Jean-Sébastien Caux

Statistical Physics and Condensed Matter Theory 1 Extension (January 2017)

How does it work?

This extension requires that you (individually, or in teams):

• choose a specific advanced topic, going beyond the contents of SPCMT1 (specific examples are given below; you are not limited to those themes)
• explore the theme as deeply as possible, by using all forms of scientific literature and eventually consultation with experts
• prepare a presentation (indication: 15 minutes per person) of your findings for the benefit of your co-students

The presentations will take place during the Projects Festival around the beginning of February.

All people who do a presentation get 3 EC credits. There is no grading, only a pass mark.

Participants should email me by Friday 13 January 2017 with their choice of subject and team composition.

You can listen to the introductory presentation to get some inspiration.

Project ideas

• The one-dimensional electron gas

  • General concepts
  • 2.2.4 Interacting fermions in 1d
  • Prob. 2.4.6 Spin-charge separation in 1d
  • 4.3 Field theoretical bosonization: a case study
  • 4.3.1 One-dimensional electron gas (fermionic theory)
  • 4.3.2 One-dimensional electron gas (bosonic theory)
  • Prob. 4.5.4 Boson-fermion duality
  • Prob. 4.5.8 Disordered quantum wires
  • Prob. 6.7.9 Functional bosonization

  Other resources:

  • J. von Delft and H. Schoeller, Bosonization for beginners — refermionization for experts (or the arXiv version)

• Tunneling and instantons

  • 3.3 Applications of the Feynman path integral
  • 3.3.1 Quantum particle in a well
  • 3.3.2 Double well potential: tunneling and instantons
  • 3.3.3 Tunneling of quantum fields: “fate of the false vacuum”
  • 3.3.4 Tunneling in a dissipative environment (Caldeira-Leggett model)
  • Prob. 3.5.3 Depinning transition and bubble nucleation
  • Prob. 3.5.4 Tunneling in a dissipative environment
  • Prob. 3.5.6 Particle in a periodic potential

  Other resources:

  • See the Scholarpedia entry for the Caldeira-Leggett model

• The Kondo problem

  • Prob. 2.4.7 The Kondo problem
  • Prob. 5.5.4 Kondo effect: perturbation theory
  • Prob. 8.8.5 Kondo effect: poor man’s scaling

  Other resources:

  • A. Hewson, The Kondo problem to heavy fermions
  • K. G. Wilson, The renormalization group: Critical phenomena and the Kondo problem

• Bose-Einstein condensation and superfluidity

  • 6.3 Bose-Einstein condensation and superfluidity
  • 6.3.1 Bose-Einstein condensation
  • 6.3.2 The weakly interacting Bose gas
  • 6.3.3 Superfluidity

  Other resources:

  • L. P. Pitaevskii and S. Stringari, Bose-Einstein Condensation

• Superconductivity

  • 6.4 Superconductivity
  • 6.4.1 Basic concepts of BCS theory
  • 6.4.2 Cooper instability
  • 6.4.3 Mean-field theory of superconductivity 6.4.4 Superconductivity from the field integral
  • 6.4.5 Ginzburg-Landau theory
  • 6.4.6 Action of the Goldstone mode
  • 6.4.7 Meissner effect and Anderson-Higgs mechanism
  • Prob. 6.7.2 Temperature profile of the BCS gap
  • Prob. 6.7.3 Fluctuation contribution to the Ginzburg-Landau action

  Other resources:

  • P.-G. de Gennes, Superconductivity of Metals and Alloys

• Electrons in disordered environments (mesoscopics)

  • 6.5 Field theory of the disordered electron gas
  • 6.5.1 Disorder in metals
  • 6.5.2 Replica field theory
  • 6.5.3 Basic notions of impurity scattering
  • 6.5.4 Diffusion
  • 6.5.5 Mean-field theory and spontaneous symmetry breaking

  Other resources:

  • K. Efetov, Supersymmetry in Disorder and Chaos

• Quantum dots and Josephson junctions

  • Prob. 6.7.4 Coulomb blockade
  • Prob. 6.7.5 Action of a tunnel junction
  • Prob. 6.7.6 Josephson junction

  Other resources:

  • The Blonder, Tinkham and Klapwijk model

• Response functions

  • 7.1 Crash course in experimental techniques
  • 7.2 Linear response theory
  • Prob. 7.6.1 Orthogonality catastrophe
  • Prob. 7.6.2 RPA dielectric function
  • Prob. 7.6.3 EM response of a quantum dot
  • Prob. 7.6.4 Hall conductivity

  Other resources:

  • Most good books on many-body physics contain a review of linear response theory and the Kubo formalism
  • You can also find good reviews for specific experimental methods, an excellent example being A. Furrer, J. Mesot and T. Strässle's book Neutron Scattering in Condensed Matter Physics

• Renormalization

  • 8.1 The one-dimensional Ising model
  • 8.3 Renormalization group: general theory
  • 8.6 Berezinskii-Kosterlitz-Thouless transition
  • Prob. 8.8.2 Quantum criticality
  • Prob. 8.8.4 Scaling theory of Anderson metal-insulator transition

  Other resources:

  • J. Cardy, Scaling and Renormalization in Statistical Physics
  • K. G. Wilson, The renormalization group: Critical phenomena and the Kondo problem

• Topology

  • 9.2 Homotopy
  • 9.3 Theta-terms
  • 9.4 Wess-Zumino terms
  • 9.5 Chern-Simons terms
  • Prob. 9.7.4 Fractional quantum Hall effect: physics at the edge

Other resources:

• D. Tong's Lecture notes on the Quantum Hall Effect