Про ефективну масу електрона за Пендрi
In 1996, J. Pendry, an English theoretical physicist put forward an idea about the dependence of the effective electron mass on the magnetic field, while interpreting the dielectric response of metal wire mesh structures. The idea was based on the well-known relation between the kinematic and canoni...
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| Дата: | 2019 |
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| Формат: | Стаття |
| Мова: | English Ukrainian |
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Publishing house "Academperiodika"
2019
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| Онлайн доступ: | https://ujp.bitp.kiev.ua/index.php/ujp/article/view/2019158 |
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| Назва журналу: | Ukrainian Journal of Physics |
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Ukrainian Journal of Physics| id |
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ujp2-article-20191582019-04-14T20:50:19Z On Pendry’s Effective Electron Mass Про ефективну масу електрона за Пендрi Gozhenko, V. V. ефективна маса магнiтне поле канонiчний iмпульс гамiльтонiан effective mass magnetic field canonical momentum Hamiltonian - In 1996, J. Pendry, an English theoretical physicist put forward an idea about the dependence of the effective electron mass on the magnetic field, while interpreting the dielectric response of metal wire mesh structures. The idea was based on the well-known relation between the kinematic and canonical momenta of a charged particle moving in the magnetic field. In this paper, proceeding from the universal character of that relation, the applicability of Pendry’s effective electron mass meff to the problem of electrons in metal mesh structures, as well as to a wide class of problems for charges moving in the magnetic field, has been examined. The general properties of meff following directly from its definition were found, and an analogy between the effective electron mass meff and m* known in the solid-state theory was established. A physical interpretation of meff was proposed. It was demonstrated in several examples that, despite the generality of the defining relation for the effective mass meff, the use of meff beyond the problem of the dielectric response of metal wire mesh structures leads to incorrect results. У 1996 р. англiйський фiзик-теоретик Дж. Пендрi, пояснюючи дiелектричний вiдгук металевих сiток, висунув iдею про залежнiсть ефективної маси електрона вiд магнiтного поля. Ця iдея ґрунтується на вiдомому спiввiдношеннi мiж кiнематичним i канонiчним iмпульсами заряду, що рухається в магнiтному полi. В данiй статтi, виходячи з унiверсальностi зазначеного спiввiдношення, дослiджується можливiсть застосування поняття ефективної маси електрона за Пендрi meff не лише до електронiв у металевих сiтках, а й до бiльш широкого кола задач про рух зарядiв у магнiтному полi. Встановлено загальнi властивостi ефективної маси meff, якi випливають безпосередньо з її означення. Виявлено аналогiю мiж meff та ефективною масою електронiв m*, що розглядається у теорiї твердого тiла. Запропоновано фiзичну iнтерпретацiю meff. На кiлькох прикладах показано, що, незважаючи на унiверсальнiсть використовуваного в означеннi meff спiввiдношення мiж кiнематичним i канонiчним iмпульсами, застосування поняття meff поза межами проблематики дiелектричного вiдгуку металевих сiток не дозволяє одержати правильнi результати. Publishing house "Academperiodika" 2019-01-10 Article Article Peer-reviewed Рецензована стаття application/pdf application/pdf https://ujp.bitp.kiev.ua/index.php/ujp/article/view/2019158 10.15407/ujpe60.10.1013 Ukrainian Journal of Physics; Vol. 60 No. 10 (2015); 1013 Український фізичний журнал; Том 60 № 10 (2015); 1013 2071-0194 2071-0186 10.15407/ujpe60.10 en uk https://ujp.bitp.kiev.ua/index.php/ujp/article/view/2019158/1103 https://ujp.bitp.kiev.ua/index.php/ujp/article/view/2019158/1104 Copyright (c) 2019 Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine |
| institution |
Ukrainian Journal of Physics |
| collection |
OJS |
| language |
English Ukrainian |
| topic |
ефективна маса магнiтне поле канонiчний iмпульс гамiльтонiан effective mass magnetic field canonical momentum Hamiltonian - |
| spellingShingle |
ефективна маса магнiтне поле канонiчний iмпульс гамiльтонiан effective mass magnetic field canonical momentum Hamiltonian - Gozhenko, V. V. Про ефективну масу електрона за Пендрi |
| topic_facet |
ефективна маса магнiтне поле канонiчний iмпульс гамiльтонiан effective mass magnetic field canonical momentum Hamiltonian - |
| format |
Article |
| author |
Gozhenko, V. V. |
| author_facet |
Gozhenko, V. V. |
| author_sort |
Gozhenko, V. V. |
| title |
Про ефективну масу електрона за Пендрi |
| title_short |
Про ефективну масу електрона за Пендрi |
| title_full |
Про ефективну масу електрона за Пендрi |
| title_fullStr |
Про ефективну масу електрона за Пендрi |
| title_full_unstemmed |
Про ефективну масу електрона за Пендрi |
| title_sort |
про ефективну масу електрона за пендрi |
| title_alt |
On Pendry’s Effective Electron Mass |
| description |
In 1996, J. Pendry, an English theoretical physicist put forward an idea about the dependence of the effective electron mass on the magnetic field, while interpreting the dielectric response of metal wire mesh structures. The idea was based on the well-known relation between the kinematic and canonical momenta of a charged particle moving in the magnetic field. In this paper, proceeding from the universal character of that relation, the applicability of Pendry’s effective electron mass meff to the problem of electrons in metal mesh structures, as well as to a wide class of problems for charges moving in the magnetic field, has been examined. The general properties of meff following directly from its definition were found, and an analogy between the effective electron mass meff and m* known in the solid-state theory was established. A physical interpretation of meff was proposed. It was demonstrated in several examples that, despite the generality of the defining relation for the effective mass meff, the use of meff beyond the problem of the dielectric response of metal wire mesh structures leads to incorrect results. |
| publisher |
Publishing house "Academperiodika" |
| publishDate |
2019 |
| url |
https://ujp.bitp.kiev.ua/index.php/ujp/article/view/2019158 |
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AT gozhenkovv onpendryseffectiveelectronmass AT gozhenkovv proefektivnumasuelektronazapendri |
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2023-03-24T08:57:22Z |
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2023-03-24T08:57:22Z |
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