formalism, Greens functions, path integral, functional integral, and the quantum kinetic equation. The concepts to be introduced include, but are not limited to, the random phase approximation, the mean field theory (aka saddle-point, or semiclassical approximation), the tunneling dynamics in imaginary time, instantons, Berry phase, coherent state path integral, renormalization group.

*Some translations represent previous versions of courses.

Syllabus

Aim of the Course

The aim of the course is two-fold. First, we shall discuss topics of interest for both condensed matter and atomic physics, focussing on the effects of quantum statistics, interactions, and correlations in many-particle systems. Our second goal will be to provide a gentle introduction to the methods of quantized fields and their applications in many-body physics. We shall try to emphasize the physical and visualizable aspects of the subject. While the course is intended for students with a wide range of interests, many examples will be drawn from condensed matter physics.

Prerequisites

Statistical Mechanics and Quantum Mechanics, introductory level courses, such as 8.044 (Statistical Physics I), 8.08 (Statistical Physics II), and 8.04 (Quantum Physics I).