Poles of Integrale Tritronquee and Anharmonic Oscillators. Asymptotic localization from WKB analysis

Abstract

Poles of integrale tritronquee are in bijection with cubic oscillators that admit the simultaneous solutions of two quantization conditions. We show that the poles lie near the solutions of a pair of Bohr-Sommerfeld quantization conditions (the Bohr-Sommerfeld-Boutroux system): the distance between a pole and the corresponding solution of the Bohr-Sommerfeld-Boutroux system vanishes asymptotically.

arXiv comment8 pages, 2 figures

References in corpus (3)

• Analytic continuation of eigenvalues of a quartic oscillator
• Poles of Integrale Tritronquee and Anharmonic Oscillators. A WKB Approach
• Monodromy approach to the scaling limits in the isomonodromy systems

Cited by in corpus (16)

• Non-perturbative approaches to the quantum Seiberg-Witten curve
• Resurgent Extrapolation: Rebuilding a Function from Asymptotic Data. Painleve I
• Proof of the Dubrovin conjecture and analysis of the tritronquée solutions of $P_I$
• Poles of Integrale Tritronquee and Anharmonic Oscillators. A WKB Approach
• Uniformization and Constructive Analytic Continuation of Taylor Series
• Poles of Painlevé IV Rationals and their Distribution
• Y-System and Deformed Thermodynamic Bethe Ansatz
• Quantum spectral problems and isomonodromic deformations
• Resurgence, Painleve Equations and Conformal Blocks
• Roots of generalised Hermite polynomials when both parameters are large
• Painleve I, Coverings of the Sphere and Belyi Functions
• Tronquée solutions of the Painlevé equation \P1
• Tronquée Solutions of the Third and Fourth Painlevé Equations
• Location of Poles for the Hastings-McLeod Solution to the Second Painlevé Equation
• The Direct Monodromy Problem of Painleve-I
• The Riemann-Hilbert approach to obtain critical asymptotics for Hamiltonian perturbations of hyperbolic and elliptic systems