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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik

MP 5: Quantenmechanik

MP 5.2: Talk

Tuesday, February 28, 2012, 15:25–15:50, ZHG 003

Magnetic Symmetries and Applications to Solid State Physics — Giuseppe De Nittis¹ and •Max Lein² — ¹LAGA, Institut Galilée, Université Paris 13, 99, avenue J.-B. Clément, F-93430 Villetaneuse, France. — ²Universität Tübingen, Mathematisches Institut, Auf der Morgenstelle 10, 72076 Tübingen

In a recent publication (J. Math. Phys. 52, 112103 (2011)), magnetic symmetries were the crucial ingredient in showing the existence of an exponentially localized Wannier basis in the presence of magnetic fields.

The hamiltonian H = P² + V has symmetry U if [H,U] = 0 where U is a unitary or anti-unitary operator. For a wide range of symmetries, we can systematically associate a magnetic symmetry U^A = λ^A U which commutes with H^A = (P−A)² + V, i.e. [H^A,U^A] = 0 holds whenever [H,U] = 0. Here, λ^A is a phase factor that can be written as the exponential of a path integral involving the vector potential A. In particular, we can “magnetize” Galilean symmetries, including magnetic rotations and magnetic time-reversal. We reckon that magnetic symmetries may be a useful tool in other applications.