Quantum Many-Body Dynamics II

Lecture

Thomas Gasenzer

Wednesday, 9:15-10:45, SR Pw 19 [LSF]
Practice group: Thursday, 9:15-10:00, kHS Pw 12

Content - Prerequisites - Literature - Additional material

Content
(Chapters 1-5 were read as part I in WT 10/11; this lecture starts with Chapter 6. The presentation will be as self-contained as possible.)

• 1. Introduction
  - From nonequilibrium statistical mechanics to many-body quantum dynamics
  
• 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
  
• 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
  
• 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
  
• 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
  
• 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 Green-Kubo relations
  
• 7. Nonequilibrium Critical Points and Turbulence
  - Four-wave kinetic and (Quantum) Boltzmann equations - Implications from conservation laws for nonequilibrium distributions - Stationary nonequilibrium distributions - Dimensional estimates and self-similarity - Stationary spectra of weak wave turbulence - Exact stationary solutions for the four-wave kinetic equation - Zakharov transformations - Constant fluxes of action and energy
  
• 8. Advanced functional methods for quantum dynamics
  - Flow-equation approach to quantum dynamics - Functional-Integral approach - Regulator for dynamical flow - Dynamical flow equation for the effective action - Flow equations for correlation functions - Dynamic equations - Loop expansion
  

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 ]
• 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: hep-ph/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 [cond-mat.other] .
• L. P. Kadanoff and P. C. Martin, Hydrodynamic Equations and Correlation Functions Annals of Physics 24, 419 (1963).