Imaginary cubic perturbation: Numerical and analytic study

Jean Zinn-Justin, Ulrich D. Jentschura

Research output: Contribution to journalArticle

17 Citations (Scopus)

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) = 5π/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 (ODMs), that take special properties of the cubic potential into account. Various ODMs 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 ODMs, demonstrating the interpolation between the two regimes made possible by this summation method.

Original languageEnglish
Article number425301
JournalJournal of Physics A: Mathematical and Theoretical
Volume43
Issue number42
DOIs
Publication statusPublished - Oct 22 2010

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Modelling and Simulation
  • Mathematical Physics
  • Physics and Astronomy(all)

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