Exact WKB analysis for adiabatic discrete-level Hamiltonians
Abstract
The dynamics of quantum systems under the adiabatic Hamiltonian has attracted attention not only in quantum control but also in a wide range of fields from condensed matter physics to high-energy physics because of its non-perturbative behavior. Here we analyze the adiabatic dynamics in the two-level systems and the multilevel systems using the exact WKB analysis, which is one of the non-perturbative analysis methods. As a result, we obtain a formula for the transition probability, which is similar to the known formula in the two-level system. Although non-perturbative analysis in the adiabatic limit has rarely been studied for multilevel systems, we show that the same analysis can be applied and also provide a concrete example. The results will serve as a basis for the application of the exact WKB analysis in various fields of physics.
Keywords
Cite
@article{arxiv.2311.05871,
title = {Exact WKB analysis for adiabatic discrete-level Hamiltonians},
author = {Takayuki Suzuki and Eiki Taniguchi and Kaito Iwamura},
journal= {arXiv preprint arXiv:2311.05871},
year = {2024}
}