Quantum ManyBody Dynamics II
Lecture
Thomas GasenzerWednesday, 9:1510:45, SR Pw 19 [LSF]
Practice group: Thursday, 9:1510:00, kHS Pw 12
Content  Prerequisites  Literature  Additional material
Content
(Chapters 15 were read as part I in WT 10/11; this lecture starts with Chapter 6. The presentation will be as selfcontained as possible.)

1. Introduction
 From nonequilibrium statistical mechanics to manybody quantum dynamics
Notes 
2. Basics of nonequilibrium quantum field theory
 Basics of quantum field theory  Correlation functions  KMS boundary condition  Fluctuationdissipation theorem  Physical information in 2point function
Notes 
3. Functionalintegral approach to Quantum Dynamics
 Feynman's path integral  Functional derivatives and integrals  Saddlepoint expansion  Perturbation theory  Generating functional  SchwingerKeldysh 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 realtime formulation  1PI and 2PI effective actions  Dynamic equations  KadanoffBaym equations
Notes 
5. Dynamic equations: Meanfield and beyond
 Meanfield approximation  Timedependent HartreeFockBogoliubov equations  Meanfield dynamics of BoseEinstein condensates  GrossPitaevskii equation  Linearized HFB equations  Conservation laws  Scattering effects and kinetic theory  Derivation of Quantum Boltzmann equation
Notes 
6. Kinetic theory and transport phenomena
 Quantum Boltzmann equation  The generalised kinetic equations  Equilibrium solutions  Conservation laws  Sound propagation: Boltzmann approach and beyond  Hydrodynamic equations  Linear response theory  Transport coefficients and GreenKubo relations
Notes 
7. Nonequilibrium Critical Points and Turbulence
 Fourwave kinetic and (Quantum) Boltzmann equations  Implications from conservation laws for nonequilibrium distributions  Stationary nonequilibrium distributions  Dimensional estimates and selfsimilarity  Stationary spectra of weak wave turbulence  Exact stationary solutions for the fourwave kinetic equation  Zakharov transformations  Constant fluxes of action and energy
Notes 
8. Advanced functional methods for quantum dynamics
 Flowequation approach to quantum dynamics  FunctionalIntegral approach  Regulator for dynamical flow  Dynamical flow equation for the effective action  Flow equations for correlation functions  Dynamic equations  Loop expansion
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. AddisonWesley, Redwood City, 1989. [ HEIDI ]
 Jørgen Rammer, Quantum field theory of nonequilibrium states. CUP, Cambridge, 2007. [ Online edition  HEIDI ]
 V. E. Zakharov, V. S. L'vov, and G. Falkovich, Kolmogorov Spectra of Turbulence I. Springer, Berlin, 1992. [ Google books ]
Additional material:
 J. Berges, Introduction to nonequilibrium quantum field theory, AIP Conf. Proc. 739, 3 (2005); arXiv.org: hepph/0409233 .
 P. Danielewicz, Quantum Theory of Nonequilibrium Processes, Annals of Physics 152, 239 (1984) .
 T. Gasenzer, Ultracold gases far from equilibrium Eur. Phys. Journ. ST 168, 89 (2009); arXiv.org: 0812.0004 [condmat.other] .
 L. P. Kadanoff and P. C. Martin, Hydrodynamic Equations and Correlation Functions Annals of Physics 24, 419 (1963).