Imaginary Cubic Perturbation: Numerical and Analytic Study

Details Imaginary Cubic Perturbation: Numerical and Analytic Study Imaginary Cubic Perturbation: Numerical and Analytic Study

2010-06-28

arxiv.org/abs/1006.5303v2

J.Phys.A 43 (2010) 425301

Physics

Mathematical Physics

18 pages; 4 figures; typographical errors corrected

Scientific paper

10.1088/1751-8113/43/42/425301

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.

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