Sigal, I. M.; Soffer, A.; Zielinski, L. On the spectral properties of Hamiltonians without conservation of the particle number. (English) Zbl 1059.81060 J. Math. Phys. 43, No. 4, 1844-1855 (2002). 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. Cited in 7 Documents MSC: 81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis 47N50 Applications of operator theory in the physical sciences PDFBibTeX XMLCite \textit{I. M. Sigal} et al., J. Math. Phys. 43, No. 4, 1844--1855 (2002; Zbl 1059.81060) Full Text: DOI Link References: [1] DOI: 10.1007/BF01872776 · Zbl 0831.47048 [2] DOI: 10.1007/BF01942331 · Zbl 0489.47010 [3] Perry P., Ann. Math. 114 pp 391– (1981) · Zbl 0477.35069 [4] DOI: 10.1215/S0012-7094-82-04947-X · Zbl 0514.35025 [5] Hunziker W., Commun. Partial Differ. Equ. 24 pp 2279– (1999) · Zbl 0944.35014 [6] Huebner M., Ann. I.H.P. Phys. Theor. 62 pp 289– (1995) [7] Derezinski J., Rev. Math. Phys. 11 pp 383– (1999) · Zbl 1044.81556 [8] Gerard C., Rev. Math. Phys. pp 383– (1999) [9] Bach V., Commun. Math. Phys. 207 pp 557– (1999) · Zbl 0962.81011 [10] Griesemer M., Ann. I.H.P. Phys. Theor. 69 pp 135– (1998) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.