Eur. Phys. J. B (2013) 86: 220
https://doi.org/10.1140/epjb/e2013-31042-4

Regular Article

Controlled dynamics on energy landscapes

¹ Institut für Physik, Technische Universität Chemnitz, 09107 Chemnitz, Germany
² Max-Planck-Institut für Festkörperforschung, Heisenbergstr. 1, 70569 Stuttgart, Germany

^a e-mail: hoffmann@physik.tu-chemnitz.de

Received: 14 November 2012
Received in final form: 25 January 2013
Published online: 16 May 2013

Abstract

In systems with complex multi-minima energy landscapes, it is often not only the global minimum which is of great importance. For example, in materials science, metastable compounds corresponding to local minima on the landscape play a crucial role in many technological applications. In order to reach such modifications, both in computational and real world situations, it is necessary to optimally control the dynamics of the system on the landscape. We present a general method, how to design optimal temperature schedules for reaching particular basins on a complex landscape, by constructing a coarse-grained transition probability matrix from stochastic global landscape explorations, and subsequently using optimal control techniques on the Master equation describing the dynamics on the simplified energy landscape. As a demonstration example, the landscape of MgF₂ is considered.