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

TL;DR

This paper introduces generalized nonanalytic expansions involving exponentials, logarithms, and powers of coupling for odd anharmonic oscillators, providing dispersion relations and higher-order formulas for resonance energies.

Contribution

It presents a novel framework of nonanalytic expansions and derives new dispersion relations and formulas for odd anharmonic oscillators.

Findings

Dispersion relations for resonance energies are established.

Higher-order formulas for cubic and quartic potentials are derived.

The approach unifies various nonanalytic behaviors in physics.

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.