Supersymmetric approach to quantum disordered systems

Basic Information

• Dates: 10.02, 12.02, 24.02, 26.02, 11.03, 13.03, 16.03, 18.03, 20.03, 23.03
  Place and time: Largo S. Leonardo Murialdo 1, Room C309 (Building C, 3rd floor), from 11:00 to 13:00

Programme

• Tuesday 10.02: Introduction to random operators, relevant examples, Efetov's supersymmetric method
• Thursday 12.02: Grassmann calculus, supersymmetric integrals, localisation theorem
• Tuesday 24.02: Random Schrödinger operators, Green's function, Wegner estimates
• Thursday 26.02: Supersymmetric cluster expansions, Lifshitz tail estimates

References

• M. Aizenman, S. Warzel. Random operators. Disorder Effects on Quantum Spectra and Dynamics. Graduate Studies in Mathemathics, vol. 168. American Mathematical Society, Providence, RI (2015)
• W. Kirsch. An invitation to random Schrödinger operators. Minicourse Lecture Notes arXiv:0709.3707 (2007)
• F.J. Wegner. Supermathematics and its Applications in Statistical Physics. Lecture Notes in Physics. Springer Berlin, Heidelberg (2016)
• L. Fresta. Supersymmetric Cluster Expansions and Applications to Random Schrödinger Operators. Math. Phys. Anal. Geom. 24, 4 (2021)
• M. Disertori. Density of states for GUE through supersymmetric approach. Rev. Math. Phys., 16(9):1191–1225 (2004)
• M. Disertori, H. Pinson, and T. Spencer. Density of states for random band matrices. Comm. Math. Phys., 232(1):83-124, (2002)
• M. Disertori, T. Spencer and M.R. Zirnbauer. Quasi-diffusion in a 3D supersymmetric hyperbolic sigma model. Commun. Math. Phys. 300 (2), 435–486 (2010)
• M. Disertori and T. Spencer. Anderson localization for a supersymmetric sigma model. Commun. Math. Phys. 300 (3), 659–671 (2010).