Method of intermediate problems in the theory of Gaussian quantum dots placed in a magnetic field
Applicability of the method of intermediate problems to the investigation of the energy eigenvalues and eigenstates
 of a quantum dot (QD) formed by a Gaussian confining potential in the presence of an external magnetic
 field is discussed. Being smooth at the QD boundaries and of fi...
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| Published in: | Condensed Matter Physics |
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| Date: | 2006 |
| Main Authors: | , , , |
| Format: | Article |
| Language: | English |
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Інститут фізики конденсованих систем НАН України
2006
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/121309 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Method of intermediate problems in the theory of Gaussian quantum dots placed in a magnetic field / A.V. Soldatov, N.N. Bogolyubov, Jr., S.P. Kruchinin // Condensed Matter Physics. — 2006. — Т. 9, № 1(45). — С. 151–159. — Бібліогр.: 18 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862705879804018688 |
|---|---|
| author | Soldatov, A.V. Bogolyubov, N.N. Kruchinin, S.P. Jr. |
| author_facet | Soldatov, A.V. Bogolyubov, N.N. Kruchinin, S.P. Jr. |
| citation_txt | Method of intermediate problems in the theory of Gaussian quantum dots placed in a magnetic field / A.V. Soldatov, N.N. Bogolyubov, Jr., S.P. Kruchinin // Condensed Matter Physics. — 2006. — Т. 9, № 1(45). — С. 151–159. — Бібліогр.: 18 назв. — англ. |
| collection | DSpace DC |
| container_title | Condensed Matter Physics |
| description | Applicability of the method of intermediate problems to the investigation of the energy eigenvalues and eigenstates
of a quantum dot (QD) formed by a Gaussian confining potential in the presence of an external magnetic
field is discussed. Being smooth at the QD boundaries and of finite depth and range, this potential can
only confine a finite number of excess electrons thus forming a realistic model of a QD with smooth interface
between the QD and its embedding environment. It is argued that the method of intermediate problems,
which provides convergent improvable lower bound estimates for eigenvalues of linear half-bound Hermitian
operators in Hilbert space, can be fused with the classical Rayleigh-Ritz variational method and stochastic
variational method thus resulting in an efficient tool for analytical and numerical studies of the energy spectrum
and eigenstates of the Gaussian quantum dots, confining small-to-medium number of excess electrons,
with controllable or prescribed precision.
|
| first_indexed | 2025-12-07T16:56:42Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-121309 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1607-324X |
| language | English |
| last_indexed | 2025-12-07T16:56:42Z |
| publishDate | 2006 |
| publisher | Інститут фізики конденсованих систем НАН України |
| record_format | dspace |
| spelling | Soldatov, A.V. Bogolyubov, N.N. Kruchinin, S.P. Jr. 2017-06-14T04:42:49Z 2017-06-14T04:42:49Z 2006 Method of intermediate problems in the theory of Gaussian quantum dots placed in a magnetic field / A.V. Soldatov, N.N. Bogolyubov, Jr., S.P. Kruchinin // Condensed Matter Physics. — 2006. — Т. 9, № 1(45). — С. 151–159. — Бібліогр.: 18 назв. — англ. 1607-324X PACS: 73.21.La, 85.35.Be, 75.75.+a, 03.65.Ge, 02.30.Tb DOI:10.5488/CMP.9.1.151 https://nasplib.isofts.kiev.ua/handle/123456789/121309 Applicability of the method of intermediate problems to the investigation of the energy eigenvalues and eigenstates
 of a quantum dot (QD) formed by a Gaussian confining potential in the presence of an external magnetic
 field is discussed. Being smooth at the QD boundaries and of finite depth and range, this potential can
 only confine a finite number of excess electrons thus forming a realistic model of a QD with smooth interface
 between the QD and its embedding environment. It is argued that the method of intermediate problems,
 which provides convergent improvable lower bound estimates for eigenvalues of linear half-bound Hermitian
 operators in Hilbert space, can be fused with the classical Rayleigh-Ritz variational method and stochastic
 variational method thus resulting in an efficient tool for analytical and numerical studies of the energy spectrum
 and eigenstates of the Gaussian quantum dots, confining small-to-medium number of excess electrons,
 with controllable or prescribed precision. This work has been supported by the RF support program “Support for Leading Scientific
 Schools”, grant No. 1758.2003.1, by the RAS research program “Mathematical Problems of Nonlinear
 Dynamics” and by the RFBR grant No. 05–02–16663–a. en Інститут фізики конденсованих систем НАН України Condensed Matter Physics Method of intermediate problems in the theory of Gaussian quantum dots placed in a magnetic field Метод проміжних задач у теорії гаусових квантових точок, поміщених у магнітне поле Article published earlier |
| spellingShingle | Method of intermediate problems in the theory of Gaussian quantum dots placed in a magnetic field Soldatov, A.V. Bogolyubov, N.N. Kruchinin, S.P. Jr. |
| title | Method of intermediate problems in the theory of Gaussian quantum dots placed in a magnetic field |
| title_alt | Метод проміжних задач у теорії гаусових квантових точок, поміщених у магнітне поле |
| title_full | Method of intermediate problems in the theory of Gaussian quantum dots placed in a magnetic field |
| title_fullStr | Method of intermediate problems in the theory of Gaussian quantum dots placed in a magnetic field |
| title_full_unstemmed | Method of intermediate problems in the theory of Gaussian quantum dots placed in a magnetic field |
| title_short | Method of intermediate problems in the theory of Gaussian quantum dots placed in a magnetic field |
| title_sort | method of intermediate problems in the theory of gaussian quantum dots placed in a magnetic field |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/121309 |
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