Berlin 2015 – wissenschaftliches Programm

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TUT: Tutorials

TUT 3: Tutorial: Nonequilibrium Renormalization Group Methods (TT)

TUT 3.1: Tutorium

Sonntag, 15. März 2015, 16:05–16:45, H 0110

From Lunar Motion to Real Time Evolution of Quantum Many-Body Systems — •Stefan Kehrein — Institute for Theoretical Physics, Georg-August-Universität Göttingen, 37077 Göttingen, Germany

While studying the real time evolution of quantum many-body systems is a fairly new topic in physics, the real time evolution of classical systems is an old one. In fact, this topic goes back to the very beginning of classical mechanics, namely its application to celestial mechanics. One of the important lessons learned in this classical setting is that naive application of perturbation theory can lead to secular terms in time which quickly invalidate the expansion. This observation gave rise to the development of canonical perturbation theory with much improved convergence properties.

In this lecture I will show how similar progress can be made for the calculation of the real time evolution of quantum systems by using unitary perturbation theory [1,2,3]. In addition, this approach permits one to deal with models with a nontrivial renormalization flow and to see how this affects the real time dynamics away from equilibrium.

[1] A. Hackl and S. Kehrein, Phys. Rev. B 78, 092303 (2008)

[2] A. Hackl and S. Kehrein, J. Phys. C 21, 015601 (2009)

[3] F. Essler, S. Kehrein, S. Manmana, and N. Robinson,

Phys. Rev. B 89, 165104 (2014)