Dilatancy mathematical theory

Our current direction is to study dynamical processes in atomic and molecular two- and three-body systems. We use a technique which formally is based on the mathematical theory of dilation analytic functions. Numerically these results axe realized though a fully three-dimensional finite element method applied to a total angular-momentum representation. We here show how generalizations of our previously published two-body methods to three-body systems are possible without formal approximations. 

A mathematical theory of dilatancy has been given by Reiner... 

Since the present differential equation, Eq. (3), derives from a complex symmetric structure, there are two main consequences, namely, (i) under appropriate perturbations there appears generic complex resonance energies and (ii) it may not be possible to bring the matrix to a diagonal form. As an example of a mathematically rigorous development, we mention the theory of dilation analytic operators [11] of current use in atomic and molecular physics. Hence, the theory outlined here should apply to atomic and molecular systems and their antiparticle partners. Considering initially the first point (the second point will be handled in the following sections), we make the apposite replacements... 

G. McKay and F.M. Leslie, A continuum theory for smectic liquid crystals allowing layer dilation and compression, Euro. Jnl of Applied Mathematics 8, 273-280 (1997). 

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