Ulrich D. Jentschura, Andrey Surzhykov, Jean Zinn-Justin, “Generalized Nonanalytic Expansions, <nobr>$\mathcal{PT}$</nobr>-Symmetry and Large-Order Formulas for Odd Anharmonic Oscillators”, SIGMA, 2009, Volume 5,005, 10 pp.

This article is cited in 6 papers

Generalized Nonanalytic Expansions, $\mathcal{PT}$-Symmetry and Large-Order Formulas for Odd Anharmonic Oscillators

Ulrich D. Jentschura^a, Andrey Surzhykov^b, Jean Zinn-Justin^c

^a Department of Physics, Missouri University of Science and Technology, Rolla MO65409-0640, USA
^b Physikalisches Institut der Universität, Philosophenweg 12, 69120 Heidelberg, Germany
^c CEA, IRFU and Institut de Physique Théorique, Centre de Saclay, F-91191 Gif-Sur-Yvette, France

Abstract: The concept of a generalized nonanalytic expansion which involves nonanalytic combinations of exponentials, logarithms and powers of a coupling is introduced and its use illustrated in various areas of physics. Dispersion relations for the resonance energies of odd anharmonic oscillators are discussed, and higher-order formulas are presented for cubic and quartic potentials.

Keywords: $\mathcal{PT}$-symmetry; asymptotics; higher-order corrections; instantons.

MSC: 81Q15; 81T15

Received: October 30, 2008; in final form January 7, 2009; Published online January 13, 2009

Language: English

DOI: 10.3842/SIGMA.2009.005