Summer term 2018, Lecture:
Quantum fields and information theory
Monday 16.07. / Wednesday 18.07. / Monday 23.07. / Wednesday 25.07., 16:15 - 18:00 h, Philosophenweg 12, R 105.
- Entropy as a measure of information
- Shannon’s information entropy
- von Neumann’s quantum entropy
- Rényi entropy
- Kullback-Leibler divergence and relative entropy
- Gaussian states
- Schrödinger functional
- Density matrix
- Correlation functions
- Unitary and symplectic transformations
- Williamson’s theorem
- Reduced density matrix
- Entanglement entropies
- Modular hamiltonian for conformal field theory
- Unruh effect
- Hawking radiation, entropy and temperature of black holes
- Entanglement in an expanding quantum string
- Entropic uncertainty relations
- Heisenberg’s uncertainty relation
- Robertson’s uncertainty relation
- Entropic uncertainty relation
- Uncertainty relations with quantum memory
- M. Wilde, Quantum Information Theory
- V. Vedral, Introduction to Quantum Information Science
- T. M. Cover and J. A. Thomas, Elements of Information Theory
- V. Vedral, The Role of Relative Entropy in Quantum Information Theory, Rev. Mod. Phys. 74, 197 (2002); arXiv:quant-ph/0102094.
- J. Berges, S. Floerchinger and R. Venugopalan, Dynamics of entanglement in expanding quantum fields, JHEP 1804, 145 (2018), arXiv:1712.09362.
- P. J. Coles, M. Berta, M. Tomamichel and S. Wehner, Entropic Uncertainty Relations and their Applications, Rev. Mod. Phys. 89, 015002 (2017), arXiv:1511.04857.
Lecture notes will be provided parallel to the course.
TEACHING IN PREVIOUS TERMS:
Summer term 2017, Lecture:
Symmetries and particle physics
These lectures are intended for Master students of physics. The implications of symmetry in physics are ubiquitous and very interesting. Mathematically, they are described by group theory. I will start from finite groups and then disuss the most important Lie groups and Lie algebras, in particular SU(2), SU(3), the Lorentz and Poincaré groups, the conformal group and grand unification.
Tuesdays, 11:15 - 13:00 h, Philosophenweg 19, Seminar Room.
- Introduction and overview
- Finite groups
- Lie algebras and Lie groups
- Classification of compact simple Lie algebras
- Lorentz and Poincaré groups
- Conformal group
- Non-abelian gauge theories
- Grand unification
- P. Ramond, Group Theory, A Physicist’s Survey
- A. Zee, Group Theory in a Nutshell for Physicsists
- J. Fuchs and C. Schweigert, Symmetries Lie Algebras and Representations
- H. Georgi, Lie Algebras in Particle Physics
- H. F. Jones, Groups, Representations and Physics
Winter term 2016/2017, Master-Seminar:
Relativistic fluid dynamics for heavy ion collisions and cosmology
The seminar is intended for Master students of physics. We will discuss different aspects of relativistic fluid dynamics (in a wide sense). This includes theoretical aspects such as the relativistic Navier-Stokes theory (and its problems), second order theories like the one of Israel & Stewart, applications to heavy ion collisions, but also aspects of fluid dynamics in the context of cosmology and structure formation.
Fridays, 14:15 - 16:00 h, Philosophenweg 12, kleiner Hörsaal.
Introduction, overview and suggested literature
- 21.10.2016, Stefan Floerchinger, Introduction and Motivation
04.11.2016, Jorrit Lion, Relativistic fluid dynamics at first order
11.11.2016, Niels Fischer, Friedmann-Robertson walker cosmologies for ideal fluids
18.11.2016, Martin Stein, The second order theory of Israel & Stewart
25.11.2016, Alaric Erschfeld, The Vlasov equation for cold dark matter and gravity
09.12.2016, Sebastian Schulz, Gravitational collapse and the theory of Press & Schechter
20.01.2017, Martin Stein, Divergence-type theories
Summer term 2016, Lecture:
These lectures are intentended for Batchelor and Master students of physics. They will start with the basics of fluid dynamics which rely on the conservation laws for energy, momentum and particle numbers as well as thermodynamics. The most important equations of fluid dynamics will be discussed as well as the phenomena they describe. More advanced topics will be turbulence and superfluidity as well as applications of fluid dynamics in current physics research, for example in the context of heavy ion physics and cosmology.
Mondays, starting from April 18th, 11:15 - 13:00 h, Philosophenweg 12, großer Hörsaal.
There was a written exam on Monday, July 25th from 11:30h to 13:00h. Results can be found here.
- Introduction and overview
- Symmetries and conservation laws
- Thermodynamics and equation of state
- Fluid dynamic equations of motion
- Ideal fluid flows
- Two-dimensional incompressible potential flows
- Laminar viscous flows
- Small perturbations and instabilities
- Fluids in a gravitational field
- Newtonian cosmology
- Relativistic fluid dynamics
- L. D. Landau and E. M. Lifshitz, Fluid Mechanics (Volume 6 of Course of Theoretical Physics)
- G. Falkovich, Fluid mechanics
- T. E. Faber, Fluid dynamics for physicists
- U. Frisch, Turbulence
- G. K. Batchelor, An Introduction to Fluid Dynamics
- D. Acheson, Elementary Fluid Dynamics
- S. Weinberg, Gravitation and cosmology
- R. P. Feynman, R. B. Leighton and M. L. Sands, The Feynman Lectures on Physics, Volume II
Lecture notes can be found here.