Polynomial potentials and coupled quantum dots in two and three dimensions

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18470%2F20%3A50016874" target="_blank" >RIV/62690094:18470/20:50016874 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/61389005:_____/20:00524208

Výsledek na webu

<a href="https://www.sciencedirect.com/science/article/pii/S0003491620300944?via%3Dihub" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0003491620300944?via%3Dihub</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.aop.2020.168161" target="_blank" >10.1016/j.aop.2020.168161</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Polynomial potentials and coupled quantum dots in two and three dimensions

Popis výsledku v původním jazyce

Polynomial potentials V(x) = x(4) + O(x(2)) and V(x) = x(6) + O(x(4)) were introduced, in the Thom&apos;s purely geometric classification of bifurcations, as the benchmark models of the so called cusp catastrophes and of the so called butterfly catastrophes, respectively. Due to their asymptotically confining property, these two potentials are exceptional, viz., able to serve similar purposes even after quantization, in the presence of tunneling. In this paper the idea is generalized to apply also to quantum systems in two and three dimensions. Two related technical obstacles are addressed, both connected with the non-separability of the underlying partial differential Schrodinger equations. The first one [viz., the necessity of a non-numerical localization of the extremes (i.e., of the minima and maxima) of V(x, y,...)] is resolved via an ad hoc reparametrization of the coupling constants. The second one [viz., the necessity of explicit construction of the low lying bound states.(x, y,...)] is circumvented by the restriction of attention to the dynamical regime in which the individual minima of V(x, y,...) are well separated, with the potential being locally approximated by the harmonic oscillator wells simulating a coupled system of quantum dots (a.k.a. an artificial molecule). Subsequently it is argued that the measurable characteristics (and, in particular, the topologically protected probability-density distributions) could bifurcate in specific evolution scenarios called relocalization catastrophes.

Název v anglickém jazyce

Polynomial potentials and coupled quantum dots in two and three dimensions

Popis výsledku anglicky

Polynomial potentials V(x) = x(4) + O(x(2)) and V(x) = x(6) + O(x(4)) were introduced, in the Thom&apos;s purely geometric classification of bifurcations, as the benchmark models of the so called cusp catastrophes and of the so called butterfly catastrophes, respectively. Due to their asymptotically confining property, these two potentials are exceptional, viz., able to serve similar purposes even after quantization, in the presence of tunneling. In this paper the idea is generalized to apply also to quantum systems in two and three dimensions. Two related technical obstacles are addressed, both connected with the non-separability of the underlying partial differential Schrodinger equations. The first one [viz., the necessity of a non-numerical localization of the extremes (i.e., of the minima and maxima) of V(x, y,...)] is resolved via an ad hoc reparametrization of the coupling constants. The second one [viz., the necessity of explicit construction of the low lying bound states.(x, y,...)] is circumvented by the restriction of attention to the dynamical regime in which the individual minima of V(x, y,...) are well separated, with the potential being locally approximated by the harmonic oscillator wells simulating a coupled system of quantum dots (a.k.a. an artificial molecule). Subsequently it is argued that the measurable characteristics (and, in particular, the topologically protected probability-density distributions) could bifurcate in specific evolution scenarios called relocalization catastrophes.

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

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2020

Kód důvěrnosti údajů

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

Název periodika

ANNALS OF PHYSICS

ISSN

0003-4916

e-ISSN

—

Svazek periodika

416

Číslo periodika v rámci svazku

May

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

13

Strana od-do

"Article Number: 168161"

Kód UT WoS článku

000528197500005

EID výsledku v databázi Scopus

2-s2.0-85082872151