Imaginary cubic perturbation: numerical and analytic study
Résumé
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.
Domaines
Physique [physics]
Origine : Fichiers produits par l'(les) auteur(s)
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