Geodesic
The Faddeev equation and the location of the essential spectrum of a model operator for several particles
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2008), pp. 59-69.

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In this paper we consider a model operator which acts in a three-particle cut subspace of the Fock space. We describe “two-particle” and “three-particle” branches of the essential spectrum and obtain an analog of the Faddeev equation for the eigenfunctions of this operator.
Keywords: Fock space, model operator, essential spectrum, Faddeev equation. 
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T. H. Rasulov. The Faddeev equation and the location of the essential spectrum of a model operator for several particles. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2008), pp. 59-69. http://geodesic.mathdoc.fr/item/IVM_2008_12_a7/

[1] Mattis D., “The few-body problem on a lattice”, Rev. Modern Phys., 58 (1986), 361–379 | DOI | MR

[2] Fridrikhs K. O., Vozmuschenie spektra operatorov v gilbertovom prostranstve, Mir, M., 1969, 232 pp. | MR

[3] Malyshev V. A., Minlos R. A., “Klasternye operatory”, Tr. semin. im. I. G. Petrovskogo, 9, 1983, 63–80 | MR | Zbl

[4] Minlos R. A., Spohn H., “The three-body problem in radioactive decay: the case of one atom and at most two photons”, Topics in Statistical and Theoretical Physics, Amer. Math. Soc. Transl. (2), 177, Amer. Math. Soc., Providence (R.I.), 1996, 159–193 | MR | Zbl

[5] Zhukov Yu. V., Minlos R. A., “Spektr i rasseyanie v modeli “spin–bozon” s ne bolee chem tremya fotonami”, Teor. i matem. fizika, 103:1 (1995), 63–81 | MR | Zbl

[6] Lakaev S. N., Rasulov T. Kh., “Model v teorii vozmuschenii suschestvennogo spektra mnogochastichnykh operatorov”, Matem. zametki, 73:4 (2003), 556–564 | MR | Zbl

[7] Lakaev S. N., Rasulov T. Kh., “Ob effekte Efimova v modeli teorii vozmuschenii suschestvennogo spektra”, Funkts. analiz i ego prilozh., 37:1 (2003), 81–84 | MR | Zbl

[8] Albeverio S., Lakaev S. N., Rasulov T. H., “On the spectrum of an Hamiltonian in Fock space. Discrete spectrum asymptotics”, J. Stat. Phys., 1 (2006) | MR

[9] Ëdgorov G. R., Muminov M. E., “O spektre odnogo modelnogo operatora v teorii vozmuscheniya suschestvennogo spektra”, Teor. i matem. fizika, 144:3 (2005), 544–554 | MR

[10] Merkurev S. P., Faddeev L. D., Kvantovaya teoriya rasseyaniya dlya sistem neskolkikh chastits, Nauka, L., 1989, 400 pp. | MR

[11] Rid M., Saimon B., Metody sovremennoi matematicheskoi fiziki. T. 4. Analiz operatorov, Mir, M., 1982, 430 pp. | MR