### 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 language | English |
---|---|

Article number | 425301 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 43 |

Issue number | 42 |

DOIs | |

Publication status | Published - Oct 22 2010 |

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### ASJC Scopus subject areas

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

### Cite this

*Journal of Physics A: Mathematical and Theoretical*,

*43*(42), [425301]. https://doi.org/10.1088/1751-8113/43/42/425301

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

Research output: Contribution to journal › Article

*Journal of Physics A: Mathematical and Theoretical*, vol. 43, no. 42, 425301. https://doi.org/10.1088/1751-8113/43/42/425301

}

TY - JOUR

T1 - Imaginary cubic perturbation

T2 - Numerical and analytic study

AU - Zinn-Justin, Jean

AU - Jentschura, U.

PY - 2010/10/22

Y1 - 2010/10/22

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=78649670557&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=78649670557&partnerID=8YFLogxK

U2 - 10.1088/1751-8113/43/42/425301

DO - 10.1088/1751-8113/43/42/425301

M3 - Article

VL - 43

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 42

M1 - 425301

ER -