Imaginary cubic perturbation

Numerical and analytic study

Jean Zinn-Justin, U. Jentschura

Research output: Contribution to journalArticle

15 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

Fingerprint

Strong Coupling
Perturbation
perturbation
Weak Coupling
Dependent
expansion
Riemann Surface
Merging
Summation
Ground state
Ground State
Critical point
Interpolation
Continue
Interpolate
Eigenvalue
Line
Term
interpolation
Energy

ASJC Scopus subject areas

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

Cite this

Imaginary cubic perturbation : Numerical and analytic study. / Zinn-Justin, Jean; Jentschura, U.

In: Journal of Physics A: Mathematical and Theoretical, Vol. 43, No. 42, 425301, 22.10.2010.

Research output: Contribution to journalArticle

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