2003/07/31 by Michele Correggi, Gianfausto Dell'Antonio, Gianfausto Dell’Antonio
Mathematics · Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics #math-ph #math.MP #quant-ph
paper · pdf · doi:10.1007/s00023-004-0182-8
published as Ann. Henri Poincare 5 (2004) 773-808 · Minor changes, to appear in Ann. H. Poincare', 35 pages, LaTeX
arxiv created 2004/04/29 · openalex publication_date 2004/08/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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 (ω→ ∞).