10/7/13

Introduction to Many Body Physics.

620 Fall 2024

Piers Coleman, Rutgers University.
NOTE: First day of class: Thursday Sept 5th 2024.
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 
 





    Introduction to Many Body Physics.

          The content of this course, with additional material will be my book "Introduction to Many Body Physics", published by Cambridge University Press and available on Amazon

Introduction to Many Body Physics.


 
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  • Texts: Here are some other good references for the course.
      •  

      • Many-Particle Physics, Third Edition  by G. Mahan. (Plenum, 2000). A classic text on Many body physics.  Focuses on diagramatic and Greens Functions method. Very thorough but a little  dated.
      • 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 (Return to top)

          Initial quiz  Answers to quiz
          Ex 1    Answers to Ex1
          Ex 2    Answers to Ex2
          Ex 3    Answers to Ex3
          Ex 4    Answers to Ex4
          Ex 5    Answers to Ex5
          Ex 6

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12.10 pm on Monday and Thursday in  Serin 287E.  Thank you everyone for voting for this new time-slot.   See: google_sheet. Occasionally, to make up for my travel, we will hold an additional  class at a time we have to determine. I apologize for this inconvenience.

Office hour:   9:50am Tuesday or by arrangement.  Tel x 9033

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 (Currently in evolution - please check back for final schedule) :


Week

 Make-up class
Probably on Weds Period 3, 12:10
Monday 12:10
Serin 287E
Thu 12:10pm
Serin 287E

1. Sept 2-6
No Class: Labor Day. Fields overview.
Einsteins phonon: the Simple Harmonic Oscillator

2 Sept 9-13
Collective Quantum Fields: 1 and 3D Collective Quantum Fields: continuum and thermodynamic limit.

3 Sept 16-Sept 20
Conserved Particles:
Canonical Commutation Rules		 Interactions
4 Sept 23-Sept 27


No Class: on Travel
 Particles in thermal equilibrium.

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

6. Oct 7- 11
Examples of 2nd Quantization: Boltzmann Density Matrix
 No Class: on Travel

7. Oct 14 - 18
No Class: on Travel
 Greens Functions:
Generating function for bosons

8. Oct 21- 25
 Adiabaticity
Gell-Mann Low Theorem

Greens Functions:
Free Fermions and Bosons 		Generating function for Fermions. Spectral decomposition.

9.  Oct 28- Nov 1
 T=0
Feynman diagrams:
Heuristic derivation 		Landau Fermi
Liquid Theory		 T=0
Feynman Rules
Linked Cluster Theorem

10.  Nov 4- 8
T=0
Electron in scattering potential. Hartree Fock. 		More Mr Feynman

11.  Nov 11 - 15
Response functions. Lindhard Function. RPA Approach.
Large N electron gas

12.  Nov 18 -Nov 22
Finite T
Imaginary time
Greens functions		 Finite T
Feynman Rules and examples

13.  Nov 25 - Nov 29

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

Class is on Tuesday

14.  Dec 2 -  Dec 6
Superconductivity   BCS Theory I Superconductivity   BCS Theory II
15.  Dec 9 - Dec 13
  		Meissner Effect
 No Class


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