Universality of the discrete spectrum asymptotics of the three-particle Schrödinger operator on a lattice

Abstract

In the present paper, we consider the Hamiltonian H(K), K T 3 := (-; ] 3 of a system of three arbitrary quantum mechanical particles moving on the three-dimensional lattice and interacting via zero range potentials. We find a finite set T 3 such that for all values of the total quasi-momentum K the operator H(K) has infinitely many negative eigenvalues accumulating at zero. It is found that for every K , the number N (K; z) of eigenvalues of H(K) lying on the left of z, z < 0, satisfies the asymptotic relation lim z-0 N (K; z)| log |z|| -1 = U 0 with 0 < U 0 < , independently on the cardinality of .

Topics

Identifiers

DOI

10.17586/2220-8054-2015-6-2-280-293

Citations and references