ON THE TWO-DIMENSIONAL QUANTUM CONFINED STARK EFFECT IN STRONG ELECTRIC FIELDS

Horia Cornean; David Krejciřik; Thomas G. Pedersen; Nicolas Raymond; Edgardo Stockmeyer

doi:10.1137/20M1386712

ON THE TWO-DIMENSIONAL QUANTUM CONFINED STARK EFFECT IN STRONG ELECTRIC FIELDS

Horia Cornean, David Krejciřik, Thomas G. Pedersen, Nicolas Raymond, Edgardo Stockmeyer

Research output: Contribution to journal › Journal article › Research › peer-review

2 Citations (Scopus)

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.

Original language	English
Journal	SIAM Journal on Mathematical Analysis
Volume	54
Issue number	2
Pages (from-to)	2114-2127
Number of pages	14
ISSN	0036-1410
DOIs	https://doi.org/10.1137/20M1386712
Publication status	Published - 2022

Bibliographical note

Publisher Copyright:
© 2022 Society for Industrial and Applied Mathematics.

Keywords

asymptotics of eigenvalues
confined semiconductor device
Stark effect
strong electric field

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10.1137/20M1386712

https://arxiv.org/pdf/2012.09145.pdf

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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.",

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AU - Krejciřik, David

AU - Pedersen, Thomas G.

AU - Raymond, Nicolas

AU - Stockmeyer, Edgardo

PY - 2022

Y1 - 2022

N2 - 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.

AB - 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.

KW - asymptotics of eigenvalues

KW - confined semiconductor device

KW - Stark effect

KW - strong electric field

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ON THE TWO-DIMENSIONAL QUANTUM CONFINED STARK EFFECT IN STRONG ELECTRIC FIELDS

Abstract

Bibliographical note

Keywords

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