Lectures by A.J. Leggett (Urbana) at U. Florida January/Feburary 2003


Lecture 1.Introduction
    The idea of a "quantum liquid":the effects of quantization and
         of indistinguishability
      Basic facts about the systems of interest (alkali gases,4-He,3-He,
         classical superconductors,cuprates)
      The phenomenology of superfluidity and superconductivity.
      Definition of (simple and "fragmented") BEC:condensate fraction,
         superfluid velocity.Reasons for occurrence and stability of BEC.
      The GP ansatz for a dilute Bose system.

Lecture 2.The simplest Bose-condensed system:ultracold alkali gases
              (single-species case)
      BEC of a noninteracting system in a harmonic trap.
      The s-wave scattering length and the effective interaction:the
         "factor of 2".GP ansatz for the alkali gases.
      Experimental signatures of BEC:density profile,MIT interference
          experiment,vortices.
      Theoretical considerations concerning superfluidity in a dilute
          spinless Bose gas (a toy model):experimental evidence for
          superfluidity.
      Brief introduction to the Bogoliubov theory.


Lecture 3:BEC in a multiple-species system.
   The hyperfine degree of freedom in the alkali gases:GP description.
   Interactions in a dilute multiple-species system (what happens to the
      "factor of 2"?)
   Ramsey-fringe experiments and phase diffusion.
   Effect of hyperfine degree of freedom on supercurrent metastability.
   The spin-1 case:the LPB state versus coherent (GP) states.
   The spin-1/2 case:intrinsic fragmentation.
   Some existing experiments on multiple-species alkali gases.

Lecture 4:Liquid 4-He.
   Phenomenology of superfluidity in 4-He (recap)
   London's hypothesis:evidence for BEC in He-II.(neutron sacttering,roton
      evaporation).
   The phonon-roton spectrum and some theoretical approaches to it (brief).
   Explanation of the phenomena of superfluidity in terms of BEC
     (including the deficiencies of the traditional Landau argument).
   Liquid helium-4 in restricted geometries:Hohenberg's theorem,Landau-
      Ginzburg description,"topological" superfluidity,Langer-Fisher and
      Kosterlitz-Thouless mechanisms.

Lecture 5:Classical superconductivity
   Phenomenology of superconductivity (recap)
   Basics of the BCS pairing hypothesis:significance and structure of the
     "pair wave function",relation to GL description.
   Pair-breaking effects:the FFLO state.
   Explanation of the Meissner effect and of supercurrent stability in
     terms of pair condensation.
   The Josephson effect at the macroscopic and mesoscopic levels:the
      "Cooper-pair box".

Lecture 6:Superfluid liquid 3-He
   The normal state of liquid 3-He:the phase diagram.
   Cooper pairing in an anisotropic state:the spin and orbital degrees of
     freedom,GL description.
   The concept of spontaneously broken spin-orbit symmetry and its
     consequences (NMR,orbital ferromagnetism,searches for parity
     violation...)
   Textures,vortices and flow in superfluid 3-He.
   Nucleation of vortices and of the B phase;the experimental data and the
     theoretical problem.

Lecture 7:Cuprate superconductivity
   General description of the cuprtae superconductors:phenomenology of
      cuprate superconductivity.
   Anomalies of the normal state.
   GL description,fluctuations.
   What do we know _for sure_ about superconductivity in the cuprates?
   Some existing theoretical approaches (brief).
   How do we formulate the questions?A "back-door" approach to the problem
      of cuprate superconductivity.

Lecture 8:BEC and related phenomena in an optical lattice
   Basics of optical trapping and lattices.
   The Munich and Florence  experiments:alkali gases as analog computers
     for solid-state problems.
   Conceptual problems in the kinetics of BEC systems.

Lecture 9:Optional topics (at discretion of audience and lecturer)

Lecture 10:Overview
   Common themes in the physics of alkali gases,helium,superonductors
   What do we and don't we fundamentally understand about quantum liquids?







Tony Leggett,
   Dept. of Physics,University of Illinois at Urbana-Champaign
   Tel:(217)-333-2077
   Fax:  "    "  9819