Phys.org April 26, 2024
Researchers in the Netherlands calculated the instanton corrections to energy spectra of one-dimensional quantum mechanical oscillators to all orders and unify them in a closed form transseries description. They clarified the resurgent structure of these transseries and demonstrated two approaches in which the Stokes constants could be derived. This formulated a minimal one-parameter transseries for the natural nonperturbative extension to the perturbative energy which captured the Stokes phenomenon in a single stroke. They derived these results in three models: quantum oscillators with cubic, symmetric double well and cosine potentials. In the latter two examples, they found that the resulting full transseries for the energy had a more convoluted structure that they could factorize in terms of a minimal and a median transseries. For the cosine potential they briefly discussed this more complicated transseries structure in conjunction with topology and the concept of the resurgence triangle… read more. Open Access TECHNICAL ARTICLEÂ
The Borel plane of BÏ•. Credit: SciPost Phys. 16, 103, published 12 April 2024Â