Order-dependent mappings: Strong-coupling behavior from weak-coupling expansions in non-Hermitian theories

DOI10.1063/1.3451104zbMath1311.81127arXiv1006.4748OpenAlexW3100879014MaRDI QIDQ5251804

Jean Zinn-Justin, Ulrich D. Jentschura

Publication date: 21 May 2015

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1006.4748

Mathematics Subject Classification ID

Perturbation theories for operators and differential equations in quantum theory (81Q15) Nonselfadjoint operator theory in quantum theory including creation and destruction operators (81Q12)

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Cites Work

• Generalized nonanalytic expansions, \(\mathcal P\mathcal T\)-symmetry and large-order formulas for odd anharmonic oscillators
• Perturbation theory of odd anharmonic oscillators
• Improved convergence proof of the delta expansion and order dependent mappings
• On the reality of the eigenvalues for a class of \(\mathcal{PT}\)-symmetric oscillators
• Convergence behavior of variational perturbation expansion---a method for locating Bender-Wu singularities
• Spectral equivalences, Bethe ansatz equations, and reality properties in 𝒫𝒯-symmetric quantum mechanics
• Numerical evidence that the perturbation expansion for a non-Hermitian PT-symmetric Hamiltonian is Stieltjes
• Must a Hamiltonian be Hermitian?
• Padé summability of the cubic oscillator
• Summation of divergent series by order dependent mappings: Application to the anharmonic oscillator and critical exponents in field theory
• Real Spectra in Non-Hermitian Hamiltonians Having<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="bold-script">P</mml:mi><mml:mi mathvariant="bold-script">T</mml:mi></mml:math>Symmetry
• Distributional Borel summability of odd anharmonic oscillators

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