Scattering problem for local perturbations of the free quantum gas

Kondratiev Y, Konstantinov AY, Röckner M, Shchepan'uk GV (1999)
COMMUNICATIONS IN MATHEMATICAL PHYSICS 203(2): 421-444.

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Zeitschriftenaufsatz | Veröffentlicht | Englisch
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Abstract / Bemerkung
Scattering theory for perturbations of the intrinsic Dirichlet (Laplace-Beltrami) operator H-0 = - div(Gamma) del(Gamma) on L-2(Gamma, pi(z)) i. e. the space of pi(z)-square integrable functions on the configuration space Gamma over R-d, is studied. Here pi(z) denotes Poisson measure with intensity z. We show that for an arbitrary regular non-zero potential V the standard wave operators W+/-(H-0, H-0 + V) do not exist, and propose to consider Dirichlet operators of perturbed Poisson measures instead of potential perturbations of the Hamiltonian H-0. As case studies, cylindric smooth densities and finite volume Gibbs perturbations of the Poisson measure are considered. In these cases the existence of the corresponding wave operators is proved.
Erscheinungsjahr
Zeitschriftentitel
COMMUNICATIONS IN MATHEMATICAL PHYSICS
Band
203
Ausgabe
2
Seite(n)
421-444
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Kondratiev Y, Konstantinov AY, Röckner M, Shchepan'uk GV. Scattering problem for local perturbations of the free quantum gas. COMMUNICATIONS IN MATHEMATICAL PHYSICS. 1999;203(2):421-444.
Kondratiev, Y., Konstantinov, A. Y., Röckner, M., & Shchepan'uk, G. V. (1999). Scattering problem for local perturbations of the free quantum gas. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 203(2), 421-444. doi:10.1007/s002200050619
Kondratiev, Y., Konstantinov, A. Y., Röckner, M., and Shchepan'uk, G. V. (1999). Scattering problem for local perturbations of the free quantum gas. COMMUNICATIONS IN MATHEMATICAL PHYSICS 203, 421-444.
Kondratiev, Y., et al., 1999. Scattering problem for local perturbations of the free quantum gas. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 203(2), p 421-444.
Y. Kondratiev, et al., “Scattering problem for local perturbations of the free quantum gas”, COMMUNICATIONS IN MATHEMATICAL PHYSICS, vol. 203, 1999, pp. 421-444.
Kondratiev, Y., Konstantinov, A.Y., Röckner, M., Shchepan'uk, G.V.: Scattering problem for local perturbations of the free quantum gas. COMMUNICATIONS IN MATHEMATICAL PHYSICS. 203, 421-444 (1999).
Kondratiev, Yuri, Konstantinov, AY, Röckner, Michael, and Shchepan'uk, GV. “Scattering problem for local perturbations of the free quantum gas”. COMMUNICATIONS IN MATHEMATICAL PHYSICS 203.2 (1999): 421-444.