Ludwig-Maximilians-Universität München

Mathematics Institute

Theresienstr. 39

80333 Munich

pickl[at]math.lmu.de

Research Group### Description

**Research focus: mathematical physics, effective theories, quantum electrodynamics**

he research focus of our group is the microscopic derivation of effective descriptions for many particle systems. Further we investigate strong field QED, in particular the possibility of pair creation.

##### Microscopic derivation of effective theories

The understanding of the behavior of macroscopic systems from first principles plays an important role to get a fundamental understanding of the macroscopic object. The rigorous derivation of effective descriptions used for the macroscopic systems is thus extensively studied in the mathematical physics community. Usually these effective descriptions are based on nonlinear equations, the non-linearity arising from the interaction between the particles.

Using new methods developed within the group, we study interacting Bose- and Fermi-gases as well as systems of second quantization, classical many body systems and models motivated from biology. Examples for the resulting effective descriptions are the Gross-Pitaevskii equation used to describe the dynamics of Bose-Einstein condensates, the Fermionic-Hartree-equation used for interacting Fermi-gases, the semi-classical Schrödinger equation as effective result from QED, the Vlasov equation describing plasmas or the Keller-Segel equation used to described one part of the live cycles of slime-molds.

**Selected publications**

- A simple derivation of mean field limits for quantum systems, Lett. Math. Phys. 97, 151 (2011).
- On Mean Field Limits for Dynamical Systems, J. Stat. Phys. 164, 1 (2016); arXiv:1307.2999.

##### Pair creation in strong fields

The planned generation of lasers and heavy ion colliders renews the hope to see electron-positron pair creation in strong classical fields (so called spontaneous pair creation). Concerning lasers our conclusion about the possibility of adiabatic pair creation is different from earlier predictions.

The figure to the right shows the bound state energy curve of a bound state ? emerging from the Dirac sea (vacuum). The state energy changes with time s due to the change of the potential well. If the potential reaches a high enough value, the bound state enters the upper continuum and scatters. If the state has enough time to escape from the potential before decreasing under the critical value (adiabatic process), a pair will be created.

**Selected publication**

- Adiabatic Pair Creation in Heavy Ion and Laser Fields, Europhys. Lett. 81, 40001 (2008).