Quantum Many-Body Dynamics

Lecture

Thomas Gasenzer

Wednesday, 9:15-10:45, SR Pw 19 [LSF]
Practice group: Tuesday, 17:00 hrs, A.-Ueb. Str. 3-5 SR I (Please register by email if you require a Schein.)

Content - Prerequisites - Literature - Additional material

Content:
  • 1. Introduction
    - From nonequilibrium statistical mechanics to many-body quantum dynamics
    Notes
  • 2. Basics of nonequilibrium quantum field theory
    - Basics of quantum field theory - Correlation functions - KMS boundary condition - Fluctuation-dissipation theorem - Physical information in 2-point function
    Notes
  • 3. Functional-integral approach to Quantum Dynamics
    - Feynman's path integral - Functional derivatives and integrals - Saddle-point expansion - Perturbation theory - Generating functional - Schwinger-Keldysh contour - Quantum vs classical path integral
    Notes
  • 4. Quantum effective action approach
    - Variational determination of the effective action - Spontaneous Symmetry Breaking - The effective action in real-time formulation - 1PI and 2PI effective actions - Dynamic equations - Kadanoff-Baym equations
    Notes
  • 5. Dynamic equations: Mean-field and beyond
    - Mean-field approximation - Time-dependent Hartree-Fock-Bogoliubov equations - Mean-field dynamics of Bose-Einstein condensates - Gross-Pitaevskii equation - Linearized HFB equations - Conservation laws - Scattering effects and kinetic theory - Derivation of Quantum Boltzmann equation
    Notes

Prerequisites:
  • Quantum Mechanics (Theoretical Physics III), Statistical Mechanics (Theor. Phys. IV), Quantum Field Theory I or Quantum Optics

Literature:
  • M. Bonitz, Quantum kinetic theory. Teubner, Stuttgart, 1998. [ Contents | HEIDI ]
  • E. Calzetta and B.-L. Hu, Nonequilibrium quantum field theory. CUP, Cambridge, 2008. [ Online fulltext | HEIDI ]
  • L.P. Kadanoff and G. Baym, Quantum statistical mechanics. Addison-Wesley, Redwood City, 1989. [ HEIDI ]
  • Jørgen Rammer, Quantum field theory of non-equilibrium states. CUP, Cambridge, 2007. [ Online edition | HEIDI ]

Additional material: