On Disagreement about Nonperturbative Corrections in Triple-well Potential

Abstract

We examine in detail nonperturbative corrections for low lying energies of a symmetric triple-well potential with non-equivalent vacua, for which there have been disagreement about asymptotic formulas and controversy over the validity of the dilute gas approximation. We carry out investigations from various points of view, including not only a numerical comparison of the nonperturbative corrections with the exact values but also the prediction of the large order behavior of the perturbation series, consistency with the perturbative corrections, and comparison with the WKB approximation. We show that all the results support our formula previously obtained from the valley method calculation beyond the dilute gas approximation.