Geodesic
Perturbation theory series in quantum mechanics: Phase transition and exact asymptotic forms for the expansion coefficients
Teoretičeskaâ i matematičeskaâ fizika, Tome 174 (2013) no. 3, pp. 416-443 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider the model of a harmonic oscillator with a power-law potential and derive new asymptotic formulas for the coefficients of the perturbation theory series in powers of the coupling constant in the case of a power-law perturbing potential $|x|^p$, $p>0$. We prove the existence of a critical value $p_0$ and compute it. It is a threshold in the sense that the asymptotic forms of the studied coefficients for $0 and for $p>p_0$ differ qualitatively. We note that the considered physical system undergoes a phase transition at $p=p_0$. The analysis uses the Laplace method for functional integrals with Gaussian measures.
Mots-clés : phase transition
Keywords: perturbation theory series, Lieb trace formula, conditional Wiener measure, Laplace method in a Banach space. 
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V. R. Fatalov. Perturbation theory series in quantum mechanics: Phase transition and exact asymptotic forms for the expansion coefficients. Teoretičeskaâ i matematičeskaâ fizika, Tome 174 (2013) no. 3, pp. 416-443. http://geodesic.mathdoc.fr/item/TMF_2013_174_3_a4/

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