On the discrete spectrum of the Schrödinger operator using the 2+1 fermionic trimer on the lattice

Abstract

We consider the three-particle discrete Schr dinger operator H , (K), K T 3 , associated with the three-particle Hamiltonian (two of them are fermions with mass 1 and one of them is arbitrary with mass m = 1/ < 1), interacting via pair of repulsive contact potentials > 0 on a three-dimensional lattice Z 3 . It is proved that there are critical values of mass ratios = 1 and = 2 such that if (0, 1 ), then the operator H , (0) has no eigenvalues. If ( 1 , 2 ), then the operator H , (0) has a unique eigenvalue; if > 2 , then the operator H , (0) has three eigenvalues lying to the right of the essential spectrum for all sufficiently large values of the interaction energy .

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Identifiers

DOI

10.17586/2220-8054-2023-14-5-518-529

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