Imaginary Cubic Perturbation: Numerical and Analytic Study
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) = 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.
Cite
@article{arxiv.1006.5303,
title = {Imaginary Cubic Perturbation: Numerical and Analytic Study},
author = {J. Zinn-Justin and U. D. Jentschura},
journal= {arXiv preprint arXiv:1006.5303},
year = {2010}
}
Comments
18 pages; 4 figures; typographical errors corrected