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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.
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Jean Zinn-Justin, Ulrich D. Jentschura. Imaginary cubic perturbation: numerical and analytic study. Journal of Physics A: Mathematical and Theoretical, IOP Publishing, 2010, 43 (42), pp.425301. ⟨10.1088/1751-8113/43/42/425301⟩. ⟨cea-02895222⟩



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