On the spectral analysis of many-body systems

Mondher Damak (1) , Georgescu Vladimir (2)

1 Université de Sfax - University of Sfax
2 AGM - UMR 8088 - Analyse, Géométrie et Modélisation

We describe the essential spectrum and prove the Mourre estimate for quantum particle systems interacting through k-body forces and creation-annihilation processes which do not preserve the number of particles. For this we compute the ``Hamiltonian algebra'' of the system, i.e. the C*-algebra C generated by the Hamiltonians we want to study, and show that, as in the N-body case, it is graded by a semilattice. Hilbert C*-modules graded by semilattices are involved in the construction of C. For example, if we start with an N-body system whose Hamiltonian algebra is B and then we add field type couplings between subsystems, then the many-body Hamiltonian algebra C is the imprimitivity algebra of a graded Hilbert B-module.

Mots clés: Many-body systems; Spectral analysis; C*-algebras; Essential spectrum; Mourre estimate; Hilbert modules

Domaines: Physique mathématique [math-ph]; Physique mathématique [math-ph]

Mondher Damak, Georgescu Vladimir. On the spectral analysis of many-body systems. 2009. ⟨hal-00436907⟩