Basic Training in Condensed Matter Theory
James P. Sethna, Erich Mueller, Tomás Arias, Veit Elser
Physics 654/683, Spring 2007, WF 2:30-4:00, Rockefeller 128
Graders: Sourish Basu, Duane Loh, Steve Hicks, and Johannes Lischner
Condensed matter theory is an enormous, rich, evolving field which is
impossible for a single professor to explain or even describe in a single
graduate course. Quasicrystals; quantum magnetism; the quantum Hall effect;
random matrix theory and mesoscopic physics; the connections between glasses,
disordered systems, and computational complexity; collective effects
in dilute cold gases; density functional theory of both electronic
structure and classical fluids; phase rigidity, order parameters,
and quantum overlaps - all are rapidly developing fields to which
educated condensed-matter physicists need to be exposed. To address this
challenge, Cornell's condensed-matter theory group has developed
Basic Training in Condensed-Matter Theory, a challenging,
modular
course taught once per year by a rotation of four condensed-matter theorists.
Students are exposed to a different set of active research areas each year,
and learn sophisticated analytical and numerical methods in the extensive
exercises.
This year our course replaces the traditional many-body physics course 654,
and will incorporate some of the tools and concepts from that field.
Tentatively, we plan to cover
- Superfluidity in Bose and Fermi Systems (Erich Mueller)
- Microscopic theory of Superfluidity in Bose and Fermi systems
- BEC/BCS crossover
- Some phenomonology: 4He, 3He, Superconductors, cold atoms
- Developing the required tools from many-body physics: Path Integrals, Grassman variables, Feynman Diagrams
- Applications of many-body theory (Tomás Arias)
- Phonons in nanotubes,
- Bethe-Salpeter equations and the GW approximation for dielectric response
- Density functional theory and the cluster expansion for classical fluids
- Rigidity (James Sethna)
- Rigidity, long-range order, and the Mermin-Wagner theorem
- Crystal rigidity: plastic flow, fracture nucleation, rigidity of glasses
- Quantum rigidity: Mössbauer effect and overlap catastrophes
- Phase rigidity in superfluids: number-phase relations and Josephson
- Rigidity and precision measurements
- Asymptotic analysis for differential equations (Veit Elser)
- Boundary layer methods
- The WKBJ expansion
- Multiple-scale analysis
Weekly homework assignments will provide practice in techniques and
broader exposure to the field. First-year students are welcome, but
the course will be at a high level of sophistication; we
expect background in condensed matter physics at least equivalent to
Ashcroft and Mermin. Experimentalists and others interested in working
through two or more modules are encouraged to register for the class.
All are welcome to audit and participate as time and background permit.
Pass-fail.
Teasers
- Teaser #1
- Teaser #2
- Teaser #3
- Teaser #4 (Crystals under gravity, M 2/19)
- Teaser #5 (Number and phase, W 2/21)
- Teaser #6 (Infrared Cat-astrophe, F 2/23)
- Teaser #7 (Stretch and Shear, F 3/09)
- Teaser #8 (Climb and Glide, W 3/14)
- Teaser #9 (Glasses, F 3/16)
- Teaser #10 (Specific heat of carbon nanotube, W 3/28)
- Teasers for Elser's asymptotic analysis unit
Homeworks
- Homework #1
- Homework Solutions #1
- Homework #2
- Homework #3
- Homework #4a (Mueller, 2/21)
- Homework #4b (Sethna, 2/21)
- Homework #5 (2/28)
- Homework #6 (3/09)
- Homework #7 (3/14), Reading: Chaikin & Lubensky section 9.3, Energies of vortices and dislocations, subsections 1-3.
- Homework #8 (4/04)
- Homework #9 (4/17)
- Homework for Elser's asymptotic analysis unit
Reading Assignments
- Week 1: Feynman, Statistical Mechanics, p312-350
- Week 2: Pitaevskii and Stringari, Bose-Einstein Condensation, p26-37,358-365
- Week 2: Negele and Orland, Quantum Many-Particle Systems, p20-39, 66-69
- Texts on Reserve
- Basic
Training Spring 2006
Last modified: Feb 5, 2007