PHYSICS 8820 : Special Topics course

[Tin-Lun Ho]

Announcement of A special topics course 

PHYSICS 8820            28233 L                   
Time:  W F  0930A-1050  
Place : CL0102       
Lecturer: T.L. Ho

Course Title:  Topics in condensed matter physics with cold atom examples

The purpose of this course is to discuss topics in condensed matter physics that are of common interests to researchers in cold atom physics and solid state physics. We shall discuss concepts and the techniques that lead directly to forefront. The course will have about 30 lectures covering the following topics: 

1. Phase Coherence: Penrose-Onsager characterization. Off-diagonal long range order. Key properties of Bose and Fermi condensates. Concept of fragmented condensates. Emergence of phase coherence through interaction and measurement processes. Bose systems with uncondensed ground states.  

2. Strong Interaction:  Resonance physics, emergence and breakdown of universality, BEC-BCS crossover, Tan’s contact and exact relations, p-wave and more intricate resonances.  

3. Quantum particles with internal degrees of freedom: Large spin boson and fermions, systems with SU(N) symmetry.  

4. Synthetic gauge fields: Bosons and fermions in abelian and nonabelian gauge fields, spin-orbit coupled bosons and fermions. 

5. Optical lattice I: Boson and fermion Hubbard model, entropy location, 
topological bands, fractional charge excitations, Majorana fermion excitations. 
p-band physics and flat band physics. 

6. Optical lattice II:  Interference of quantum many-body states, measurement of entanglement entropy.  

7. Many-body localization: Anderson localization, interaction effects in disordered systems (many-body localization), thermalization 

8. Many-body systems in curve space: Realization of curved manifolds in experiments, condensates and strongly correlated states on curved surfaces. 

9. Quantum geometry and topology: higher Chern numbers

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