Affiliation:
1. DiSAT, Sezione di Matematica, Università dell’Insubria, via Valleggio 11, I-22100 Como, Italy
2. Dipartimento di Matematica e Fisica, Università degli Studi Roma Tre, L.go S.L. Murialdo 1, I-00146 Roma, Italy
Abstract
We consider the quantum evolution [Formula: see text] of a Gaussian coherent state [Formula: see text] localized close to the classical state [Formula: see text], where [Formula: see text] denotes a self-adjoint realization of the formal Hamiltonian [Formula: see text], with [Formula: see text] the derivative of Dirac’s delta distribution at [Formula: see text] and [Formula: see text] a real parameter. We show that in the semi-classical limit such a quantum evolution can be approximated (with respect to the [Formula: see text]-norm, uniformly for any [Formula: see text] away from the collision time) by [Formula: see text], where [Formula: see text], [Formula: see text] and [Formula: see text] is a suitable self-adjoint extension of the restriction to [Formula: see text], [Formula: see text], of ([Formula: see text] times) the generator of the free classical dynamics. While the operator [Formula: see text] here utilized is similar to the one appearing in our previous work [C. Cacciapuoti, D. Fermi and A. Posilicano, The semi-classical limit with a delta potential, Ann. Mat. Pura Appl. 200 (2021) 453–489], in the present case the approximation gives a smaller error: it is of order [Formula: see text], [Formula: see text], whereas it turns out to be of order [Formula: see text], [Formula: see text], for the delta potential. We also provide similar approximation results for both the wave and scattering operators.
Publisher
World Scientific Pub Co Pte Ltd
Subject
Mathematical Physics,Statistical and Nonlinear Physics
Cited by
1 articles.
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