On the two-dimensional quantum confined Stark effect in strong electric fields
Mathematical Physics
2022-08-22 v1 Analysis of PDEs
math.MP
Spectral Theory
Quantum Physics
Abstract
We consider a Stark Hamiltonian on a two-dimensional bounded domain with Dirichlet boundary conditions. In the strong electric field limit we derive, under certain local convexity conditions, a three-term asymptotic expansion of the low-lying eigenvalues. This shows that the excitation frequencies are proportional to the square root of the boundary curvature at a certain point determined by the direction of the electric field.
Cite
@article{arxiv.2012.09145,
title = {On the two-dimensional quantum confined Stark effect in strong electric fields},
author = {Horia Cornean and David Krejcirik and Thomas Garm Pedersen and Nicolas Raymond and Edgardo Stockmeyer},
journal= {arXiv preprint arXiv:2012.09145},
year = {2022}
}