Imaginary cubic perturbation: numerical and analytic study

The analytic properties of the ground state resonance energy $E(g)$ of the cubic potential areinvestigated as a function of the complex coupling parameter $g$. We explicitly show that it is possibleto analytically continue $E(g)$ by means of a resummed strong coupling expansion, to the secondsheet o...

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Published in:Journal of physics. A, Mathematical and theoretical Mathematical and theoretical, 2010-10, Vol.43 (42), p.425301
Main Authors: Zinn-Justin, Jean, Jentschura, Ulrich D
Format: Article
Language:English
Subjects:
Exact sciences and technology
Physics
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Summary:The analytic properties of the ground state resonance energy $E(g)$ of the cubic potential areinvestigated as a function of the complex coupling parameter $g$. We explicitly show that it is possibleto analytically continue $E(g)$ by means of a resummed strong coupling expansion, to the secondsheet of the Riemann surface, and we observe a merging of resonance and antiresonance eigenvaluesat a critical point along the line arg($g$) = 5$\pi$/4. In addition, we investigate the convergence of theresummed weak-coupling expansion in the strong coupling regime, by means of various modificationsof 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 alarge number of terms of the strong coupling expansion by resumming the weak-coupling expansionusing the ODM, demonstrating the interpolation between the two regimes made possible by thissummation method.
ISSN:1751-8121
1751-8113
1751-8121
DOI:10.1088/1751-8113/43/42/425301