An exactly solvable system from quantum optics
Mathematical Physics
2015-04-23 v1 math.MP
Quantum Physics
Abstract
We investigate a generalisation of the Rabi system in the Bargmann-Fock representation. In this representation the eigenproblem of the considered quantum model is described by a system of two linear differential equations with one independent variable. The system has only one irregular singular point at infinity. We show how the quantisation of the model is related to asymptotic behaviour of solutions in a vicinity of this point. The explicit formulae for the spectrum and eigenfunctions of the model follow from an analysis of the Stokes phenomenon. An interpretation of the obtained results in terms of differential Galois group of the system is also given.
Cite
@article{arxiv.1504.05886,
title = {An exactly solvable system from quantum optics},
author = {Andrzej J. Maciejewski and Maria Przybylska and Tomasz Stachowiak},
journal= {arXiv preprint arXiv:1504.05886},
year = {2015}
}
Comments
9 pages, 5 figures