# Prof. Dr. Peter Pickl

Vorsitzender des Prüfungsauschusses des Fachs Mathematik für Lehramt Gymnasium

## Kontakt

Mathematisches Institut LMU

Theresienstr. 39

D-80333 München

Theresienstr. 39

D-80333 München

Raum:
208

Telefon:
+49 (0)89 2180 4473

Email:
pickl@math.lmu.de

## Forschung

A very old and yet timely and active field of research is the justification of macroscopic effective descriptions emerging from microscopic dynamics of many particles. Famous examples for classical systems are the Boltzmann equation and Vlasov equations of various types; for quantum systems the Hartree, or Hartree Fock as well as the Gross Pitaevskii equation. Our main focus is on mean field descriptions of classical and quantum systems employing the new alpha-method for proving mean field results. In addition to the justification of the effective description we are also interested in describing physical effects in the mean field situation, for example Cherenkov radiation of fast particles entering a Bose-Einstein condensate.Our research is also directed towards a better understanding of the quantum field vacuum in QED, where we try to understand its effective action and behaviour as it emerges from its mathematically equivalent description of the so called Dirac sea. One focus is here on experimentally controllable effects like adiabatic pair creation and annihilation which can be described with mathematical rigor.

### Ausgewählte Publikationen

- D. Dürr, P. Pickl
*Flux-Across-Surfaces Theorem for a Dirac Particle*

J. Math. Phys. 44, 423 (2003) [arXiv:math-ph/0207010] - P. Pickl
*Generalized eigenfunctions for Dirac operators near criticality*

J. Math. Phys. 48 (2007) [download] - P. Pickl, D. Dürr
*On Adiabatic Pair Creation*

Comm. Math. Phys. 282, 161-198 (2008) [download] - P. Pickl and D. Dürr
*Adiabatic Pair Creation in Heavy Ion and Laser Fields*

EPL, 81 (2008) [arXiv:hep-th/0609200] - P. Pickl
*A simple derivation of mean field limits for quantum systems*

Lett. Math. Phys. 97, 151-164 (2011) [arXiv:0907.4464] - P. Pickl
*Derivation of the Time Dependent Gross Pitaevskii Equation with External Fields*

(2010) [arXiv:1001.4894]