Many Body Physics 620

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

Instructor: Gabriel Kotliar, Room 267 .

Graders: Viktor Udovenko, Indranil Paul

If you have any enquiries about this course or the homework contact me via email at : kotliar@physics.rutgers.edu You can also get help from Viktor at udo@physics.rutgers.edu .

Time and Place: We will meet in ARC 205, on Mondays and Thursdays, 2:50-4:10 am. Classes begin Thursday September 7th

Time and Place:

The last lecture will take place on ......

Office hour: Contact me by email to set a time

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)

Scope of Course:

Many body physics, 620, 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: concepts and techniques. It is an essential course for all students intending to study physics at the graduate level. 621 will be a second semester continuation of 620 (Many Body I). We will introduce the ideas of effective theories, quasiparticle excitations, broken symmetries, deffects in ordered structures. We will develop techniques based on Greens functions, path integrals as well as exact diagonalizations of small systems.

Many body physics provides the right language to describe the results of experimental investigations and we will connect experimental results to theory via the notions of correlation and response functions. This aspect of the course as well as the conceptual aspects of many body physics, make this course relevant to experimentalists.

Course Outline:

Schedule:

Organizational Meeting, Outline (9/6/00)
Review of Quantum Mechanics, States, Operators, Density Matrices, Second Quantization of Fermions and Bosons (9/7/00)
No Lecture (9/11/00)
Second Quantization continued, First Assigment (9/13/00)

Assigment 1: pdf ps.gz

Solution to Assigment 1 (R. Magyar) pdf ps.gz
Second Quantization, Bosons (9/14/00)
Elementary Excitations, Particle Content, Quasiparticles, Phonons (9/18/00)
Elementary Excitations continued ( 9/21/00)
Second Quantization and Mathematica (9/25/00)

Mathematica Notebook (courtesy of M. Sindel): notebook

First Assigment is Due, Solutions of the assigments will be provided (9/28/00)
Experimental measurements and Many Body theory, response and correlation functions, second assigment is handeed out (10/2/00)

Assigment 2: pdf ps.gz

No Lecture (10/5/00)
Scattering and Correlation Functions (10/9/00)
Linear Response Theory (10/12/00)
Second Assigment is Due (10/16/00)
Review of the homework assigment (10/19/00)
Finite Temperature and Zero Temperature Greens Functions(10/23/00)
Assigment2: Solution (Viktor Udovenko's) math.nb

Assigment 3 (due 11/2/00) : pdf ps.gz

Assigment 4 (due 11/30/00) : pdf ps.gz

Assigment 3 Solutions, courtesy of Indranil Paul : pdf ps.gz

Finite Temperature Greens Functions (10/26/00)
Finite Temperature Greens Functions (10/26/00)
Spectral Representation (10/30/00)
Spectra l Representation(11/2/00)
Fluctuation Dissipation Theorem(11/9/00)
Equations of Motion, connection to observables (11/13/00)
NO LECTURE (11/16/00)
Perturbation Theory (11/20/00)
Perturbation Theory (11/21/00) [instead of thanksgiving thursday]
Perturbation Theory Feynman Diagrams (11/27/00) Fourth Assigment is DUE
Feyman Rules Feynman Graphs (11/30/00)

Make up Assigment (due 12/7/00) : pdf ps.gz

(12/4/00)Self energy and quasiparticles . Conclusion of the Course.

Texts:

I put the following texts on reserve ``Many-Particle Physics'' by G. Mahan. (Plenum) and Quantum Many Particle Physics by Negele and Orland. Additional reading will be posted on the web as the course progresses.

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