Perturbative Analysis of Possible Failures in the Traditional Adiabatic Conditions.pdfVIP

Perturbative Analysis of Possible Failures in the 5 0 Traditional Adiabatic Conditions 0 2 v 1 T. V´ertesi1 and R. Englman2 o Section of Theoretical Physics, Institute of Nuclear Research N of the Hungarian Academy of Sciences, Debrecen, Hungary 5 2 Soreq NRC, Yavne 81800, Israel 1 e-mails:tvertesi@dtp.atomki.hu; englman@vms.huji.ac.il 1 v February 1, 2008 1 4 1 Keywords: Adiabatic Approximation, Adiabatic Condition, Berry phase. 1 1 Abstract 5 0 Recently, Marzlin and Sanders (2004) demonstrated an inconsis- / tency when the adiabatic approximation was applied to specific, ”in- h p verse” time-evolving systems. Following that, Tong et al. (2005) t- showed that the widely used traditional adiabatic conditions are in- n sufficient to guarantee the validity of the adiabatic approximation for a this class of systems. In this article we explore the origin of these obser- u q vations by a perturbative approach and find that in first order approxi- : mation certain nonzero terms appear in the solution which gives rise to v the breakdown of the adiabatic approximation (despite the fact that i X the traditional adiabatic conditions are satisfied). We argue that in r this case the Hamiltonian of Marzlin and Sanders’ inverse time evolv- a ing system cannot b