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

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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. His ideas are based on holography (AdS/CFT) and D-brane technology from string theorists. It did not fit here, but a good general reference for D-branes is [https://www.google.com/books/edition/D_Branes/pnClL_tua_wC?hl=en&gbpv=1&printsec=frontcover Clifford Johnson's book] 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.
+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. His ideas are based on holography (AdS/CFT) and D-brane technology from string theorists. It did not fit here, but a good general reference for D-branes is [https://www.google.com/books/edition/D_Branes/pnClL_tua_wC?hl=en&gbpv=1&printsec=frontcover Clifford Johnson's book] 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. It is a bit more advanced, covering connections to number theory, hydrodynamics, quantum gravity, but [https://www.google.com/books/edition/Random_Matrices/Kp3Nx03_gMwC?hl=en&gbpv=1&printsec=frontcover references an introductory text by Mehta] where basic results like Wigner's semicircle law and nuclear structure can be picked up. Wigner's original book on nuclear structure [https://www.google.com/books/edition/Nuclear_Structure/51bWCgAAQBAJ?hl=en&gbpv=1 can be found here].
 We end on another more physics-text discussing the appearance of gauge and other field theories in condensed matter, because it explains some recent progress. Finally, a text on the Integer and Fractional Quantum Hall effects featuring many legendary and some Nobel-prize winning condensed matter physicists and the promised text on quantum information theory applications of tensor geometry by Landsberg.