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

Vladimir S Rabinovich, Steffen Roch
2009 Journal of Physics A: Mathematical and Theoretical  
This paper is devoted to estimates of the exponential decay of eigenfunctions of difference operators on the lattice Z^n which are discrete analogs of the Schr\"{o}dinger, 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 so-called pseudodifference operators (i.e., pseudodifferential operators on the group Z^n) with analytic symbols and on the limit operators
more » ... 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 Schr\"{o}dinger operators on Z^n, Dirac operators on Z^3, and square root Klein-Gordon operators on Z^n.
doi:10.1088/1751-8113/42/38/385207 fatcat:lrm2cb25tjdplitghaynn2v744