Modern Computational Methods in Solids
by Adrian Feiguin
Publisher: University of Wyoming 2009
Number of pages: 99
The purpose of this course is to introduce students to a series of paradigmatic physical problems in condensed matter, using the computer to solve them. The course will feel like a natural extension of introductory condensed matter, with extra degrees of complexity that make the problems analytically intractable to some extent. Therefore, it will also serve as a complementary condensed matter course.
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Important progress in understanding the behavior of hadronic matter at high density has been achieved recently. We discuss the phase diagram of QCD as a function of temperature and density, and close with a look at possible astrophysical signatures.
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DFT is not just another way of solving the Schroedinger equation. Density functional theory is a completely different, rigorous way of approaching any interacting problem, by mapping it exactly to a much easier-to-solve non-interacting problem.
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Various topics at the interface between condensed matter physics and the physics of ultra-cold fermionic atoms in optical lattices are discussed. Lectures given at the Enrico Fermi Summer School on 'Ultracold Fermi Gases' in 2006.
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Contents: Basic Formalism; Goldstone Modes and Spontaneous Symmetry Breaking; Critical Fluctuations and Phase Transitions; Symmetry-Breaking In Fermion Systems; Gauge Fields and Fractionalization; Localized and Extended Excitations in Dirty Systems.