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

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.

References in corpus (4)

• PT-symmetric quantum mechanics
• Unified Treatment of Even and Odd Anharmonic Oscillators of Arbitrary Degree
• Structure, Time Propagation and Dissipative Terms for Resonances
• Two-field cosmological models and large-scale cosmic magnetic fields

Cited by in corpus (4)

• Remark on the Dunne-Unsal relation in exact semi-classics
• Order-dependent mappings: strong coupling behaviour from weak coupling expansions in non-Hermitian theories
• Calculation of the Characteristic Functions of Anharmonic Oscillators
• Instantons in ${\varphi }^4$ Theories: Transseries, Virial Theorems and Numerical Aspects