1306.4405 (Gerald V. Dunne et al.)

Generating Energy Eigenvalue Trans-series from Perturbation Theory    [PDF]

Gerald V. Dunne, Mithat Unsal

We show that the full resurgent trans-series expression for energy eigenvalues, containing all orders of perturbative, non-perturbative and quasi-zero-mode terms, may be generated directly from the perturbative expansion, combined with a single global boundary condition. For quantum mechanical problems with degenerate harmonic vacua, such as the double-well or periodic Sine-Gordon potentials, this global boundary condition follows from the asymptotic behavior in the complex plane of the parabolic cylinder functions. This extends the results of Zinn-Justin and Jentschura and provides a dramatic realization of the concept of resurgence.

View original: http://arxiv.org/abs/1306.4405