Physics – Quantum Physics
Scientific paper
1996-05-23
Physics
Quantum Physics
Paper and .eps files. Author Information at http://www.physik.fu-berlin.de/~kleinert/institution.html . Paper at http://www.
Scientific paper
10.1103/PhysRevA.55.915
We present an approximative calculation of the ground-state energy for the anisotropic anharmonic oscillator Using an instanton solution of the isotropic action $\delta = 0$, we obtain the imaginary part of the ground-state energy for small negative $g$ as a series expansion in the anisotropy parameter $\delta$. From this, the large-order 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 ground-state 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 large-order 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 $k_{{\rm cross} \sim 1/ |{\delta}|$.
Kleinert Hagen
Thoms Silke
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