Abstract:
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.
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