Geodesic
Bound states of two-particle cluster operator
Teoretičeskaâ i matematičeskaâ fizika, Tome 79 (1989) no. 2, pp. 163-179
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Spectrum of the two-particle cluster operator $$ (Af)(T)=\sum_{T'}[\omega(t_1-t_1',t_2-t_2')+\omega(t_1-t_2',t_2-t_1')+\beta S(T,T')]f(T'), $$ $T=(t_1,t_2)$, $T'=(t_1',t_2')$, $t_i,t_i'\in Z^\nu$, $i=1,2$, $f\in l_2(C^2_{Z^\nu})$, $C^2_{Z^\nu}$ is the set of all two-element subsets of the lattice $Z^\nu$ and $\beta$ is a small parameter, is studied. For the functions $\omega$ and $S$ of the general form it is shown that the operator $A$ in the dimensions $\nu\geqslant3$ possesses only the continuous two-particle spectrum while in the dimensions $\nu=1,2$ it may have, in the general case, branches of bound states in some regions of quasimomentum values. The location of these regions is investigated in detail and it is found, under which conditions on the functions $\omega$ and $S$ the branches of bound states really do appear. 
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     author = {Sh. S. Mamatov and R. A. Minlos},
     title = {Bound states of~two-particle cluster operator},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {163--179},
     year = {1989},
     volume = {79},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1989_79_2_a0/}
}
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Sh. S. Mamatov; R. A. Minlos. Bound states of two-particle cluster operator. Teoretičeskaâ i matematičeskaâ fizika, Tome 79 (1989) no. 2, pp. 163-179. http://geodesic.mathdoc.fr/item/TMF_1989_79_2_a0/

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