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Cubo (Temuco)

versión On-line ISSN 0719-0646

Cubo vol.14 no.2 Temuco  2012

http://dx.doi.org/10.4067/S0719-06462012000200006 

CUBO A Mathematical Journal Vol.14, No 02, (91-109). June 2012

Texto completo disponíble en formato PDF

Higher order terms for the quantum evolution of a Wick observable within the Hepp method

 

Sébastien Breteaux

IRMAR, UMR-CNRS 6625, Universite de Rennes 1, campus de Beaulieu, 35042 Rennes Cedex, France.

ENS de Cachan, Antenne de Bretagne, Campus de Ker Lann, Av. R. Schuman,35170 Bruz, France. email: sebastien.breteaux@ens-cachan. org


ABSTRACT

The Hepp method is the coherent state approach to the mean field dynamics for bosons or to the semiclassical propagation. A key point is the asymptotic evolution of Wick observables under the evolution given by a time-dependent quadratic Hamiltonian. This article provides a complete expansion with respect to the small parameter which makes sense within the infinite-dimensional setting and fits with finite-dimensional formulae.

Keywords and Phrases: Mean field limit, semiclassical limit, coherent states, squeezed states


RESUMEN

El metodo de Hepp describe en terminos de estados coherentes la dinamica en campo medio de bosones o la propagación semiclasica. Un punto clave es la evolución asintótica de observables de Wick bajo la evolucion dada por un Hamiltoniano cuadratico dependiente del tiempo. Este artículo proporciona una expansion completa con respecto al parámetro pequeno valido en dimension infinita y que corresponde a formulas en dimension finita conocidas.

 


 

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Received: October 2011. Revised: November 2011.