Geodesic
Spectrum of the Three-Particle Schrödinger Difference Operator on a Lattice
Matematičeskie zametki, Tome 71 (2002) no. 5, pp. 686-696 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

For a three-particle operator on a lattice, we study the properties of its spectrum that depend on pairwise interactions and are determined by a parameter characterizing the intensity of interaction. 
@article{MZM_2002_71_5_a4,
     author = {S. N. Lakaev and Zh. I. Abdullaev},
     title = {Spectrum of the {Three-Particle} {Schr\"odinger} {Difference} {Operator} on a {Lattice}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {686--696},
     year = {2002},
     volume = {71},
     number = {5},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2002_71_5_a4/}
}
TY  - JOUR
AU  - S. N. Lakaev
AU  - Zh. I. Abdullaev
TI  - Spectrum of the Three-Particle Schrödinger Difference Operator on a Lattice
JO  - Matematičeskie zametki
PY  - 2002
SP  - 686
EP  - 696
VL  - 71
IS  - 5
UR  - http://geodesic.mathdoc.fr/item/MZM_2002_71_5_a4/
LA  - ru
ID  - MZM_2002_71_5_a4
ER  - 
%0 Journal Article
%A S. N. Lakaev
%A Zh. I. Abdullaev
%T Spectrum of the Three-Particle Schrödinger Difference Operator on a Lattice
%J Matematičeskie zametki
%D 2002
%P 686-696
%V 71
%N 5
%U http://geodesic.mathdoc.fr/item/MZM_2002_71_5_a4/
%G ru
%F MZM_2002_71_5_a4
S. N. Lakaev; Zh. I. Abdullaev. Spectrum of the Three-Particle Schrödinger Difference Operator on a Lattice. Matematičeskie zametki, Tome 71 (2002) no. 5, pp. 686-696. http://geodesic.mathdoc.fr/item/MZM_2002_71_5_a4/

[1] Efimov V. N., “Svyazannye sostoyaniya trekh rezonansno vzaimodeistvuyuschikh chastits”, Yadernaya fizika, 12:5 (1970), 1080–1091

[2] Merkurev S. P., Faddeev L. D., Kvantovaya teoriya rasseyaniya dlya sistem neskolkikh chastits, Nauka, M., 1985

[3] Amado R. D., Noble J. V., “Efimov's effect: a new pathology of three-particle systems, II”, Phys. Rev. D, 5:8 (1971), 1992–2002 | DOI

[4] Yafaev D. R., “K teorii diskretnogo spektra trekhchastichnogo operatora Shrëdingera”, Matem. sb., 94(136):4(8) (1974), 567–593 | MR | Zbl

[5] Ovchinnikov Yu. N., Sigal I. M., “Number of bound states of three-body systems and Efimov's effect”, Ann. Physics, 123 (1989), 274–295 | DOI | MR

[6] Tamura H., “The Efimov effect of three-body Schrödinger operators”, J. Funct. Anal., 95 (1991), 433–459 | DOI | MR | Zbl

[7] Sobolev A. V., “The Efimov Effect. Discrete Spectrum Asymptotics”, Commun. Math. Phys., 156 (1993), 101–126 | DOI | MR | Zbl

[8] Mattis D. C., “The few-body problem on lattice”, Rev. Modern Phys., 58:2 (1986), 361–379 | DOI | MR

[9] Malyshev V. A., Minlos R. A., “Klasternye operatory”, Tr. sem. im. I. G. Petrovskogo, no. 9, Izd-vo Mosk. un-ta, M., 1983, 63–80 | MR | Zbl

[10] Mogilner A. I., “The problem of few quasi-particles in solid state physics”, Applications of Self-Adjoint Extensions in Quantum Physics, Lecture Notes in Phys., 324, eds. P. Exner, P. Seba, Springer-Verlag, Berlin, 1988

[11] Lakaev S. N., “Ob effekte Efimova v sisteme trekh odinakovykh kvantovykh chastits”, Funktsion. analiz i ego prilozh., 27:3 (1993), 15–28 | MR | Zbl

[12] Rid M., Saimon B., Metody sovremennoi matematicheskoi fiziki. T. 4. Analiz operatorov, Mir, M., 1982

[13] Abdullaev Zh. I., Lakaev S. N., “Konechnost diskretnogo spektra trekhchastichnogo operatora Shrëdingera na reshetke”, TMF, 111:1 (1997), 94–108 | MR | Zbl

[14] Yafaev D. R., “O singulyarnom spektre v sisteme trekh chastits”, Matem. sb., 106 (148):4 (8) (1978), 622–640 | MR | Zbl