syllabus-628a_13_
DESCRIPTION
SYLLABUS 628 Fall 2013TRANSCRIPT
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YALE UNIVERSITY
PHYSICS 628a SYLLABUS 2013 Autumn Term, 2:30 3:45 PM Tuesday and Thursday, Room SPL63 First class: Thursday, August 29, 2013 Prof. Leonid Glazman Office: Physics SPL55A Office Hour: Tuesday, 4:30 PM Telephone: (203)432-6920, e-mail: [email protected] TA: Filip Kos, [email protected]
Supplementary texts : 1. Statistical Physics, Part 1, L.D. Landau and E.M. Lifshitz, Pergamon Press, 1979. 2. Statistical Physics of Fields, Mehran Kardar, Cambridge University Press, 2007 3. Statistical Mechanics, Kerson Huang, John Wiley & sons, 1987. 4. Introduction to Statistical Field Theory, Edouard Brezin, Cambridge University Press 2010. 5. Principles of Condensed Matter Physics, P.M. Chaikin and T.C. Lubensky, Cambridge University Press 1997. Tutorial articles: 1. The renormalization group and the -expansion. K.G. Wilson, J. Kogut, Physics Reports, v. 12C, p. 75 (1974) 2. Continuous quantum phase transitions. S.L. Sondhi, S.M. Girvin, J.P. Carini, D. Shahar, Rev. Mod. Phys. v. 69, p. 315 (1997) 3. Topological insulators. M.Z. Hasan, C.L. Kane, Rev. Mod. Phys. v. 82, p. 3045 (2010)
Course Outline 1. Phase transitions.
-Mean field theory of phase transitions -Fluctuations near the phase transition point -Scaling and critical exponents
2. The Renormalization Group theory for the continuous phase transitions. -The idea of coarse-graining. Exactly-solvable example of 1D Ising model. -The Renormalization Group construction. -Fixed points. Relevant, irrelevant, and marginal perturbations. -Finding the critical exponents from the RG. - Landau-Wilson model, non-trivial fixed points, and critical exponents at small =4-d. 3. Berezinskii-Kosterlitz-Thouless transition.
-Two-dimensional degenerate systems. -Low- and high-temperature asymptotes of the spin correlation function. -Topological defects: vortices. Vortex-antivortex unbinding transition; RG analysis. -Examples of BKT transitions.
4. Quantum phase transitions. -Ground state, partition function and path integral of a quantum system. -Phenomenology of superconductivity, Josephson effect, and Coulomb blockade. -Superconductor-insulator transition in a 1D array of Josephson junctions.
5. Topological phases, Majorana fermions. -Spin-1/2 quantum Ising and XY models in 1D. -1D Kitaev model, Majorana fermions.
Assignments: Homework nominally will be given every week and due before the class in a week from the assignment date. Grading: Homeworks
2. Statistical Physics of Fields, Mehran Kardar, Cambridge University Press, 2007Course Outline