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Resummation of anisotropic quartic oscillator. Crossover from anisotropic to isotropic largeorder behavior  H. Kleinert
; S. Thoms
;  Date: 
23 May 1996  Subject:  quantph  Abstract:  We present an approximative calculation of the groundstate energy for the anisotropic anharmonic oscillator Using an instanton solution of the isotropic action $delta = 0$, we obtain the imaginary part of the groundstate energy for small negative $g$ as a series expansion in the anisotropy parameter $delta$. From this, the largeorder behavior of the $g$expansions accompanying each power of $delta$ are obtained by means of a dispersion relation in $g$. These $g$expansions are summed by a Borel transformation, yielding an approximation to the groundstate energy for the region near the isotropic limit. This approximation is found to be excellent in a rather wide region of $delta$ around $delta = 0$. Special attention is devoted to the immediate vicinity of the isotropic point. Using a simple model integral we show that the largeorder behavior of an $delta$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 $k_{{
m cross} sim 1/ {delta}$.  Source:  arXiv, quantph/9605033  Services:  Forum  Review  PDF  Favorites 


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