# Imaginary cubic perturbation: numerical and analytic study

* Corresponding author
Abstract : The analytic properties of the ground state resonance energy $E(g)$ of the cubic potential are investigated as a function of the complex coupling parameter $g$. We explicitly show that it is possible to analytically continue $E(g)$ by means of a resummed strong coupling expansion, to the second sheet of the Riemann surface, and we observe a merging of resonance and antiresonance eigenvalues at a critical point along the line arg($g$) = 5$\pi$/4. In addition, we investigate the convergence of the resummed weak-coupling expansion in the strong coupling regime, by means of various modifications of order-dependent mappings (ODM), that take special properties of the cubic potential into account. The various ODM are adapted to different regimes of the coupling constant. We also determine a large number of terms of the strong coupling expansion by resumming the weak-coupling expansion using the ODM, demonstrating the interpolation between the two regimes made possible by this summation method.
Keywords :
Document type :
Journal articles
Domain :

Cited literature [25 references]

https://hal-cea.archives-ouvertes.fr/cea-02895222
Contributor : Bruno Savelli <>
Submitted on : Thursday, July 9, 2020 - 3:27:41 PM
Last modification on : Saturday, July 11, 2020 - 3:22:14 AM
Long-term archiving on: : Monday, November 30, 2020 - 6:05:49 PM

### File

Jjen.pdf
Files produced by the author(s)

### Citation

Jean Zinn-Justin, Ulrich D. Jentschura. Imaginary cubic perturbation: numerical and analytic study. Journal of Physics A: Mathematical and Theoretical, IOP Publishing, 2010, 43 (42), pp.425301. ⟨10.1088/1751-8113/43/42/425301⟩. ⟨cea-02895222⟩

Record views