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  The solutions
of the homework were written by Indranil Paul who can also help answer your questions
ipaul@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,
Last lecture Thursday Dec 13th. (No exam). Notice there are some lectures after
the reading period.
 
 

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)
• Hubbard Hamiltonian , second quantization, Second Quantization for Bose particles (9/27/01)
• Assigment 2: solve excercises 2,3,4 from the list of excercises below (due  10/8/01)
• Assigment 3: solve excercises 1 1 from the list of excercises below (due  10/29/01)
•  familiaze yourself with mathematica. Exact diagonalization, symbolic manipulation
• Exact diagonalization, symbolic manipulation. Hubbard Hamiltonian , Hubbard molecule.  second quantization
•  (10/4/01) you are expected to familiarize yourself with the solution of excercise 11, with Mathematica
• Helium 3 and Helium 4, phenomenology, phases of correlated materials, crystals, superfluids, gases, liquids.(10/8/01)
• Electron phonon hamiltonian, broken symmetry, order parameters (10/11/01)
• Elementary excitations: phonons in crystals, particles and fields,  (10/15/01)
• Spectrum of excitations in a crystal. Goldstone modes.(10/18/01)
• Assigment 4: Solve Excercieses 15 and  16 from the list below (due 10/29/01)
• Elasticity, continuum theories, effective theories. Jastrow wave functions (10/22/01)
• 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
• Pertrubation Theory : ps ps.gz
• Perturbation Theory   : zero and finite temperature
• Perturbation Theory Feynman Diagrams
• Assigment 5:  Excercise 17.
• Feyman Rules Feynman Graphs
• Assigment 6 : Excercise 18. This excercise is optional, you can hand it in, if you want.
• Self energy and quasiparticles
• One and two particle irreducibility,.
• Screening, plasma oscillations.
 
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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