, Volume 5, Issue 4, pp 773-808

Rotating Singular Perturbations of the Laplacian

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Abstract.

We study a system of a quantum particle interacting with a singular time-dependent uniformly rotating potential in 2 and 3 dimensions: in particular we consider an interaction with support on a point (rotating point interaction) and on a set of codimension 1 (rotating blade). We prove the existence of the Hamiltonians of such systems as suitable self-adjoint operators and we give an explicit expression for the unitary dynamics. Moreover we analyze the asymptotic limit of large angular velocity and we prove strong convergence of the time-dependent propagator to some one-parameter unitary group as \( \omega \to \infty. \)

Communicated by Gian Michele Graf
Submitted 07/10/03, accepted 09/12/03