Many Body Physics 621

The many body problem is anybody's problem !!!

Instructor: Gabriel Kotliar, Room 267 .

Grader: Indranil Paul

If you have any enquiries about this course or the homework, please do not hesitate to contact me via email at : kotliar@physics.rutgers.edu

Time and Place: We will meet in SEC 217, on Mondays and Thursdays, 9:50-11:10 am. Classes began Tuesday January 26

Office hour: Time to be arranged and also by appointment. Tel 445-4331

Grades: Grades will be determined on the basis of take home assignments and homework.

Current Exercises: (This page will be frequently updated to list the homework)

• Homework1

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• Solution1 pdf ps.gz

• Homework2

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• Homework3

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• Solution3

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• Homework4

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  Solution4

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Scope of Course:

Many body physics, 621, will be an introduction to the study of non relativistic systems containing a large number of degrees of freedom. There will be equal emphasis on: a) concepts, b) general results, c) techniques. It is an essential course for those students intending to study condensed matter physics. 621 will be a second semester continuation of 620 (Many Body I).

Many body physics provides the right language to describe the results of experimental investigations. Concepts will be stressed throughout the course which will make it very suitable for students interested in experimental physics.

Course Outline:

• Review of the basic Greens functions and their physical content Approximation techniques, RPA, Hartree Fock, Density Functional
• One dimensional systems. Bosonization. Impurity models.
• Fermi liquid theory, phenomenology and microscopic foundations. Renormalization group methods for fermi systems.
• Dynamical Mean Field Methods. Theories of the Mott transition.

Texts:

The official text will be ``Many-Particle Physics'' by G. Mahan. (Plenum) as in the previous semester, so 621 does not require extra cash . For additional references see below:

Basic Notions in Condensed Matter Physics by P. W. Anderson. A classic reference. Excellent discussion of the basic concepts.

``Methods of Quantum Field Theory in Statistical Physics'' by Abrikosov, Gorkov and Dzyalozinskii. (Dover Paperback) - Classic text from the sixties, known usually as AGD. Good discussion of Greens functions and Fermi Liquid Theory

``Greens functions for Solid State Physics'' S.Doniach and E. H. Sondheimer. Frontiers in Physics series no 44. Good discussion of the Kubo formula

``Hydrodynamic Flucturations Broken symmetry and Correlation Functions '' Dieter Forster. Frontiers in Physics series no 47. Good discussion of Correlation Functions

`` The Quantum Statistics of Dynamic Processes '' Fick and Sauerman. Springer Series in Solid State Sciences 86. Classic reference on Mori theory

``Quantum Many Particle Systems'' by J. W. Negele and H. Orland. Functional Integral Formalism

Many interesting review articles can be found in Reviews of Modern Physics. This semester we will use:

`` Quantum Field Theoretical Methods in Transport Theory'' Reviews of Modern Physics 58, 2, 323 (1986) J. Rammer and H. Smith

R. Shankar, Rev Mod Phys 66 129 (1994) for Fermi Liquid Theory, and A. Georges et. al. Rev Mod Phys 68 13 (1996) for Dynamical Mean Field Theory.

``Field Theories of Condensed Matter Physics'' by E. Fradkin. (Frontiers in Physics, Addison Wesley). Interesting material on the fractional statistics and the fractional quantum Hall effect.

``Quantum Field Theory in Condensed Matter Physics'' by A. Tsvelik. (Cambridge paper back) Very good for one dimensional systems. No exercises.

The Theory of Quantum Liquids by D. Pines and P. Nozieres. Excellent introduction to Fermi liquid theory that avoids the use of field theory.

Statistical Physics, vol II by Lifshitz and Pitaevskii. Pergammon. Marvellous book on applications of many body physics, mainly to condensed matter physics.