Rostock 2019 – wissenschaftliches Programm

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MO: Fachverband Molekülphysik

MO 10: Posters 1: Cold Molecules, High Resolution Spectroscopy, and Theory

MO 10.19: Poster

Dienstag, 12. März 2019, 16:30–18:30, S Foyer LLM

Optimized Sampling of Mixed-State Observables — •Marec W. Heger, Christiane P. Koch, and Daniel M. Reich — Theoretische Physik, Universität Kassel, Heinrich Plett-Straße 40, 34132 Kassel, Germany

Quantum dynamical simulations of statistical ensembles pose a significant computational challenge due to the fact that mixed states need to be represented by a density matrix instead of a wave function. If the underlying dynamics are fully unitary, for example in coherent control at finite temperatures, one approach to approximate time-dependent observables in this context is to sample the density matrix by solving the Schrödinger equation for a set of wave functions with randomized phases.

We present an in-depth analysis of the average performance for the random-phase wave functions and compare them to deterministic sampling of the energetically lowest-lying eigenstates. In particular, the performance crossing point between these two approaches allows an estimation of the more efficient sampling scheme for an average observable. Moreover, we prove that minimization of the worst-case error among arbitrary observables is uniquely attained by eigenstate-based sampling. Finally, we point out how the structure of low-rank observables can be exploited to further improve eigenstate-based sampling schemes.