Affordable Access

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

Authors
Publication Date
Disciplines
  • Law

Abstract

Propagation of singularities in many-body scattering in the presence of bound states JOURNÉES ÉQUATIONS AUX DÉRIVÉES PARTIELLES ANDRAS VASY Propagation of singularities in many-body scattering in the presence of bound states Journées Équations aux dérivées partielles (1999), p. 1-20. <http://www.numdam.org/item?id=JEDP_1999____A16_0> © Journées Équations aux dérivées partielles, 1999, tous droits réservés. L’accès aux archives de la revue « Journées Équations aux dérivées partielles » (http://www. math.sciences.univ-nantes.fr/edpa/), implique l’accord avec les conditions générales d’utili- sation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression sys- tématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fi- chier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/ Journees Equations aux derivees partielles Saint-Jean-de-Monts, 31 mai-4 juin 1999 GDR 1151 (CNRS) Propagation of singularities in many-body scattering in the presence of bound states Andras Vasy Abstract In these lecture notes we describe the propagation of singularities of tem- pered distributional solutions u E S ' of (H—\)u = 0, where H is a many-body Hamiltonian . H ' = A + V , A ^ O , y = V^^Va, and A is not a threshold of jy, under the assumption that the inter-particle (e.g. two-body) interactions Va are real-valued polyhomogeneous symbols of order —1 (e.g. Coulomb-type with the singularity at the origin removed). Here the term 'singularity? pro- vides 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 Jf, 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

There are no comments yet on this publication. Be the first to share your thoughts.