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Now you are in the subtree of Deep Learning Quantum Physics of Many-Body Systems project. 

Theory of Linear Response and Transport

Goals: Learn the theory of linear response, applied to simple and complex systems near equilibrium.

Prelude

  • General linear response theory; Kubo formula.
  • Consequences of symmetries: temporal and spatial translation invariance.
  • Analytic properties of the response function: Causality, Kramers-Kronig relations.
  • Fluctuation-dissipation theorem.

Application of linear response in simplest system

  • Conductivity in a non-interacting Fermi sea; Drude theory
  • Magnetism of a non-interacting Fermi sea
  • Paramagnetism: Curi's law
  • Charge transport: response to electromagnetic fields
  • Neutron scattering: Fermi's Golden rule
  • X-ray/photon scattering: light-matter interaction

Response at the mean-field level

  • Conductivity in resonant-level model: Charge transport in Graphene.
  • Conductivity and magnetism in an interacting Fermi liquid within Hartree-Fock approximation.
  • Conductivity and magnetism in Anderson model within mean-field.
  • Conductivity and magnetism in the anomalous slave-boson mean-field theory for the s-d model; Kondo physics.

Response in presence of interactions

  • RPA and screening in a Fermi liquid; elementary excitations: plasmons
  • Scattering at random impurities; Born approximation

Phase transitions

  • Goldstone modes and symmetry breaking

References:

  • Fetter, A. L. and Walecka, J. D. “Quantum theory of many-particle systems”. Dover (2013).
  • Bruus, H., and K. Flensberg. “Many-body quantum theory in condensed matter physics”. Oxford University Press (2004).
  • Sólyom, J. “Fundamentals of the Physics of Solids: Vol. 1: Structure and Dynamics”. Springer (2007).
  • Sólyom, J. “Fundamentals of the Physics of Solids: Vol. 2: Electronic Properties”. Springer (2009).
  • Sólyom, J. “Fundamentals of the Physics of Solids: Vol. 3: Normal, Broken-Symmetry, and Correlated Systems”. Springer (2010).
  • Ziman, J. M. “Principles of the Theory of Solids”. CUP (1972).
  • Doniach, S., and E. H. Sondheimer. “Green's functions for solid state physicists”. World Scientific (1998).
  • Jülich lecture notes for Autumn school on correlated electrons.
  • Jishi, R. A. “Feynman diagram techniques in condensed matter physics”. CUP (2013).
  • Mazenko, G. F. “Nonequilibrium statistical mechanics”. Wiley (2008).
  • Pines, D. “Elementary excitations in solids”. Perseus (1966).