TEACHING
Summer term 2018, Lecture:
Quantum fields and information theory
Venue
Monday 16.07. / Wednesday 18.07. / Monday 23.07. / Wednesday 25.07., 16:15  18:00 h, Philosophenweg 12, R 105.
Content
 Entropy as a measure of information
 Shannon’s information entropy
 von Neumann’s quantum entropy
 Rényi entropy
 KullbackLeibler divergence and relative entropy
 Gaussian states
 Schrödinger functional
 Density matrix
 Correlation functions
 Unitary and symplectic transformations
 Williamson’s theorem
 Entanglement
 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
Literature
 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:quantph/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
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.
Venue
Tuesdays, 11:15  13:00 h, Philosophenweg 19, Seminar Room.
Content
 Introduction and overview
 Finite groups
 Lie algebras and Lie groups
 SU(2)
 SU(3)
 Classification of compact simple Lie algebras
 Lorentz and Poincaré groups
 Conformal group
 Nonabelian gauge theories
 Grand unification
Literature
 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
Lecture notes
Lecture notes have been kindly compiled by Alaric Erschfeld and can be found here. There is also a summary of suggested exercises.
Winter term 2016/2017, MasterSeminar:
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 NavierStokes 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.
Venue
Fridays, 14:15  16:00 h, Philosophenweg 12, kleiner Hörsaal.
Introduction, overview and suggested literature
 21.10.2016, Stefan Floerchinger, Introduction and Motivation
Seminar talks

04.11.2016, Jorrit Lion, Relativistic fluid dynamics at first order

11.11.2016, Niels Fischer, FriedmannRobertson 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, Divergencetype theories
Summer term 2016, Lecture:
Hydrodynamics
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.
Venue
Mondays, starting from April 18th, 11:15  13:00 h, Philosophenweg 12, großer Hörsaal.
Exam
There was a written exam on Monday, July 25th from 11:30h to 13:00h. Results can be found here.
Content
 Introduction and overview
 Symmetries and conservation laws
 Thermodynamics and equation of state
 Fluid dynamic equations of motion
 Ideal fluid flows
 Twodimensional incompressible potential flows
 Laminar viscous flows
 Small perturbations and instabilities
 Fluids in a gravitational field
 Newtonian cosmology
 Superfluidity
 Relativistic fluid dynamics
Literature
 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
Lecture notes can be found here.