The Scattering Matrix and Associated Formulas in Hamiltonian Mechanics |
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Authors: | Vladimir Buslaev Alexander Pushnitski |
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Institution: | (1) Department of Mathematics, University of Kentucky, Lexington, KY 40506-0027, USA;(2) Department of Mathematics, The University of Toledo, Toledo, OH, 43606-3390, U.S.A |
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Abstract: | We prove two new identities in scattering theory in Hamiltonian mechanics and discuss the analogy between these identities
and their counterparts in quantum scattering theory. These identities involve the Poincaré scattering map, which is analogous
to the scattering matrix. The first of our identities states that the Calabi invariant of the Poincaré scattering map can
be expressed as the regularised phase space volume. This is analogous to the Birman-Krein formula. The second identity relates
the Poincaré scattering map to the total time delay and is analogous to the Eisenbud-Wigner formula. |
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