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Propagators weakly associated to a family of Hamiltonians and the adiabatic theorem for the Landau Hamiltonian
 

Summary: Propagators weakly associated to a family of Hamiltonians
and the adiabatic theorem for the Landau Hamiltonian
with a time-dependent Aharonov­Bohm flux
J. Asch
Centre de Physique Théorique, CNRS, Luminy, Case 907, Marseille Cedex 9, France and
CPT-PhyMat, Université du Sud Toulon-Var, BP 20132, F-83957 La Garde
Cedex, France
I. Hradecký and P. Sovícek
Department of Mathematics, Faculty of Nuclear Science, Czech Technical University,
Trojanova 13, 120 00 Prague, Czech Republic
Received 7 February 2005; accepted 24 February 2005; published online 14 April 2005
We study the dynamics of a quantum particle moving in a plane under the influence
of a constant magnetic field and driven by a slowly time-dependent singular flux
tube through a puncture. The known standard adiabatic results do not cover directly
these models as the Hamiltonian has time-dependent domain. We give a meaning to
the propagator and prove an adiabatic theorem. To this end we introduce and
develop the new notion of a propagator weakly associated to a time-dependent
Hamiltonian. © 2005 American Institute of Physics. DOI: 10.1063/1.1895865
I. INTRODUCTION
The model under consideration originates from Laughlin's12

  

Source: Asch, Joachim - Centre De Physique Theorique, Campus de Luminy, Case 907

 

Collections: Mathematics