Estimates of Initial Scales for Layers with Small Random Negative-Definite Perturbations

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18470%2F19%3A50016362" target="_blank" >RIV/62690094:18470/19:50016362 - isvavai.cz</a>

Výsledek na webu

<a href="https://link.springer.com/content/pdf/10.1007/s10958-019-04443-2.pdf" target="_blank" >https://link.springer.com/content/pdf/10.1007/s10958-019-04443-2.pdf</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s10958-019-04443-2" target="_blank" >10.1007/s10958-019-04443-2</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Estimates of Initial Scales for Layers with Small Random Negative-Definite Perturbations

Popis výsledku v původním jazyce

In this work, we consider the Schrödinger operator in a multi-dimensional layer with small random perturbations. Perturbations are distributed in periodicity cells of an arbitrarily chosen periodic lattice. To each cell, we put in correspondence a random variable; these random variables are independent and have the same distributions. Perturbations are described by the same abstract symmetric operator depending on the random variable multiplied by a global small parameter. We consider the case where the perturbations shift the bottom part of the spectrum of the unperturbed operator to the left by a quantity of order of the square of the small parameter. Under these conditions, we establish the main result, which is the estimate of initial scales. We also present particular examples that demonstrate the main result.

Název v anglickém jazyce

Estimates of Initial Scales for Layers with Small Random Negative-Definite Perturbations

Popis výsledku anglicky

In this work, we consider the Schrödinger operator in a multi-dimensional layer with small random perturbations. Perturbations are distributed in periodicity cells of an arbitrarily chosen periodic lattice. To each cell, we put in correspondence a random variable; these random variables are independent and have the same distributions. Perturbations are described by the same abstract symmetric operator depending on the random variable multiplied by a global small parameter. We consider the case where the perturbations shift the bottom part of the spectrum of the unperturbed operator to the left by a quantity of order of the square of the small parameter. Under these conditions, we establish the main result, which is the estimate of initial scales. We also present particular examples that demonstrate the main result.

Druh

J_SC - Článek v periodiku v databázi SCOPUS

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

—

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

Journal of mathematical sciences

ISSN

1072-3374

e-ISSN

—

Svazek periodika

241

Číslo periodika v rámci svazku

5

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

31

Strana od-do

518-548

Kód UT WoS článku

—

EID výsledku v databázi Scopus

2-s2.0-85070786674