Regensburg 2019 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 21: Statistical Physics (General) II

DY 21.4: Talk

Tuesday, April 2, 2019, 14:45–15:00, H6

Mori-Zwanzig formalism for systems with time-dependent Hamiltonians* — •Michael te Vrugt and Raphael Wittkowski — Institut für Theoretische Physik, Westfälische Wilhelms-Universität Münster, D-48149 Münster, Germany

The Mori-Zwanzig projection operator formalism is a powerful method for the derivation of mesoscopic and macroscopic theories based on known microscopic equations of motion. It has applications in a large number of areas including dynamical density functional theory and spin relaxation theory. In its present form, however, the formalism cannot be directly applied to systems with time-dependent Hamiltonians. Such systems are relevant in a lot of scenarios like, for example, NMR or driven soft matter.

We derive a generalization of the present Mori-Zwanzig formalism that is able to treat time-dependent Hamiltonians in both classical and quantum systems. Moreover, we develop a variety of approximation techniques that enhance the practical applicability of our formalism. Our method is demonstrated for the important case of spin relaxation in a time-dependent external magnetic field. The Bloch equations are derived together with microscopic expressions for the relaxation times.
*Funded by the Deutsche Forschungsgemeinschaft (DFG) – WI 4170/3-1