TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.16.4.103
TI  - Exact instanton transseries for quantum mechanics
PY  - 2024/04/12
UR  - https://www.scipost.org/SciPostPhys.16.4.103
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 16
IS  - 4
SP  - 103
A1  - van Spaendonck, Alexander
AU  - Vonk, Marcel
AB  - 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.
ER  -

@Article{10.21468/SciPostPhys.16.4.103,
	title={{Exact instanton transseries for quantum mechanics}},
	author={Alexander van Spaendonck and Marcel Vonk},
	journal={SciPost Phys.},
	volume={16},
	pages={103},
	year={2024},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.16.4.103},
	url={https://scipost.org/10.21468/SciPostPhys.16.4.103},
}