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 6th,

I will be away on Monday  October 1st and 11th.
The last lecture will take place on  Monday Dec  10th.

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:

• Introduction, motivation for the study of many particle physics(9/6/01)
• Review of Quantum Mechanics, States, Operators, Density Matrices  ( 9/10/01)
• Open and closed systems, interaction with a reservoir,  master equation (9/13/01)
• Assigment 1: solve excercises 1 , 6 and 7 from the list of excercises below (due  9/20/01)
• The Hilbert Space of Many particle systems : second Quantization of Fermions and Bosons (9/17/01)
• Second Quantization continued, First Assigment (9/20/01)
• Elementary excitations: phonons in crystals, particles and fields
• Electron phonon hamiltonian
• Particles and electro-magnetic fields.
• Exact diagonalization, symbolic manipulation
• Hubbard Hamiltonian , second quantization
• Assigment 2: pdf ps.gz
• Experimental measurements :  response and correlation functions
• Experimental measurements: scattering and correlation Functions
• Linear Response Theory
• Discussion of second ofassigment (10/19/00)
• Finite Temperature and Zero Temperature Greens Functions(10/23/00
• Assigment 3: pdf ps.gz
• Finite Temperature Matsubara  Greens Functions (10/26/00)
• Equilibrium and non equilibrium  Greens Functions (10/26/00)
• Spectral Representation  (10/30/00)
• Spectra l  Representation(11/2/00)Spectral Representation
• Fluctuation Dissipation Theorem(11/9/00)
• Greens Functions Equations of Motion,  connection to observables (11/13/00)
• Perturbation Theory : general structure
• Assigment 4  : pdf ps.gz
• Perturbation Theory   : zero and finite temperature
• Perturbation Theory Feynman Diagrams
• Feyman Rules Feynman Graphs
• Additional homework : pdf ps.gz
• Self energy and quasiparticles
• Fermi liquid theory
• Functional Integrals
• Grassman integrals
• Approximation schemes: Hartree, Hartree Fock,  Density functional theory
• Theory of superconductivity.
 
Excercises, they will be used in homework assigments download HERE:

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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