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Exact instanton transseries for quantum mechanics
by Alexander van Spaendonck, Marcel Vonk
This Submission thread is now published as
Submission summary
| Submission information |
| Preprint Link: |
https://arxiv.org/abs/2309.05700v3
(pdf)
|
| Date accepted: |
2024-03-25 |
| Date submitted: |
2024-02-07 09:25 |
| Submitted by: |
van Spaendonck, Alexander |
| Submitted to: |
SciPost Physics |
| Ontological classification |
| Academic field: |
Physics |
| Specialties: |
|
| Approach: |
Theoretical |
Abstract
We calculate the instanton corrections to energy spectra of one-dimensional quantum mechanical oscillators to all orders and unify them in a closed form transseries description. Using alien calculus, we clarify the resurgent structure of these transseries and demonstrate two approaches in which the Stokes constants can be derived. As a result, we formulate a minimal one-parameter transseries for the natural nonperturbative extension to the perturbative energy, which captures the Stokes phenomenon in a single stroke. We derive these results in three models: quantum oscillators with cubic, symmetric double well and cosine potentials. In the latter two examples, we find that the resulting full transseries for the energy has a more convoluted structure that we can factorise in terms of a minimal and a median transseries. For the cosine potential we briefly discuss this more complicated transseries structure in conjunction with topology and the concept of the resurgence triangle.
