| Date | Hmwk. | Notes | Subject of Lecture and References |
|---|---|---|---|
| # | # | ||
| 8/25 | 1 | 1 | Introduction to Course; Overview of Condensed Matter Physics Beyond the Independent-particle Approximation ( Notes presented in class - pdf file ) |
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PART I: Elementary Excitations |
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| 8/30 | 2 | Fundamental Theory-- Identifying the Basic Excitations: Adiabatic approx., Hellmann-Feynman theorem, ... (Phillips Ch. 1,2; Pines, Ch. 1; Class Notes) | |
| 9/1 | 3 | Electrons: Hartree approx., Hartree-Fock approx., exchange, Homegeneous Electron Gas (Jellium), pair correlation function, structure factor, difficulties of treating correlation (Phillips 4,5; A&M 3,17; Pines 3-1,3-2; Mahan 1.6,5.1; Fulde, Ch. 2) | |
| 3a | Density Functional Theory, Local Density Approximation (LDA): successful for many ground state properties, problems for excited state properties. (classnotes) | ||
| 9/6 | 4 | Second quantization; nuclear vibrations; highly-correlated motion of the nuclei; transformation to phonons - elementary excitations; non-interacting electrons; interaction terms in the hamiltonian; Hartree-Fock revisited; correlation. (Phillips 3-5; Mahan 1.1,1.2,1.3A; Pines p. 18, p. 67; Fetter and Walecka) | |
| 9/8 | 2 | 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 Phillips 8; (P. C. Martin; Mahan 3; Fetter 5) |
| 9/13 | 5a | Continued from last time | |
| 9/15 | 5b | Dielectric response function: Dynamic structure factor,
scattering of charged particles, sum rules (Pines 3-4 - 3-5; Phillips 8.4; Mahan 5.6 - 5.7; Doniach 6.4; Fetter 5) | |
| 9/20 | 6 | Green's functions in many-body perturbation theory: Interaction
Representation, time ordering, Wick's theorem,
Dyson's Equation (Mahan 2-3; Fetter 3) | |
| 9/22 | 3 | 6a | Continue Green's functions |
| 9/27 | 7 | Quasiparticles and Self energies: Spectral functions, broadening (Mahan 3.3-3.4; Fetter 3) | |
| 9/29 | 8 | 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) | |
| 10/4 | 9 | Phonons and Electron-Phonon interactions in metals -
renormalization of electrons near $E_F$ - induced
electron-electron interactions Phillips; Pines, ch. 5 (See also Nozieres and Pines, vol. 1, p 237 ff); Mahan, Ch. 2.7-8, 6.4 | |
| 10/6 | 4 | 10 | Summary to this point: Electrons, Phonons, Plasmons in
Solids;
Fermi Liquid Theory; Luttinger Theorem Phillips, Pines, ch. 4 and supplementary material |
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PART II: Strongly Interacting Electron Systems |
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| 10/11 | 11 | Overview of strongly correlated systems: new phenomena
emerging from collective effects, crossovers and transitions.
The local moment problem: the Kondo effects, new energy scales
caused by collective effects of interacting electrons Phillips, Ch. 6 and 7; notes |
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| 10/13 | 11a | Continue Localized States in Metals; Exact solution
of Anderson and Kondo Models - Understanding in terms of scaling
- Large Degeneracy Limit Phillips 6; Mahan Ch. 11; Notes |
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| 10/18 | 12 | Broken Symmetry Transitions and Order Parameters (Notes) | |
| 10/20 | 5 | 13 | Strongly Interacting Electron Problems: Magnetism, Mott Metal Insulator Transitions, Heavy Fermion Systems, etc. Anderson and Hubbard Models. Phillips, Ch. 6; Mahan, Ch 1; Review by Imada, et. al.; Mahan p. 57-59, 249, 977 ff |
| 10/25 | 14 | Finite Temperature Greens Functions; Matsubara functions provides retarded functions at finite T. Mahan Ch. 3. | |
| 10/27 | 15 | Dynamical Mean Field Theory (DMFT) - approximate mapping of the Hubbard model
onto a self-consistent impurity model - low energy scales - accurate in large
dimension limit |
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| 11/1 | No Class | ||
| 11/3 | 16 | Survey of Strongly-Interacting Electron Systems - Hi Tc materials and
phenomena Imada, et al., Rev Mod Phys review; Notes |
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| 11/8 | 17 | Low Dimensional systems: Bosonization and the Luttinger Liquid |
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PART III: Quantum Phases of Matter: Metals, Insulators, Superconductivity, Quantum Hall Effect, . . . |
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| 11/10 | 18 | Superconductivity: Paradigm of quantum state of matter -
Experimental Facts, Electrodynamics Phillips 11, 14; DeGennes, Ch. 1,2,3 (p 48-65) |
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| 11/15 | 19 | Superconductivity: BCS Theory Phillips 11; Mahan, ch. 9; de Gennes, Ch. 4; Tinkham, "Intro. to Superconductivity", Ch 2 |
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| 11/17 | 6 | 20 |
Superconductivity: The Superconducting Condensed State Phillips 11; de Gennes, Ch 5-1,5-2; 6-1 - 6-5; Tinkham, "Intro. to Superconductivity", Ch 4, 6 |
| 11/19 - 11/27 | NO CLASSES - Fall Thanksgiving Break WORK ON INDIVIDUAL PROJECTS |
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| 11/29 | 21 | Quantum Hall Effect Phillips 14 | |
| 11/30 | 22 | Fractionized phases of matter: Fractional QHE Phillips, Ch. 14 NOTE THIS CLASS IS ON WEDNESDAY 11/30 |
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| 12/1 | NO CLASS | ||
| 12/6 | 23 | Classification of states by topology of wavefunction:
Bohm-Aharonov effect,
Berry's phase, . . . TAKE HOME FINAL PASSED OUT |
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| 12/8 | 24 25 |
Metals, Insulators, superconductors, . . .: Drude weight,
Luttinger theorem,
localization, polarization, superfluidity in terms of response of the system
to "twisted"
boundary conditions Review of Course |
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| 12/14 | Finals Period: Presentation of Individual Projects; Written Reports on Individual Projects Due; Take Home Final Due |