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Statistical Physics part 2 - quantum theory (Book): Difference between revisions
Statistical Physics part 2 - quantum theory (Book) (edit)
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As such, it has already shown to be an important proving grounds both experimentally and theoretically for methods in quantum field theory, and this continues to be the case. Modern problems focus on the engineering of artificial atoms (Quantum Dots), the theory of superconductivity for high critical temperatures (this is not explained by the usual low Tc theory), the Integer and Fractional Quantum Hall Effects; From those come emergent gauge fields, Chern-Simons theory, Topological Quantum Computing, Anyons, the Twisted-Equivariant cohomology classification of topological phases (Kitaev, Freed), and applications of AdS/CFT. Condensed matter, due to this and the immense wealth produced by the development of semiconductors and modern computing devices, is the largest and most active area of physics today. | As such, it has already shown to be an important proving grounds both experimentally and theoretically for methods in quantum field theory, and this continues to be the case. Modern problems focus on the engineering of artificial atoms (Quantum Dots), the theory of superconductivity for high critical temperatures (this is not explained by the usual low Tc theory), the Integer and Fractional Quantum Hall Effects; From those come emergent gauge fields, Chern-Simons theory, Topological Quantum Computing, Anyons, the Twisted-Equivariant cohomology classification of topological phases (Kitaev, Freed), and applications of AdS/CFT. Condensed matter, due to this and the immense wealth produced by the development of semiconductors and modern computing devices, is the largest and most active area of physics today. | ||
For resources, Heidelberg University has a Condensed Matter group which focuses on engineering quantum systems: [https://www.kip.uni-heidelberg.de/cmm/teaching/2020/quantum_materials/tutorials/tut5?lang=en kondo effect in quantum dots], [http://www.kip.uni-heidelberg.de/synqs/ synthetic quantum systems]. A master's student thesis on twisted equivariant cohomology and the 10-fold way/K-theory classification is [https://webspace.science.uu.nl/~0554804/publications/bachelor.pdf here]. | For resources, Heidelberg University has a Condensed Matter group which focuses on engineering quantum systems: [https://www.kip.uni-heidelberg.de/cmm/teaching/2020/quantum_materials/tutorials/tut5?lang=en kondo effect in quantum dots], [http://www.kip.uni-heidelberg.de/synqs/ synthetic quantum systems]. A master's student thesis on twisted equivariant cohomology and the 10-fold way/K-theory classification is [https://webspace.science.uu.nl/~0554804/publications/bachelor.pdf here]. Otherwise, Freed's and Kitaev's ideas will be encountered in their full form in the books here or their papers. Note that Dan Freed works in the developed language of cohomology theories in algebraic topology, changing between geometric methods like those in Spin Geometry and gauge theory, or simplicial methods/spectra from formal algebraic topology. Additionally, [https://www.damtp.cam.ac.uk/user/tong/qhe.html David Tong's page] contains many online condensed matter/quantum hall effect lecture notes and external resources. | ||
For the following books, Anderson gives speculation as to the actual theory of high Tc, and some philosophy and misgivings about the direction of the field. He has valuable insight. Sachdev helps run a condensed matter group at Harvard, these books by him cover the basic ideas of the quantum hall effect and these further applications to topological field theory, while remaining grounded in the application. The later books are much more mathematical, and follow from the previous topics. | |||
=== Applications === | === Applications === | ||