Abstract
We consider a two-particle Hamiltonian on the d-dimensional lattice ℤd. We find a sufficient condition for the positivity of a family of operators h(k) appearing after the “separation of the center of mass” of a system of two particles depending on the values of the total quasimomentum k ∈ Td (where Td is a d-dimensional torus). We use the obtained result to show that the operator h(k) has positive eigenvalues for nonzero k ∈ Td.
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