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

Sébastien Breteaux (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

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 ε > 0 which makes sense within the infinite-dimensional setting and fits with finite-dimensional formulae.

Mots clés: mean field limit; semiclassical limit; coherent states; squeezed states

Domaines: Physique mathématique [math-ph]

Sébastien Breteaux. Higher order terms for the quantum evolution of a Wick observable within the Hepp method. Cubo, a Mathematical Journal, 2012, 14 (2), pp.91-123. ⟨10.4067/S0719-06462012000200006⟩. ⟨hal-00567206⟩