Resummation of anisotropic quartic oscillator: Crossover from anisotropic to isotropic large-order behavior

Using an instanton solution for the isotropic limit d50, we obtain the imaginary part of the ground-state energy for small negative g as a series expansion in the anisotropy parameter d . From this, the large-order behavior of the g expansions accompanying each power of d are obtained by means of a dispersion relation in g . The g expansions are summed by a Borel transformation, yielding an approximation to the ground-state energy for the region near the isotropic limit. This approximation is found to be excellent in a rather wide region of d around d50. Special attention is devoted to the immediate vicinity of the isotropy point. Using a simple model integral we show that the large-order behavior of a d-dependent series expansion in g undergoes a crossover from an isotropic to an anisotropic regime as the order k of the expansion coefficients passes the value kcross;1/udu. @S1050-2947~97!08801-X#