Statistical Physics part 2 - quantum theory (Book): Difference between revisions

Statistical Physics part 2 - quantum theory (Book) (edit)

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 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]. An exceptional 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. It is worth emphasizing that the foundation of these effects/phases is the crystal lattice structure of metals (basic theory, Bloch functions, in Landau). It is a mathematical reinterpretation of this situation that gives us point symmetry groups acting on the Brillouin torus, bundles and band structures over the torus.
-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. A text on random matrices in physics is provided before the foray into the matrix model and Chern-Simons gauge theory. It is consistent with our previous philosophy that mathematical and specifically statistical ideas are best seen through the lens of physics/statistical mechanics and geometry.
+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. A text on random matrices in physics is provided before the foray into the matrix model and Chern-Simons gauge theory (notably featuring Parisi, Marino, Di Francesco). It is consistent with our previous philosophy that mathematical and specifically statistical ideas are best seen through the lens of physics/statistical mechanics and geometry.
 === Applications ===