Asymptotic dependence of Gross–Tulub polaron ground-state energy in the strong coupling region
The properties of the translationally invariant polaron functional have been investigated in the strong- and extremely-strong-coupling regimes. It has been shown that the Gross–Tulub polaron functional obtained earlier using field-theoretic methods was derived only for the region α ≤ 10, where α is...
Saved in:
| Published in: | Semiconductor Physics Quantum Electronics & Optoelectronics |
|---|---|
| Date: | 2017 |
| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
2017
|
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/214998 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Asymptotic dependence of Gross–Tulub polaron ground-state energy in the strong coupling region / N.I. Kashirina // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2017. — Т. 20, № 4. — С. 430-436. — Бібліогр.: 21 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862722395168571392 |
|---|---|
| author | Kashirina, N.I. |
| author_facet | Kashirina, N.I. |
| citation_txt | Asymptotic dependence of Gross–Tulub polaron ground-state energy in the strong coupling region / N.I. Kashirina // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2017. — Т. 20, № 4. — С. 430-436. — Бібліогр.: 21 назв. — англ. |
| collection | DSpace DC |
| container_title | Semiconductor Physics Quantum Electronics & Optoelectronics |
| description | The properties of the translationally invariant polaron functional have been investigated in the strong- and extremely-strong-coupling regimes. It has been shown that the Gross–Tulub polaron functional obtained earlier using field-theoretic methods was derived only for the region α ≤ 10, where α is the Fröhlich constant of the electron-phonon coupling. Various representations of exact and approximate polaron functionals have been considered. Asymptotic dependences of the polaron energy have been obtained using a functional extending the Gross–Tulub functional to the region of extremely strong coupling. The asymptotic dependence of polaron energies for an extremely strong coupling is Ep ≈ −0.31683α⁴/ ³ (for the one-parameter variational function fₖ), and Ep ≈ −0.31767α⁴/ ³ (for a two-parameter function f′ₖ ). It has been shown that the virial theorem 1:3:4 holds for the two-parameter function f′ₖ. Minimization of the approximate functional obtained by expanding the exact Gross–Tulub functional in a series on 1/α leads to a quadratic dependence of the polaron energy. This approximation is justified for α ≈ 7.5...8 . For a two-parameter function f′ₖ, the corresponding dependence has the form Ep ≈ −0.125α². However, the use of approximate functionals, in contrast to the strict variational procedure, when the exact polaron functional varies, does not guarantee obtaining the upper limit for the polaron energy.
|
| first_indexed | 2026-03-21T04:33:54Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-214998 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1560-8034 |
| language | English |
| last_indexed | 2026-03-21T04:33:54Z |
| publishDate | 2017 |
| publisher | Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
| record_format | dspace |
| spelling | Kashirina, N.I. 2026-03-06T09:54:43Z 2017 Asymptotic dependence of Gross–Tulub polaron ground-state energy in the strong coupling region / N.I. Kashirina // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2017. — Т. 20, № 4. — С. 430-436. — Бібліогр.: 21 назв. — англ. 1560-8034 PACS: 71.38, 71.38.-k, 74.20.-z, 74.72-h https://nasplib.isofts.kiev.ua/handle/123456789/214998 https://doi.org/10.15407/spqeo20.04.430 The properties of the translationally invariant polaron functional have been investigated in the strong- and extremely-strong-coupling regimes. It has been shown that the Gross–Tulub polaron functional obtained earlier using field-theoretic methods was derived only for the region α ≤ 10, where α is the Fröhlich constant of the electron-phonon coupling. Various representations of exact and approximate polaron functionals have been considered. Asymptotic dependences of the polaron energy have been obtained using a functional extending the Gross–Tulub functional to the region of extremely strong coupling. The asymptotic dependence of polaron energies for an extremely strong coupling is Ep ≈ −0.31683α⁴/ ³ (for the one-parameter variational function fₖ), and Ep ≈ −0.31767α⁴/ ³ (for a two-parameter function f′ₖ ). It has been shown that the virial theorem 1:3:4 holds for the two-parameter function f′ₖ. Minimization of the approximate functional obtained by expanding the exact Gross–Tulub functional in a series on 1/α leads to a quadratic dependence of the polaron energy. This approximation is justified for α ≈ 7.5...8 . For a two-parameter function f′ₖ, the corresponding dependence has the form Ep ≈ −0.125α². However, the use of approximate functionals, in contrast to the strict variational procedure, when the exact polaron functional varies, does not guarantee obtaining the upper limit for the polaron energy. en Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України Semiconductor Physics Quantum Electronics & Optoelectronics Asymptotic dependence of Gross–Tulub polaron ground-state energy in the strong coupling region Article published earlier |
| spellingShingle | Asymptotic dependence of Gross–Tulub polaron ground-state energy in the strong coupling region Kashirina, N.I. |
| title | Asymptotic dependence of Gross–Tulub polaron ground-state energy in the strong coupling region |
| title_full | Asymptotic dependence of Gross–Tulub polaron ground-state energy in the strong coupling region |
| title_fullStr | Asymptotic dependence of Gross–Tulub polaron ground-state energy in the strong coupling region |
| title_full_unstemmed | Asymptotic dependence of Gross–Tulub polaron ground-state energy in the strong coupling region |
| title_short | Asymptotic dependence of Gross–Tulub polaron ground-state energy in the strong coupling region |
| title_sort | asymptotic dependence of gross–tulub polaron ground-state energy in the strong coupling region |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/214998 |
| work_keys_str_mv | AT kashirinani asymptoticdependenceofgrosstulubpolarongroundstateenergyinthestrongcouplingregion |