We consider a non-relativistic quantum system consisting of K heavy and N light particles in dimension three, where each heavy particle interacts with the light ones via a two-body potential αV. No interaction is assumed among particles of the same kind. Choosing an initial state in a product form and assuming α sufficiently small we characterize the asymptotic dynamics of the system in the limit of small mass ratio, with an explicit control of the error. In the case K = 1 the result is extended to arbitrary α. The proof relies on a perturbative analysis and exploits a generalized version of the standard dispersive estimates for the Schrödinger group. Exploiting the asymptotic formula, an application to the problem of the decoherence effect produced on a heavy particle by the interaction with the light ones is also outlined.

On the asymptotic dynamics of a quantum system composed by heavy and light particles / R., Adami; Figari, Rodolfo; D., Finco; A., Teta. - In: COMMUNICATIONS IN MATHEMATICAL PHYSICS. - ISSN 0010-3616. - STAMPA. - 268:(2006), pp. 819-852. [10.1007/s00220-006-0115-0]

On the asymptotic dynamics of a quantum system composed by heavy and light particles

FIGARI, RODOLFO;
2006

Abstract

We consider a non-relativistic quantum system consisting of K heavy and N light particles in dimension three, where each heavy particle interacts with the light ones via a two-body potential αV. No interaction is assumed among particles of the same kind. Choosing an initial state in a product form and assuming α sufficiently small we characterize the asymptotic dynamics of the system in the limit of small mass ratio, with an explicit control of the error. In the case K = 1 the result is extended to arbitrary α. The proof relies on a perturbative analysis and exploits a generalized version of the standard dispersive estimates for the Schrödinger group. Exploiting the asymptotic formula, an application to the problem of the decoherence effect produced on a heavy particle by the interaction with the light ones is also outlined.
2006
On the asymptotic dynamics of a quantum system composed by heavy and light particles / R., Adami; Figari, Rodolfo; D., Finco; A., Teta. - In: COMMUNICATIONS IN MATHEMATICAL PHYSICS. - ISSN 0010-3616. - STAMPA. - 268:(2006), pp. 819-852. [10.1007/s00220-006-0115-0]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11588/325634
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