Geodesic
Essential spectrum of three-particle discrete operator corresponding to a system of three fermions on a lattice
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2017), pp. 76-88

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We consider a family of three-particle discrete Shrödinger operators $H_\mu(K)$, associated to a system of Hamiltonian of three identical particles (fermions) with pairwise two-particles interactions on neighboring junctions on $d$-dimensional lattice $\mathbb{Z}^{d}$. The location and structure of the essential spectrum of the operator $H_\mu(K)$ is described for all three-particles quasi-momentum $K\in \mathbb{T}^d$ and interaction energy $\mu>0$.
Keywords: spectral properties, three-particle Shrödinger operators, Hamiltonian of systems of three fermions, essential spectrum, eigenvalue. 
@article{IVM_2017_9_a7,
     author = {A. M. Khalkhuzhaev},
     title = {Essential spectrum of three-particle discrete operator corresponding to a system of three fermions on a lattice},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {76--88},
     publisher = {mathdoc},
     number = {9},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2017_9_a7/}
}
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A. M. Khalkhuzhaev. Essential spectrum of three-particle discrete operator corresponding to a system of three fermions on a lattice. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2017), pp. 76-88. http://geodesic.mathdoc.fr/item/IVM_2017_9_a7/