Jean-Sébastien Caux

Statistical Physics and Condensed Matter Theory 1 Extension (January 2018)

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 J-S or Jasper by Monday 15 January 2017 with their choice of subject and team composition.

You can listen to last year's 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