Spectral properties of two particle Hamiltonian on one-dimensional lattice

We consider a system of two arbitrary quantum particles on a one-dimensional lattice with special dispersion functions (describing site-to-site particle transport), where the particles interact by a chosen attraction potential. We study how the number of eigenvalues of operator family () depends on the particle interaction energy and the total quasimomentum T (where T is a one-dimensional torus). Subject to the particle interaction energy, we obtain conditions for existence of multiple eigenvalues below the essential spectrum of operator ().

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