- 03-352 Michele Correggi, Gianfausto Dell'Antonio
- Rotating Singular Perturbations of the Laplacian
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Jul 28, 03
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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 their unitary semigroups. 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 \( \omega \rightarrow \infty \).