Propagation of singularities in many-body scattering in the presence of bound states

Vasy, András

Vasy, András

Journées équations aux dérivées partielles, (1999), p. 1-20 / Harvested from Numdam

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Résumé

In these lecture notes we describe the propagation of singularities of tempered distributional solutions $u \in 𝒮^{'}$ of $(H - λ) u = 0$ , where $H$ is a many-body hamiltonian $H = Δ + V$ , $Δ \geq 0$ , $V = \sum_{a} V_{a}$ , and $λ$ is not a threshold of $H$ , under the assumption that the inter-particle (e.g. two-body) interactions $V_{a}$ are real-valued polyhomogeneous symbols of order $- 1$ (e.g. Coulomb-type with the singularity at the origin removed). Here the term “singularity” provides a microlocal description of the lack of decay at infinity. Our result is then that the set of singularities of $u$ is a union of maximally extended broken bicharacteristics of $H$ . These are curves in the characteristic variety of $H$ , which can be quite complicated due to the existence of bound states. We use this result to describe the wave front relation of the S-matrices. Here we only present the statement of the results and sketch some of the ideas in proving them, the complete details will appear elsewhere.

Publié le : 1999-01-01

MR 2000j:81284 | 1 citation dans Numdam

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     author = {Vasy, Andr\'as},
     title = {Propagation of singularities in many-body scattering in the presence of bound states},
     journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
     year = {1999},
     pages = {1-20},
     mrnumber = {2000j:81284},
     language = {en},
     url = {http://dml.mathdoc.fr/item/JEDP_1999____A16_0}
}

Vasy, András. Propagation of singularities in many-body scattering in the presence of bound states. Journées équations aux dérivées partielles,  (1999), pp. 1-20. http://gdmltest.u-ga.fr/item/JEDP_1999____A16_0/

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