2025-02-22T10:34:43-05:00 DEBUG: VuFindSearch\Backend\Solr\Connector: Query fl=%2A&wt=json&json.nl=arrarr&q=id%3A%22irk-123456789-121073%22&qt=morelikethis&rows=5
2025-02-22T10:34:43-05:00 DEBUG: VuFindSearch\Backend\Solr\Connector: => GET http://localhost:8983/solr/biblio/select?fl=%2A&wt=json&json.nl=arrarr&q=id%3A%22irk-123456789-121073%22&qt=morelikethis&rows=5
2025-02-22T10:34:43-05:00 DEBUG: VuFindSearch\Backend\Solr\Connector: <= 200 OK
2025-02-22T10:34:43-05:00 DEBUG: Deserialized SOLR response
How to solve Fokker-Planck equation treating mixed eigenvalue spectrum?
An analogy of the Fokker-Planck equation (FPE) with the Schrödinger equation allows us to use quantum mechanics technique to find the analytical solution of the FPE in a number of cases. However, previous studies have been limited to the Schrodinger potential with discrete eigenvalue spectrum. Here...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Інститут фізики конденсованих систем НАН України
2013
|
| Series: | Condensed Matter Physics |
| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/121073 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| id |
irk-123456789-121073 |
|---|---|
| record_format |
dspace |
| spelling |
irk-123456789-1210732017-06-14T03:05:11Z How to solve Fokker-Planck equation treating mixed eigenvalue spectrum? Brics, M. Kaupuzs, J. Mahnke, R. An analogy of the Fokker-Planck equation (FPE) with the Schrödinger equation allows us to use quantum mechanics technique to find the analytical solution of the FPE in a number of cases. However, previous studies have been limited to the Schrodinger potential with discrete eigenvalue spectrum. Here we will show how this approach can be applied also for mixed eigenvalue spectrum with bounded and free states. We solve the FPE with boundaries located at x=±L/2 and take the limit L→∞, considering examples with constant Schrödinger potential and with Pöschl-Teller potential. An oversimplified approach has been earlier proposed by M.T. Araujo and E. Drigo Filho. A detailed investigation of the two examples shows that the correct solution, obtained in this paper, is consistent with the expected Fokker-Planck dynamics. Аналогiя рiвняння Фоккера-Планка (FPE) з рiвнянням Шредингера дозволяє використати метод квантової механiки для знаходження аналiтичного розв’язку FPE для низки випадкiв. Проте, попереднi дослiдження обмежувалися потенцiалом Шредингера з дискретним спектром власних значень. Тут ми покажемо, як цей пiдхiд можна також застосувати до спектру змiшаних власних значень зi зв’язаними i вiльними станами. Ми розв’язуємо FPE з границями, що знаходяться при x = ±L/2 i беремо границю L → ∞, розглядаючи приклади з постiйним потенцiалом Шредингера i потанцiалом Пешля-Теллера. Спрощений пiдхiд ранiше запропонували M.T. Араухо та E. Дрiго Фiльйо. Детальне дослiдження двох прикладiв показує, що коректний розв’язок, отриманий в цiй статтi, узгоджується з очiкуваною динамiкою Фоккера-Планка. 2013 Article How to solve Fokker-Planck equation treating mixed eigenvalue spectrum? / M. Brics, J. Kaupuzs, R. Mahnke // Condensed Matter Physics. — 2013. — Т. 16, № 1. — С.13002:1–13. — Бібліогр.: 13 назв. — англ. 1607-324X PACS: 05.10.Gg DOI:10.5488/CMP.16.13002 arXiv:1303.5211 http://dspace.nbuv.gov.ua/handle/123456789/121073 en Condensed Matter Physics Інститут фізики конденсованих систем НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
An analogy of the Fokker-Planck equation (FPE) with the Schrödinger equation allows us to use quantum mechanics technique to find the analytical solution of the FPE in a number of cases. However, previous studies have been limited to the Schrodinger potential with discrete eigenvalue spectrum. Here we will show how this approach can be applied also for mixed eigenvalue spectrum with bounded and free states. We solve the FPE with boundaries located at x=±L/2 and take the limit L→∞, considering examples with constant Schrödinger potential and with Pöschl-Teller potential. An oversimplified approach has been earlier proposed by M.T. Araujo and E. Drigo Filho. A detailed investigation of the two examples shows that the correct solution, obtained in this paper, is consistent with the expected Fokker-Planck dynamics. |
| format |
Article |
| author |
Brics, M. Kaupuzs, J. Mahnke, R. |
| spellingShingle |
Brics, M. Kaupuzs, J. Mahnke, R. How to solve Fokker-Planck equation treating mixed eigenvalue spectrum? Condensed Matter Physics |
| author_facet |
Brics, M. Kaupuzs, J. Mahnke, R. |
| author_sort |
Brics, M. |
| title |
How to solve Fokker-Planck equation treating mixed eigenvalue spectrum? |
| title_short |
How to solve Fokker-Planck equation treating mixed eigenvalue spectrum? |
| title_full |
How to solve Fokker-Planck equation treating mixed eigenvalue spectrum? |
| title_fullStr |
How to solve Fokker-Planck equation treating mixed eigenvalue spectrum? |
| title_full_unstemmed |
How to solve Fokker-Planck equation treating mixed eigenvalue spectrum? |
| title_sort |
how to solve fokker-planck equation treating mixed eigenvalue spectrum? |
| publisher |
Інститут фізики конденсованих систем НАН України |
| publishDate |
2013 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/121073 |
| citation_txt |
How to solve Fokker-Planck equation treating mixed eigenvalue spectrum? / M. Brics, J. Kaupuzs, R. Mahnke // Condensed Matter Physics. — 2013. — Т. 16, № 1. — С.13002:1–13. — Бібліогр.: 13 назв. — англ. |
| series |
Condensed Matter Physics |
| work_keys_str_mv |
AT bricsm howtosolvefokkerplanckequationtreatingmixedeigenvaluespectrum AT kaupuzsj howtosolvefokkerplanckequationtreatingmixedeigenvaluespectrum AT mahnker howtosolvefokkerplanckequationtreatingmixedeigenvaluespectrum |
| first_indexed |
2023-10-18T20:37:53Z |
| last_indexed |
2023-10-18T20:37:53Z |
| _version_ |
1796150707938656256 |