Imaginary Cubic Perturbation: Numerical and Analytic Study
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.
J. Zinn-Justin and U. D. Jentschura, "Imaginary Cubic Perturbation: Numerical and Analytic Study," Journal of Physics A: Mathematical and Theoretical, vol. 43, no. 42, IOP Publishing, Oct 2010.
The definitive version is available at https://doi.org/10.1088/1751-8113/43/42/425301
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01 Oct 2010