| Date | Hmwk. | Notes | Subject of Lecture and References |
|---|---|---|---|
| # | # | ||
| 1/18 | 1 | 1 | Introduction to Course; Overview of Solid State Physics Beyond the One-particle Approximation ( Class Notes) |
PART I: Elementary Excitations |
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| 1/20 | 2 | Fundamental Theory-- Identifying the Basic Excitations: Adiabatic approx., Hellmann-Feynman theorem, ... (Class Notes; Pines, Ch. 1) | |
| 1/25 | 3 | Electrons: Hartree approx., Hartree-Fock approx., exchange, Homegeneous Eelectron Gas (Jellium), pair correlation function, structure factor, difficulties of treating correlation (A&M 3,17; Pines 3-1,3-2; Mahan 1.6,5.1; Fulde, Ch. 2) | |
| 1/25 | 3a | Density Functional Theory, Local Density Aproximation (LDA): succesful for many ground state properties, problems for excited state properties. (classnotes) | |
| 1/27 | 2 | 4 | Second quantization for oscillators; harmonic and anharmonic hamiltonian; experimental probes for scattering, correlation functions, Green's functions (Second quantization: Mahan 1.1,1.2,1.3A, Pines p. 18, p. 67; Fetter; other texts; Correlation functions: class notes, Doniach, Ch. 1; Pines, Ch. 2) |
| 1/27 | 4a | Second quantization for fermions; interacting particle hamiltonian; experimental probes, correlation functions, Green's functions (Second quantization: same as above; Correlation functions: class notes, Pines, Ch. 3) | |
| 2/1 | 5 | Linear Response Theory: Classical damped oscillator, causality, analyticity, and Kramers-Kronig relations, sum rules, fluctuation-dissipation theorem, relations to Green's functions, correlation functions, spectral representation, inelastic scattering (P. C. Martin; Mahan 3; Fetter 5) | |
| 2/3 | Conitnued from last time | ||
| 2/8 | 5a | Dielectric response function: Dynamic structure factor,
scattering of charged particles, sum rules (Pines 3-4 - 3-5; Mahan 5.6 - 5.7; Doniach 6.4; Fetter 5) | |
| 2/10 | 3 | 6 | Green's functions in many-body perturbation theory: Interaction
Representation, time ordering, Wick's theorem,
Dyson's Equation (Mahan 2-3; Fetter 3) |
| 2/15 | Continuation of previous topic | ||
| 2/17 | 7 | Quasiparticles and Self energies: Spectral functions, broadening (Mahan 3.3-3.4; Fetter 3) | |
| 2/22 | 8 | Beyond Hartree-Fock:Electron-Phonon Interaction Random Phase Approximation and the One-electron Green's function (Pines p. 136-163; Mahan 2.8,3.4,5.5B,5.6,5.8; Fetter Sec. 12) | |
| 2/24 | 9 | Continue One-electron Green's function and spectral functions;
Start Electron-Phonon Interaction Pines, ch. 5 (See also Nozieres and Pines, vol. 1, p 237 ff); Mahan, Ch. 2.7-8, 6.4 | |
| 2/29 | 10 | Electrons, Phonons, Plasmons in Solids;
Fermi Liquid Theory Pines, ch. 4 and supplementary material | |
| 3/2 | 4 | 11 | Finite Temperature Greens Functions; Matsubara functions provides retarded functions at finite T. Mahan Ch. 3. |
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PART II: Stongly Interacting Electron Systems |
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| 3/7 | 12 | Broken Symmetry Transitions and Order Parameters (Notes) | |
| 3/9 | 13 , 14 | Introduction to Strongly Interacting Electron Problems: Magnetism, Mott Metal Insulator Transitions, Heavy Fermion Systems, etc. Anderson and Hubbard Models. Mahan, Ch 1; Aschroft and Mermin, Ch. 32; Jones and March, p. 341 ff; Review by Imada, et. al.; The Anderson Impurity and Kondo Problems - where "expected" broken symmetry does not occur; Mahan p. 57-59, 249, 977 ff |
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| 3/14 - 3/23 | NO CLASSES - APS Meeting and Spring Break WORK ON INDIVIDUAL PROJECTS |
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| 3/28 | 14 | Continue Localized States in Metals; Exact solution
of Anderson Model in Large Degeneracy Limit Mahan Ch. 11 |
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| 3/30 | 15 | Survey of Strongly-Interacting Electron Systems Imada, et al., Rev Mod Phys review |
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| 4/4 | Strongly-Interacting Electron Systems Continued | ||
| 4/6 | 16 | Quantum Hall Effect | |
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PART III: Superconductivity |
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| 4/11 | 5 | 17 | Superconductivity: Experimental Facts, Electrodynamics DeGennes, Ch. 1,2,3 (p 48-65) |
| 4/13 | Experimental Facts, Electrodynamics Continued | ||
| 4/18 | 18 | Superconductivity: BCS Theory Mahan, ch. 9; de Gennes, Ch. 4; Tinkham, "Intro. to Superconductivity", Ch 2; Brief summaries in Aschroft & Mermin and Kittel, "Intro. to SSP" |
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| 4/20 | BCS Theory Continued | ||
| 4/25 | 19 | Superconductivity: The Superconducting Condensed State de Gennes, Ch 5-1,5-2; 6-1 - 6-5; Tinkham, "Intro. to Superconductivity", Ch 4, 6; Brief summaries in Aschroft & Mermin and Kittel. |
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| 4/27 | Superconducting Condensed State Continued; Take Home Final Passed Out | ||
| 5/2 | 20 | Review of Course | |
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| 5/08 | 1:30 - 4:30 - Finals Period: Presentation of Individual Projects; Written Reports on Individual Projects Due; Take Home Final Due |