10/7/13

Introduction to Many Body Physics.

620 Fall 2013

Piers Coleman, Rutgers University

Images Monograph Texts
Exercises
Times of Course
Syllabus outline
Timetable

 





Maxwellian construction of a Fermi Surface


Cuprate superconductor levitating a magnet.



Quantum Critical Point:
"Black hole" in the material phase diagram.


Adiabatic concept: basis of perturbation theory.

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Instructor: Piers Coleman, Room 268
If you have any enquiries about this course or the homework, please do not hesitate to contact me via email at : coleman@physics.rutgers.edu

Scope of Course. Many body physics provides the framework for understanding the collective behavior of vast assemblies of interacting particles. This course provides an introduction to this field, introducing you to the main techniques and concepts, aiming to give you first-hand experience in calculations and problem solving using these methods.

Students with disabilities 
 





    The evolving monograph.


          The content of this course, with additional material is being written up as a monograph. Feel free
to download the text of the course.

      pdf

(Updated 2014-03-23 ).

Please do not hesitate to email me corrections and typos.
 


 

Note: this material is has copywrite protection.
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  • Texts: The main reference text will be
    •  
      ``Many-Particle Physics'', Third Edition  by G. Mahan. (Plenum).
       
    but I  shall be basically teaching from my monograph.   Here are some other good references:

      Overview

      • Condensed Matter Field Theory by Alexander Altland and Ben Simons.(CUP, 2006)
        An excellent introduction to Field Theory applied in condensed matter physics. I almost decided to make this the main text, as I like it greatly. 
      • Basic Notions in Condensed Matter Physics by P. W. Anderson. A classic reference. Many of us still turn to this book for inspiration, and philosophy. It also has a fine selection of important reprints at the back.


      Traditional Many Body Theory and Greens Functions
       

      • ``Methods of Quantum Field Theory in Statistical Physics'' by Abrikosov, Gorkov and Dzyalozinskii. (Dover Paperback) - Classic text from the sixties, known usually as AGD.
      • ``A guide to Feynman Diagrams in the Many-Body problem by R. D. Mattuck. A light introduction to the subject. Reprinted by Dover.
      • ``Greens functions for Solid State Physics'' S.Doniach and E. H. Sondheimer. Not as thorough as AGD, but less threatening and somehow more manageable. Frontiers in Physics series no 44.
      • ``Quantum Many Particle Systems'' by J. W. Negele and H. Orland. Alas all the good physics is in the unsolved excercises! However, it is the only one of this set to touch on the subject of functional integrals.


      Newer approaches to Many-Body Problem.
       

      • R. Shankar, Rev Mod Phys 66 129 (1994). An amazingly self-contained review of the renormalization group and functional integral techniques written by one of the best expositors of condensed matter physics.
      • ``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.


      Further references:

      • 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.

      Online references     (Check it out- this is a great link).

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Exercises 620
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          Initial quiz 
          Exercise 1 (2013)   Answers to Ex 1 (2013)
          Exercise 2 (2013)   Answers to Ex 2 (2013)
          Exercise 3 (2013)   Answers to Ex 3 (2013)
          Exercise 4 (2013)   Answers to Ex 4 (2013)
          Exercise 5 (2013)  
          Exercise 6 (2012)

(Return to top)        Note: this material is copywritten and should not be posted without permission.


Times: 12.00 am on Wednesday  and 1.40 pm on Fridays in  ARC-212. We will start one week late, due do my travel, on Wednesday,  September 11th. Quite frequently, to make up for my travel, we will hold an aadditional  class. provisionally at 3:20 pm in the CMT reading room on Mondays. (See schedule below)

Office hour:   9.50 Fridays or by arrangement.  Tel x 5082.

Assessment:   Assessment will be made on the basis of weekly assignments, a take-home mid-term and a take-home final exam. I want to encourage an interactive class and will take this into account when grading!

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Outline
  We will make a selected sortie through the following list. Asterisks indicate areas that will be high priority

  • Second Quantization. ``Free'' systems-- the building block of the quasiparticle concept. *
  • Phonons and photons, Fermi and Bose fluids; spin-systems (x-y) model. Interactions.*
  • Green's Functions and Feynman diagrams .*
  • Finite temperature Green Functions.  *
  • Application of Finite temperature  Feynman Diagrams to (i) electron-phonon problem * ; (ii) transport theory.
  • Functional Integral Approach (if time permits).
  • Broken Symmetry and Superconductivity.  *



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         Schedule:


Week

Extra class
Time: 8.40 am

CMT Reading Room

Weds 12:00 ARC 212

Fri 1:40pm ARC 212

1. Sept 2-6

No Classes This Week No Class
No Class


2 Sept 9-13
No Class Fields overview.
Einsteins phonon: the Simple Harmonic Oscillator
Collective Quantum Fields: 1 and 3D

3 Sept 16-20
No Class
No Class
Collective quantum fields: continuum and thermodynamic limit.

4 Sep 23-Sept 27
Conserved Particles:
Canonical Commutation Rules
Interactions Particles in thermal equilibrium.

5 Oct 30-4
Examples of 2nd Quantization
Jordan Wigner Transformation, 1D Ferromagnet.
Examples of 2nd Quantization
1 D Antiferromagnet. Hubbard Model
Examples of 2nd Quantization
Free Bosons, Fermions

6 Oct 7-  11
Greens functions:
Interaction rep/Driven Oscillator
Greens Functions:
Free Fermions and Bosons
No class


7. Oct 14- 18
No class
Catch up and review.
Adiabaticity  I
Gell-Mann Low Theorem

8. Oct 21 - 25
Adiabaticity  II
Landau Fermi
Liquid Theory
Adiabaticity  II
Landau Fermi
Liquid Theory
T=0
Feynman diagrams:
Heuristic derivation

9. Oct 28 -Nov 1
T=0
Feynman Rules
Linked Cluster Theorem
Linked Cluster Theorem. Electron in scattering potential. Hartree Fock. Response functions. Lindhard Function.

10.  Nov 4 -  8
No class
No class
No class

11.  Nov 11- 15
RPA Approach.
Large N electron gas
Finite T
Imaginary time   Green functions
Finite T
Feynman Rules and examples

12.  Nov 18 - 22
Finite T
Feynman Rules:
Electron in a disordered potential
Finite T:
Electron Phonon
interaction: self energy; Migdal's theorem.

Superconductivity:
Introduction

13. Nov 25 - Nov 29
Superconductivity   BCS Theory I Note: Friday Schedule. Meet 1.40pm. Superconductivity   BCS Theory II
No class- Thanksgiving

14.  Dec 2 - Dec 6
 Nambu Green functions. The Meissner effect No class.

15.  Dec 9 -Dec 13

Anisotropic Pairing
 


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