18/1/16

Statistical Mechanics

611 Spring 2017

Piers Coleman, Rutgers University.
First day of class: Weds Jan 18th, 3.20pm ARC 205
Last day of class:  Monday May 1, ARC 205

Images Texts
Exercises
Times of Course
Syllabus outline
Timetable

 



Ludwig Boltzmann


White Dwarf Star: Degenerate Fermi Matter



Bose Einstein Condensate: Degenerate Bose matter


(a) Non Ergodic and (b) Ergodic Motion of Billiards.

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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.  The aim of the course is to give students a thorough grounding in the fundamentals of statistical mechanics at an advanced level, combining an understanding of the main principles and technicques, and the ability to solve the standard problems.  We will accomplish this with the help of the required textbook, "Statistical Mechanics" by R. K. Pathria and P. D. Beale, 3rd edition. The more recent book "Statistical Mechanics in a Nutshell" by L. Peliti is very readable and a good compliment to Pathria. You should have handy an elementary text,  such as "An Introduction to Thermal Physics" by Schroeder. Lastly, if you need further stimulation on this subject, you might like to watch the MIT lectures on Statistical Mechanics by Mehran Kardar.

Students with disabilities 
 


``Statistical Mechanics in a Nutshell", by L. Peliti. (Princeton U. Press).

(You may buy or rent these at the Rutgers Bookstore, )
  • Online reference material can be found at:
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Exercises 611

Exercise 1   Solution to Exercise 1

Exercise 2.  Solution to Exercise 2

Exercise 3.  Solution to Exercise 3

Exercise 4.

Ising Snippets Mathematica Notebook   (Pdf copy)

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Times: 3.20-4.40 pm Monday and Wednesday in  ARC-205, starting Weds 18th Jan, 2016. Quite frequently, to make up for my travel, we will hold an additional  class in ARC 207 at noon on Fridays.

Office hour:   3-4.00 Thursdays or by arrangement.  Tel x 5082.

Assessment:   Assessment will be made on the basis of weekly assignments, a mid-term during class time on March 8th and a  final exam 9-12am, May 3rd. 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 (with the possibility of other topics being added).

  • The statistical basis of Thermodynamics.
  • Ensembles: Liouville's Theorem, Canonical and Grand Canonical. spin-systems (x-y) model.
  • Quantum Statistical Mechanics.
  • Ideal Gases: General Theory,
  • Bosons: Bose Einstein Condensation and Ultra-cold Atomic Gases.
  • Fermions, Fermi-Liquid, electron gas, Paramagnetism. White Dwarf Stars and the Chandrasakhar Limit.
  • Phase transitions and Broken Symmetry. Ising Model. Landau Theory. Criticality, Universality and Scaling.
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         Schedule (To be determined in detail).


Week


Mon:  3.20-4.40pm 
ARC 205


Weds 3.20-4.40pm 
ARC 205
Makeup Class
Fri 12.00-1.20pm
ARC 207

1. Jan 16-20


Ch. 1.  Statistical Basis of Thermodynamics
Notes: Chapter 1
No Class

2. Jan 23-27
Ch. 1. Classical Ideal Gas: Microcanonical Ensemble.
Notes: Chapter 1
No Class
No Class

3. Jan 30- Feb 3
Ch. 1. Entropy of Mixing.
Gibbs Paradox
Notes: Chapter 1
Chapter 2:
Concept of Ensembles
Notes: Chapter 2

Einstein on Stat Mech
Chapter 3
Canonical Ensemble
Notes: Chapter 3

4. Feb 6-10
Ch 3. Canonical Ensemble:
Energy Fluctuations
Notes: Chapter 3
Ch. 3.
Canonical Ensemble:
Equipartition, Virial Thm.
Notes: Chapter 3
Extra Cl. ARC 207
Canonical Ensemble:
Quantum systems.
Einsteins 1907 Paper
Notes: Chapter 3

5. Feb 13-17
Ch 3.
Magnetic Moments
Negative temperature
Notes: Chapter 3
Ch 4. Grand Canonical Ensemble.
Classical Gas.
Notes: Chapter 4
Extra Cl. ARC 207
Ch4. Grand Canonical Ensemble.  Phase Equilibria.
Notes: Chapter 4

6. Feb 20-24
Ch 5. Formulation of
Quantum Statistics
Density Matrix
Notes: Chapter 5
Ch. 5.
Density Matrices:
Examples.
Notes: Chapter 5
No Class

7. Feb 27-Mar 3
No Class
No Class
No Class

8. Mar 6-10
REVIEW
In Class Midterm.
No Class

9. Mar 13-17

Spring Break

Spring Break

No Class


10.  Mar 20-24
Ch. 5.
One and two particle density matrices in a quantum gas of Bosons or Fermions.
Notes: Chapter 5
Ch. 6. Quantum Gases: Grand Canonical Ensemble
Notes: Chapter 6
Extra Cl. ARC 207
Ch. 6. Quantum Gases: Microcanonical Ensemble
Notes: Chapter 6

11.  Mar 27-31
Ch. 7. Bose Einstein Condensation
Notes: Chapter 7
Ch. 7. Black Body Radiation
Notes: Chapter 7
No Class.

12.  Apr 3-7
Ch. 7. Debye Model Solids
Notes: Chapter 7
Ch. 8. Fermi systems I
Notes: Chapter 8
No Class

13. Apr 10-14
Ch. 8. Fermi Systems II
Notes: Chapter 8
Ch. 8. Chandrasakhar's theory of Stellar Collapse
Notes: Chapter 8
No Class

14.  Apr 17-21
Ch. 6. Molecular systems
Notes: Chapter 6.5
Ch. 12. Phase Transitions & Broken Symmetry
Van der Waals; Lattice Gas.
Notes: Chapter 12
No Class

15.  Apr 24-28
Ch. 12 Ising Model
Notes: Chapter 12
Ch. 12. Order Parameter Concept; Landau Theory; Scaling, Broken Continuous Symmetries.
Notes: Chapter 12
No Class
16.  May 1-5
REVIEW
3rd May. SEC 202. 9-12am
FINAL EXAM



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