Propagators weakly associated to a family of Hamiltonians and the adiabatic theorem for the Landau Hamiltonian with a time-dependent Aharonov-Bohm flux

Details Propagators weakly associated to a family of Hamiltonians and the adiabatic theorem for the Landau Hamiltonian with a time-dependent Aharonov-Bohm flux Propagators weakly associated to a family of Hamiltonians and the adiabatic theorem for the Landau Hamiltonian with a time-dependent Aharonov-Bohm flux

2005-02-08

arxiv.org/abs/math-ph/0502030v2

Physics

Mathematical Physics

Title and Abstract changed, will appear in Journal of Mathematical Physics

Scientific paper

10.1063/1.1895865

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 adiabatic results do not cover 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.

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