A1 Refereed original research article in a scientific journal

Geometry of adiabatic Hamiltonians for two-level quantum systems



Authors: Lehto JMS, Suominen KA

Publisher: IOP Publishing LTD

Publication year: 2015

Journal: Journal of Physics A: Mathematical and Theoretical

Journal name in source: JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL

Journal acronym: J Phys A-Math Theor

Article number: ARTN 235301

Volume: 48

Issue: 23

Number of pages: 13

ISSN: 1751-8113

DOI: https://doi.org/10.1088/1751-8113/48/23/235301


Abstract

We present the formulation of the problem of the coherent dynamics of quantum mechanical two-level systems in the adiabatic region in terms of the differential geometry of plane curves. We show that there is a natural plane curve corresponding to the Hamiltonian of the system for which the geometrical quantities have a simple physical interpretation. In particular, the curvature of the curve has the role of the nonadiabatic coupling.




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