A Sharp Upper Bound on the Spectral Gap for Graphene Quantum Dots

Kód výsledku v IS VaVaI

RIV/61389005:_____/19:00504281 - isvavai.cz

Výsledek na webu

https://doi.org/10.1007/s11040-019-9310-z

DOI - Digital Object Identifier

10.1007/s11040-019-9310-z

Jazyk výsledku

angličtina

Název v původním jazyce

A Sharp Upper Bound on the Spectral Gap for Graphene Quantum Dots

Popis výsledku v původním jazyce

The main result of this paper is a sharp upper bound on the first positive eigenvalue of Dirac operators in two dimensional simply connected C-3-domains with infinite mass boundary conditions. This bound is given in terms of a conformal variation, explicit geometric quantities and of the first eigenvalue for the disk. Its proof relies on the min-max principle applied to the squares of these Dirac operators. A suitable test function is constructed by means of a conformal map. This general upper bound involves the norm of the derivative of the underlying conformal map in the Hardy space H-2(D). Then, we apply known estimates of this norm for convex and for nearly circular, star-shaped domains in order to get explicit geometric upper bounds on the eigenvalue. These bounds can be re-interpreted as reverse Faber-Krahn-type inequalities under adequate geometric constraints.

Název v anglickém jazyce

A Sharp Upper Bound on the Spectral Gap for Graphene Quantum Dots

Popis výsledku anglicky

The main result of this paper is a sharp upper bound on the first positive eigenvalue of Dirac operators in two dimensional simply connected C-3-domains with infinite mass boundary conditions. This bound is given in terms of a conformal variation, explicit geometric quantities and of the first eigenvalue for the disk. Its proof relies on the min-max principle applied to the squares of these Dirac operators. A suitable test function is constructed by means of a conformal map. This general upper bound involves the norm of the derivative of the underlying conformal map in the Hardy space H-2(D). Then, we apply known estimates of this norm for convex and for nearly circular, star-shaped domains in order to get explicit geometric upper bounds on the eigenvalue. These bounds can be re-interpreted as reverse Faber-Krahn-type inequalities under adequate geometric constraints.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10301 - Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect)

Projekt

GA17-01706S: Matematicko-fyzikální modely nových materiálů

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2019

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Mathematical Physics, Analysis and Geometry

ISSN

1385-0172

e-ISSN

—

Svazek periodika

22

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

30

Strana od-do

13

Kód UT WoS článku

000463990200001

EID výsledku v databázi Scopus

2-s2.0-85064241875