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Abstract: This paper is devoted to estimates of the exponential decay of eigenfunctionsof difference operators on the lattice Z^n which are discrete analogs of theSchr\-{o}dinger, Dirac and square-root Klein-Gordon operators. Ourinvestigation of the essential spectra and the exponential decay ofeigenfunctions of the discrete spectra is based on the calculus of so-calledpseudodifference operators i.e., pseudodifferential operators on the groupZ^n with analytic symbols and on the limit operators method. We obtain adescription of the location of the essential spectra and estimates of theeigenfunctions of the discrete spectra of the main lattice operators of quantummechanics, namely: matrix Schr\-{o}dinger operators on Z^n, Dirac operators onZ^3, and square root Klein-Gordon operators on Z^n.



Author: Vladimir Rabinovich, Steffen Roch

Source: https://arxiv.org/







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