10/17/04

Introduction to Many Body Physics.

620 Fall 2004

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.
 
 





    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.

     postscript(large print), pdf(large print)

(Updated April 17th 2009 with fairly complete chapter on Landau Fermi liquid theory).
Still to come - broken symmetry, heavy fermions, revised exercises, references.

Please do not hesitate to email me corrections and typos.
 


 
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  • Texts: The official text will be
      •  
      ``Many-Particle Physics'', Third Edition  by G. Mahan. (Plenum).
       
       
    but I  shall be making draft chapters of a monograph I am writing available as the course progresses. Here are some other good references:

      Overview
      • 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. Unfortunately out of print.
      • ``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 (Return to top)

          Initial quiz   (ps)   ,  (pdf) ,   Answers to initial quiz  (ps), (pdf)
          Exercise 1    (ps)   ,  (pdf) ,   Solutions to Exercise 1  (ps), (pdf)
          Exercise 2    (ps)   ,  (pdf) ,   Solutions to Exercise 2  (ps), (pdf)
          Exercise 3    (ps)   ,  (pdf) ,   Solutions to Exercise 3  (ps), (pdf)
          Exercise 4    (ps)   ,  (pdf) ,   Solutions to Exercise 4  (ps), (pdf)
          Exercise 5    (ps)   ,  (pdf) ,   Solutions to Exercise 5  (ps), (pdf)
          Exercise 6    (ps)   ,  (pdf) ,   Solutions to Exercise 6  (ps), (pdf)
          Exercise 7    (ps)   ,  (pdf) ,   Solution to Exercise 7   (ps), (pdf)

Exercises 621

          Exercise 1: Finite Temperature Green Functions    (ps)   ,  (pdf) ,   Solutions  (ps), (pdf)


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Times: 9:50am on Monday  and Wednesdays in  ARC-212 starting Wednesday,  September 1st.
On some weeks, when I am travelling, we will arrange an alternate class at 9.50am on Fridays in
room 287 (Theory reading room).
 

Office hour:   9.50 Fridays or by arrangement.  Tel 445-5082.

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  Since this year, I am only teaching 620, we will make a selected sortie through the following list. Asterisks indicate areas that we will aim to cover.

  • 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.
  • Broken Symmetry and Superconductivity. Anderson Higg's mechanism. *
  • Local moments and Heavy Electron Physics



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Week
Mon 9.50
Weds 9.50
Friday 9.50
(additional day)

1 Aug30-Sep3
  ----------
Scales  and complexity
  ----------

2 Sept 6-10
Quantum Fields: overview
Phonons in  0 and 1 D
  ----------

3 Sept 13-18
Collective Quantum Fields: continuum limit.


Conserved Particles:
Canonical Commutation Rules
  ----------
 

4 Sept 21-25
Interactions
Conserved Particles in Thermal equilibrium
 Examples of 2nd Quantization
Jordan Wigner Transformation
  ----------
 

5 Sep 28-Oct2
 Examples of 2nd Quantization
1 D Ferromagnet.
 Examples of 2nd Quantization
Hubbard Model
  ----------
 

6 Oct 5 -  9
 Examples of 2nd Quantization
Free Bosons; Free Fermions
Greens functions:
Interaction rep/Driven Oscillator
  ----------
 

7 Oct 11-  16
No class
Greens Functions:
Free Fermions and Bosons
  Adiabaticity concept I
  Gell-Mann Low

8. Oct 18- 23
Adiabaticity  II
Landau Fermi
Liquid Theory
 Zero temperature
Feynman diagrams:
Heuristic derivation
 No office hour
 

9 Oct 26 -  30
 T=0
Feynman Rules
Linked Cluster Theorem
Hartree Fock, RPA.
Large N electron gas.
Finite T
Imaginary time   Green functions

10 Nov 1 -  5
Finite temperature
Feynman Rules:
Electron in a disordered potential
Electron Phonon
interaction: self energy; Migdal's theorem.
  Fluctuation dissipation and the Kubo formula.
 

11 Nov 8 -  12
No class
No class
  No office hour
 

12 Nov 15- 19
 Spectroscopy : a brief guide.


No class.


  Resistivity of a metal.
 The f-sum rule.

13 Nov 22 - 26
 Path integrals:
Coherent states.


Broken symmetry
Hubbard Stratonovich

 Superconductivity and  BCS Theory
 

14 Nov 30- Dec 3
Nambu Green functions. BCS wavefunction
The Meissner effect
"Anderson-Higgs"
mechanism
  ----------
 

15 Dec 6 - 10
Local Moments
Kondo effect and heavy electrons.
  ----------
 

16 Dec 13-Dec 17
  
No Class.
  ----------
 
  ----------
 


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