On absence of bound states for weakly attractive delta'-interactions supported on non-closed curves in R-2

Kód výsledku v IS VaVaI

RIV/61389005:_____/16:00458647 - isvavai.cz

Nalezeny alternativní kódy

RIV/68407700:21340/16:00304345

Výsledek na webu

http://dx.doi.org/10.1063/1.4939749

DOI - Digital Object Identifier

10.1063/1.4939749

Jazyk výsledku

angličtina

Název v původním jazyce

On absence of bound states for weakly attractive delta'-interactions supported on non-closed curves in R-2

Popis výsledku v původním jazyce

Let Lambda subset of R-2 be a non-closed piecewise-C-1 curve, which is either bounded with two free endpoints or unbounded with one free endpoint. Let u(+/-)|(Lambda) is an element of L-2 (Lambda) be the traces of a function u in the Sobolev space H-1 (R-2 Lambda) onto two faces of.. We prove that for a wide class of shapes of Lambda the Schrodinger operator H-omega(Lambda) with delta'-interaction supported on. of strength omega is an element of L-infinity(Lambda;R) associated with the quadratic form H-1 (R-2 Lambda) q2 (sic) u bar right arrow integral(2)(R) vertical bar del u vertical bar(2) dx - integral(Lambda) omega vertical bar u(+)vertical bar(Lambda) - u(-)vertical bar Lambda vertical bar(2)ds has no negative spectrum provided that omega is pointwise majorized by a strictly positive function explicitly expressed in terms of Lambda. If, additionally, the domain R-2 Lambda is quasi-conical, we show that sigma(H-omega(Lambda)) = [0,+infinity). For a bounded curve. in our class and non-varying interaction strength omega is an element of R, we derive existence of a constant omega* > 0 such that sigma(H omega(Lambda)) = [0,+infinity) for all omega is an element of (-infinity,omega*]; informally speaking, bound states are absent in the weak coupling regime.

Název v anglickém jazyce

On absence of bound states for weakly attractive delta'-interactions supported on non-closed curves in R-2

Popis výsledku anglicky

Let Lambda subset of R-2 be a non-closed piecewise-C-1 curve, which is either bounded with two free endpoints or unbounded with one free endpoint. Let u(+/-)|(Lambda) is an element of L-2 (Lambda) be the traces of a function u in the Sobolev space H-1 (R-2 Lambda) onto two faces of.. We prove that for a wide class of shapes of Lambda the Schrodinger operator H-omega(Lambda) with delta'-interaction supported on. of strength omega is an element of L-infinity(Lambda;R) associated with the quadratic form H-1 (R-2 Lambda) q2 (sic) u bar right arrow integral(2)(R) vertical bar del u vertical bar(2) dx - integral(Lambda) omega vertical bar u(+)vertical bar(Lambda) - u(-)vertical bar Lambda vertical bar(2)ds has no negative spectrum provided that omega is pointwise majorized by a strictly positive function explicitly expressed in terms of Lambda. If, additionally, the domain R-2 Lambda is quasi-conical, we show that sigma(H-omega(Lambda)) = [0,+infinity). For a bounded curve. in our class and non-varying interaction strength omega is an element of R, we derive existence of a constant omega* > 0 such that sigma(H omega(Lambda)) = [0,+infinity) for all omega is an element of (-infinity,omega*]; informally speaking, bound states are absent in the weak coupling regime.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BE - Teoretická fyzika

OECD FORD obor

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Projekt

GA14-06818S: Rigorózní metody v kvantové dynamice: geometrie a magnetická pole

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2016

Kód důvěrnosti údajů

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

Název periodika

Journal of Mathematical Physics

ISSN

0022-2488

e-ISSN

—

Svazek periodika

57

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

20

Strana od-do

—

Kód UT WoS článku

000371620000027

EID výsledku v databázi Scopus

2-s2.0-84955488333