Original paper

Annales Henri Poincaré

, Volume 5, Issue 4, pp 773-808

First online:

Rotating Singular Perturbations of the Laplacian

  • Michele CorreggiAffiliated withInternational School for Advanced Studies, SISSA/ISAS Email author 
  • , Gianfausto Dell’AntonioAffiliated withCentro Linceo Interdisciplinare Email author 

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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 \( \omega \to \infty. \)