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 finite depth and r...
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| Veröffentlicht in: | Condensed Matter Physics |
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| Datum: | 2006 |
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| Sprache: | English |
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Інститут фізики конденсованих систем НАН України
2006
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/121309 |
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| Zitieren: | 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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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 |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Method of intermediate problems in the theory of Gaussian quantum dots placed in a magnetic field |
| 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_short |
Method of intermediate problems in the theory of Gaussian quantum dots placed in a magnetic field |
| 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_sort |
method of intermediate problems in the theory of gaussian quantum dots placed in a magnetic field |
| author |
Soldatov, A.V. Bogolyubov, N.N. Kruchinin, S.P. Jr. |
| author_facet |
Soldatov, A.V. Bogolyubov, N.N. Kruchinin, S.P. Jr. |
| publishDate |
2006 |
| language |
English |
| container_title |
Condensed Matter Physics |
| publisher |
Інститут фізики конденсованих систем НАН України |
| format |
Article |
| title_alt |
Метод проміжних задач у теорії гаусових квантових точок, поміщених у магнітне поле |
| 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.
|
| issn |
1607-324X |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/121309 |
| 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. |
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