Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


SIGMA 5 (2009), 005, 10 pages      arXiv:0901.1858      http://dx.doi.org/10.3842/SIGMA.2009.005
Contribution to the Proceedings of the VIIth Workshop ''Quantum Physics with Non-Hermitian Operators''

Generalized Nonanalytic Expansions, PT-Symmetry and Large-Order Formulas for Odd Anharmonic Oscillators

Ulrich D. Jentschura a, Andrey Surzhykov b and 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

Received October 30, 2008, in final form January 07, 2009; Published online January 13, 2009

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.

Key words: PT-symmetry; asymptotics; higher-order corrections; instantons.

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