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Lecture Notes on Condensed Matter Physics (A Work in …

Lecture Notes on Condensed Matter Physics (A Work in Progress)Daniel ArovasDepartment of PhysicsUniversity of California, San DiegoMarch 14, ..vi0 Introductory ..21 Boltzmann .. Equation in Solids .. Dynamics and Distribution Functions .. Equilibrium .. of Normal Metals .. Time Approximation .. Reflectivity of Metals and Semiconductors .. Conductivity of Semiconductors .. Conductivity and the Fermi Surface .. of the Scattering Time .. Scattering and Fermi s Golden Rule .. and the Transport Lifetime.

Lecture Notes on Condensed Matter Physics (A Work in Progress) Daniel Arovas Department of Physics University of California, San Diego March 14, 2010

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Transcription of Lecture Notes on Condensed Matter Physics (A Work in …

1 Lecture Notes on Condensed Matter Physics (A Work in Progress)Daniel ArovasDepartment of PhysicsUniversity of California, San DiegoMarch 14, ..vi0 Introductory ..21 Boltzmann .. Equation in Solids .. Dynamics and Distribution Functions .. Equilibrium .. of Normal Metals .. Time Approximation .. Reflectivity of Metals and Semiconductors .. Conductivity of Semiconductors .. Conductivity and the Fermi Surface .. of the Scattering Time .. Scattering and Fermi s Golden Rule .. and the Transport Lifetime.

2 Equation for Holes .. of Holes .. and Hall Effect .. Theory for ( ,B) .. Resonance in Semiconductors .. : Two-Band Model .. Effect in High Fields .. Transport .. Theory .. Heat Equation .. of Transport Coefficients .. Relations .. Scattering .. Remarks .. Interaction .. Equation for Electron-Phonon Scattering ..482 .. Landauer Formula .. : Potential Step .. Systems .. Matrices: The Pichard Formula .. of the Pichard Formula .. Quantum Resistors in Series.

3 Quantum Resistors in Parallel .. Conductance Fluctuations in Dirty Metals .. Localization .. Localization .. of Localized and Extended States .. Studies of the Localization Transition .. Theory of Localization .. Temperature ..893 Linear Response and Resonance .. Dissipation .. Relations .. Mechanical Response Functions .. Representation .. Dissipation .. Functions .. Systems .. :S=12 Object in a Magnetic Field .. Equations .. Response .. Invariance and Charge Conservation.

4 Sum Rule .. and Transverse Response .. Systems .. Meissner Effect and Superfluid Density .. Correlations .. Rules .. Structure Factor for the Electron Gas .. 0 Calculation .. Systems: Screening and Dielectric Response .. of the Charge Response Functions .. Screening: Thomas-Fermi Approximation .. Frequency Behavior of (q, ) .. Phase Approximation (RPA) .. 1254 .. of Orbital Magnetism within Classical Physics .. Atomic Physics .

5 Electron Hamiltonian .. Darwin Term .. electron Hamiltonian .. Periodic Table .. of Configurations: Hund s Rules .. Interaction .. Field Splittings .. Susceptibility of Atomic and Ionic Systems .. Shells: Larmor Diamagnetism .. Filled Shells: van Vleck Paramagnetism .. Magnetism of Noninteracting Systems .. Paramagnetism .. Diamagnetism .. Formation in Interacting Itinerant Systems .. Hubbard Model .. Mean Field Theory.

6 Solution .. Field Phase Diagram of the Hubbard Model .. of Local Moments: the Heisenberg Model .. Exchange of Orthogonal Orbitals .. Theory of the H2 Molecule .. of Heitler-London Theory .. s approach .. Field Theory .. Probability Distribution .. Ordering .. Field Theory of Anisotropic Magnetic Systems .. Chains .. Spin Wave Theory .. Ferromagnetic Spin Waves .. Static Correlations in the Ferromagnet .. Antiferromagnetic Spin Waves.

7 Specific Heat due to Spin Waves .. PrefaceThis is a proto-preface. A more complete preface will be written after these Notes Lecture Notes are intended to supplement a graduate level course in Condensed 0 Introductory InformationInstructor:Daniel ArovasContact :Mayer Hall 5671 / 534-6323 / Th / 9:30 am - 10:50 am / Mayer Hall 5301 Office Hours:W 2:00 pm - 3:30 pm / Mayer Hall 5671A strong emphasis of this class will be on learning how to calculate. I plan to cover thefollowing topics this quarter:Transport: Boltzmann equation, transport coefficients, cyclotron resonance, magnetore-sistance, thermal transport, electron-phonon scatteringMesoscopic Physics : Landauer formula, conductance fluctuations, Aharonov-Bohm ef-fect, disorder, weak localization, Anderson localizationMagnetism: Weak vs.

8 Strong, local vs. itinerant, Hubbard and Heisenberg models, spinwave theory, magnetic ordering, Kondo effectOther: Linear response theory, Fermi liquid theory (time permitting)There will be about four assignments and a take-home final examination. I will be followingmy own Notes , which are available from the course web 0. INTRODUCTORY References D. Feng and G. Jin, Introduction to Condensed Matter Physics (I)(World Scientific, Singapore, 2005)New and with a distinctly modern flavor and set of topics. Looks good.

9 N, Ashcroft and N. D. Mermin,Solid State Physics (Saunders College Press, Philadelphia, 1976)Beautifully written, this classic text is still one of the best comprehensive guides. M. Marder, Condensed Matter Physics (John Wiley & Sons, New York, 2000)A thorough and advanced level treatment of transport theory in gases, metals, semi-conductors, insulators, and superconductors. D. Pines,Elementary Excitations in Solids(Perseus, New York, 1999)An advanced level text on the quantum theory of solids, treating phonons, electrons,plasmons, and photons.

10 P. L. Taylor and O. Heinonen,A Quantum Approach to Condensed Matter Physics (Cambridge University Press, New York, 2002)A modern, intermediate level treatment of the quantum theory of solids. J. M. Ziman, Principles of the Theory of Solids(Cambridge University Press, New York, 1979).A classic text on solid state Physics . Very REFERENCES3 C. Kittel,Quantum Theory of Solids(John Wiley & Sons, New York, 1963)A graduate level text with several detailed derivations. H. Smith and H. H. Jensen,Transport Phenomena(Oxford University Press, New York, 1989).


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