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arXiv · 0911.5126

On the spectral analysis of many-body systems

Mondher Damak·Vladimir Georgescu
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Abstract

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.

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Mondher Damak, Vladimir Georgescu. 2009-11-26. On the spectral analysis of many-body systems. https://arxiv.org/abs/0911.5126

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