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An Isaac Newton Institute Workshop

Effective Computational Methods for Highly Oscillatory Problems: The Interplay between Mathematical Theory and Applications

The Magnus expansion in the adiabatic picture

Author: Fernando Casas (Universitat Jaume I)

Abstract

In this talk we review the main aspects of the Magnus expansion for treating time-dependent systems evolving in a near-adiabatic regime. We discuss its applicability and the convergence domain. We will show, in particular, how this procedure alllows us to obtain very accurate approximations to the transition probability for time-dependent two-state quantum systems even far from the adiabatic limit.