Geodesic
Investigation of the spectrum of a model operator in a Fock space
Teoretičeskaâ i matematičeskaâ fizika, Tome 161 (2009) no. 2, pp. 164-175 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We consider a model operator $H$ corresponding to a quantum system with a nonconserved finite number of particles on a lattice. Based on an analysis of the spectrum of the channel operators, we describe the position of the essential spectrum of $H$. We obtain a Faddeev-type equation for the eigenvectors of $H$.
Keywords: model operator, system with nonconserved finite number of particles, Faddeev equation, essential spectrum, channel operator. 
@article{TMF_2009_161_2_a2,
     author = {T. H. Rasulov},
     title = {Investigation of the~spectrum of a~model operator in {a~Fock} space},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {164--175},
     year = {2009},
     volume = {161},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2009_161_2_a2/}
}
TY  - JOUR
AU  - T. H. Rasulov
TI  - Investigation of the spectrum of a model operator in a Fock space
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2009
SP  - 164
EP  - 175
VL  - 161
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TMF_2009_161_2_a2/
LA  - ru
ID  - TMF_2009_161_2_a2
ER  - 
%0 Journal Article
%A T. H. Rasulov
%T Investigation of the spectrum of a model operator in a Fock space
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2009
%P 164-175
%V 161
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_2009_161_2_a2/
%G ru
%F TMF_2009_161_2_a2
T. H. Rasulov. Investigation of the spectrum of a model operator in a Fock space. Teoretičeskaâ i matematičeskaâ fizika, Tome 161 (2009) no. 2, pp. 164-175. http://geodesic.mathdoc.fr/item/TMF_2009_161_2_a2/

[1] G. M. Zhislin, Trudy MMO, 9, 1960, 81–120 | MR | Zbl

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

[3] S. N. Lakaev, M. E. Muminov, TMF, 135:3 (2003), 478–503 | DOI | MR | Zbl

[4] M. E. Muminov, TMF, 148:3 (2006), 428–443 | DOI | MR | Zbl

[5] R. A. Minlos, H. Spohn, “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. Ser. 2, 177, ed. R. L. Dobrushin, AMS, Providence, RI, 1996, 159–193 | MR | Zbl

[6] Yu. V. Zhukov, R. A. Minlos, TMF, 103:1 (1995), 63–81 | DOI | MR | Zbl

[7] G. R. Edgorov, M. E. Muminov, TMF, 144:3 (2005), 544–554 | DOI | MR

[8] T. Kh. Rasulov, Matem. zametki, 83:1 (2008), 86–94 | DOI | MR | Zbl

[9] M. I. Muminov, T. H. Rasulov, The Faddeev Equation and Essential Spectrum of a Hamiltonian in Fock Space, ICTP Preprint IC/2008/027

[10] T. Kh. Rasulov, Izv. vuzov. Matem., 2008, no. 12, 59–69 | DOI | Zbl

[11] S. N. Lakaev, T. Kh. Rasulov, Matem. zametki, 73:4 (2003), 556–564 | DOI | MR | Zbl

[12] S. N. Lakaev, T. Kh. Rasulov, Funkts. analiz i ego pril., 37:1 (2003), 81–84 | DOI | MR | Zbl

[13] S. Albeverio, S. N. Lakaev, T. H. Rasulov, J. Stat. Phys., 127:2 (2007), 191–220 | DOI | MR | Zbl

[14] T. Kh. Rasulov, TMF, 152:3 (2007), 518–527 | DOI | MR | Zbl