Real time evolution of quantum many-particle systems: The flow equation approach
Nano-Physics Seminar by Prof. Dr. Stefan Kehrein, Arnold Sommerfeld Center for Theoretical Physics, Universität München.
The analytical evaluation of the real time evolution of a quantum many-particle system far out of equilibrium poses a challenging problem. Without prior knowledge about the long-time behavior, perturbative calculations suffer from spurious terms (secular terms), which grow in an uncontrolled way for large times. The flow equation approach (infinitesimal unitary transformation approach) can overcome some of these problems by studying the real time evolution of observables in the Heisenberg picture in a suitable energy-diagonal basis. This basis is obtained by an approximate renormalization group-like diagonalization of the Hamiltonian. In this talk I will review the method and show its application to various quantum many-particle problems.