Rotating Singular Perturbations of the Laplacian

Details Rotating Singular Perturbations of the Laplacian Rotating Singular Perturbations of the Laplacian

2003-07-28

arxiv.org/abs/math-ph/0307056v2

Ann. Henri Poincare 5 (2004) 773-808

Physics

Mathematical Physics

Minor changes, to appear in Ann. H. Poincare', 35 pages, LaTeX

Scientific paper

10.1007/s00023-004-0182-8

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 \to \infty).

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