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A non-commutative Landau-Zener formula

✍ Scribed by Clotilde Fermanian Kammerer

Publisher
John Wiley and Sons
Year
2004
Tongue
English
Weight
337 KB
Volume
271
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

We study semi‐classical measures of families of solutions to a 2 × 2 Dirac system with 0 mass, which presents bands crossing. We focus on constant electro‐magnetic fields. The fact that these fields are orthogonal or not leads to different geometric situations. In the first case, one reduces to some well‐understood model problem. For studying the second case, we introduce some two‐scale semi‐classical measures associated with symplectic submanifold. These measures are operator‐valued measures and the transfer of energy at the crossing is described by a non‐commutative Landau‐Zener formula for these measures. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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