Essential spectra and exponential estimates of eigenfunctions of lattice operators of quantum mechanics

This paper is devoted to estimates of the exponential decay of eigenfunctions of difference operators on the lattice which are discrete analogs of the Schrödinger, Dirac and square-root Klein-Gordon operators. Our investigation of the essential spectra and the exponential decay of eigenfunctions of the discrete spectra is based on the calculus of pseudodifference operators (i.e., pseudodifferential operators on the group with analytic symbols), and the limit operators method. We obtain a description of the location of the essential spectra and estimates of the eigenfunctions of the discrete spectra of the main lattice operators of quantum mechanics, namely: matrix Schrödinger operators on , Dirac operators on and square root Klein-Gordon operators on .