M2 ICFP: Statistical Physics for Condensed Matter

Master iCFP - First semester course

Part A: 28 hours divided into seven four hour sessions. Each session has 2 hours of lectures and 2h of tutorials. On Mondays: 04/09, 11/09, 18/09, 25/09, 02/10, 09/10, 16/10.
Location: 08:30-10:30 Lecture hall 12E on Sept 4th, and then in 6C for the remaining six lectures; 10:45-12:45 Rooms 310B or 411B or 415B.  Bldg: Halle aux farines on the Univ. Paris Diderot campus.

Part B is intended for students of the Quantum Physics and Condensed Matter curricula.

Part B: 24 hours divided into six four hour sessions. Each session has 2:30 hours of lectures and 1:30 hours of training exercises. On Mondays: 30/10, 13/11, 20/11, 27/11, 4/12, 11/12. 
Location: 08:30-11:00 Lecture Hall 1; 11:15-12:45 Rooms 411B and 415B. Bldg Olympe de Gouges, Univ. Paris Diderot campus.

Tutorials will take place under the supervision of Maurizio Fagotti and myself.

No lectures on 23/10 and 06/11.

Exam is on Monday, December 18th, 2017.

Course outline:
Previously on ICFP Statistical Physics:
I Introduction to phase transitions and critical phenomena
II First order phase transitions
III Critical phenomena : qualitative approaches
IV Renormalisation group ideas

... Towards condensed matter

I Quantum Phase transitions (2.5 lectures)
1­ Experiments and rationale
2 Ising model in one dimension
3 Quantum rotors

Suggested reading: [S] p3 thru 8.
Content: Define a quantum phase transition and identify the mechanisms playing the role of entropy. Existence of scale invariance and universality classes. Connection to classical thermal phase transitions. Coarse-grained description for continuous phase transitions. Technically: the momentum shell RG, Jordan-Wigner in d=1, Bogoliubov transformation for fermions.

II Interacting atomic gases (1.5 lectures)
1­ Ideal Bose gas
2 Weakly Interacting Bose gas
3 Hard-core bosons in one dimension
4 The Bose-Hubbard Model

Suggested reading: [PeSm] pp 225-234; [S] pp193-202.
Content: Start from atomic physics and connect to hard condensed matter by increasing the interaction strength. How is the Bose-Einstein condensation affected by interactions. Technically: Bogoliubov for bosons, RG for the Bose-Hubbard model.

III Disorder, classical and quantum (2 lectures)
1­ Classical diffusion in random media
2­ Spin glasses
3­ Localization
4­ Random matrices

Suggested reading: [H] pp386-397 (on random walks);  [N] pp 11-22 (order parameter, replicas, in spin glasses) ; [CC] pp 1-16 (same but somewhat more mathematical).
Content: Quenched vs Annealed disorder. Typical vs rare realizations. Self-averaging. Edwards-Anderson order parameter. Absence of extended states in low dimensions in the presence of disorder.
Technically: Statistics of extremes, the Replica Trick, Replica Symmetry Breaking, Random Matrices.

IV Quantum dynamics at finite temperature (0.5 lecture)
1­ Quantum Brownian Motion
2­ Quantum Tunneling
3­ Quantum Master Equation
4 Mesoscopic systems
5 Linear response theory
Suggested reading: [Z] chapter 6.
Content: Dissipation as information loss. Influence. Memory kernel. Classical limit. Quantum Jarzynski equality. Fluctuation-Dissipation Theorem.

Useful references :
[S] S. Sachdev, Quantum Phase Transitions, Cambridge, 2001.
[PS] L. Pitaevskii and S. Stringari, Bose-Einstein Condensation, Clarendon, Oxford, 2003.
[PeSm] C.J. Pethick and H. Smith, Bose-Einstein Condensation in Dilute Gases, Cambridge, 2008.
[N] H. Nishimori, Statistical physics of spin glasses and information processing: an introduction, Oxford UP, 2001.
[CC] P. Contucci and C. Giardina, Perpsectives on spin glasses, Cambridge UP, 2013.
[H] B. Hugues, Random and Random Environments: vol 2, Random Environments, Oxford UP, 1995.
[Z] R. Zwanzig, Nonequilibrium Statistical Mechanics, Oxford, 2001.