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On the spectral properties of Hamiltonians without conservation of the particle number. (English) Zbl 1059.81060
Summary: We consider quantum systems with variable but finite number of particles. For such systems we develop geometric and commutator techniques. We use these techniques to find the location of the spectrum, to prove absence of singular continuous spectrum, and identify accumulation points of the discrete spectrum. The fact that the total number of particles is bounded allows us to give relatively elementary proofs of these basic results for an important class of many-body systems with nonconserved number of particles.

MSC:
81Q10Selfadjoint operator theory in quantum theory, including spectral analysis
47N50Applications of operator theory in quantum physics
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