Correction of The Ground State Energy of One-Dimensional Gross-Pitaevskii Equation with Gain-Loss Term
| Main Author: | Teguh Budi Prayitno; Physics Department, Faculty of Mathematics and Natural Science, Universitas Negeri Jakarta, Jakarta 13220 |
|---|---|
| Format: | Article application/pdf eJournal |
| Bahasa: | eng |
| Terbitan: |
Directorate of Research and Community Engagement, Universitas Indonesia
, 2012
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| Subjects: | |
| Online Access: |
http://journal.ui.ac.id/index.php/science/article/view/1071 |
| ctrlnum |
article-1071 |
|---|---|
| fullrecord |
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<dc schemaLocation="http://www.openarchives.org/OAI/2.0/oai_dc/ http://www.openarchives.org/OAI/2.0/oai_dc.xsd"><title lang="en-US">Correction of The Ground State Energy of One-Dimensional Gross-Pitaevskii Equation with Gain-Loss Term</title><creator>Teguh Budi Prayitno; Physics Department, Faculty of Mathematics and Natural Science, Universitas Negeri Jakarta, Jakarta 13220</creator><subject lang="en-US">Bose-Einstein condensation; Gross-Pitaevskii; quantum oscillator</subject><subject lang="en-US"/><description lang="en-US">We consider the correction of ground state energy of one-dimensional Gross-Pitaevskii equation by adding a gain-loss term as a time-dependent external potential. The interesting purpose of this term is that it can be used to explain the experimental results especially in the nonlinear fiber optics regarding the pulse propagation and collapse-revival of the condensate in the Bose-Einstein condensation. In the Bose-Einstein condensation itself, the function can represent that condensate can interact with the normal atomic cloud. Some analytical solutions have been obtained by choosing an ansatz solution of the wave function and its solution can be dark or bright soliton. Since the Gross-Pitaevskii equation can be treated as a macroscopic quantum oscillator, we can use time-dependent perturbation theory as in ordinary quantum mechanics to find the ground state energy correction if we assume other terms to be very small. In addition, time-dependent potential allows a transition from one energy level to others. In this case, we expand the solution of nonstationary one-dimensional wave function as a linear superposition of harmonic oscillator normalized eigen functions. To get the recursive formulas, we suggest an option to formulate the coefficients after inserting the initial condition which must be satisfied such as in quantum mechanics.</description><publisher lang="en-US">Directorate of Research and Community Engagement, Universitas Indonesia</publisher><contributor lang="en-US"/><date>2012-03-28</date><type>Journal:Article</type><type>File:application/pdf</type><identifier>http://journal.ui.ac.id/index.php/science/article/view/1071</identifier><source lang="en-US">Makara Journal of Science; Vol 15, No 2 (2011): November; 197-200</source><language>eng</language><recordID>article-1071</recordID></dc>
|
| language |
eng |
| format |
Journal:Article Journal File:application/pdf File Journal:eJournal |
| author |
Teguh Budi Prayitno; Physics Department, Faculty of Mathematics and Natural Science, Universitas Negeri Jakarta, Jakarta 13220 |
| title |
Correction of The Ground State Energy of One-Dimensional Gross-Pitaevskii Equation with Gain-Loss Term |
| publisher |
Directorate of Research and Community Engagement, Universitas Indonesia |
| publishDate |
2012 |
| topic |
Bose-Einstein condensation Gross-Pitaevskii quantum oscillator |
| url |
http://journal.ui.ac.id/index.php/science/article/view/1071 |
| contents |
We consider the correction of ground state energy of one-dimensional Gross-Pitaevskii equation by adding a gain-loss term as a time-dependent external potential. The interesting purpose of this term is that it can be used to explain the experimental results especially in the nonlinear fiber optics regarding the pulse propagation and collapse-revival of the condensate in the Bose-Einstein condensation. In the Bose-Einstein condensation itself, the function can represent that condensate can interact with the normal atomic cloud. Some analytical solutions have been obtained by choosing an ansatz solution of the wave function and its solution can be dark or bright soliton. Since the Gross-Pitaevskii equation can be treated as a macroscopic quantum oscillator, we can use time-dependent perturbation theory as in ordinary quantum mechanics to find the ground state energy correction if we assume other terms to be very small. In addition, time-dependent potential allows a transition from one energy level to others. In this case, we expand the solution of nonstationary one-dimensional wave function as a linear superposition of harmonic oscillator normalized eigen functions. To get the recursive formulas, we suggest an option to formulate the coefficients after inserting the initial condition which must be satisfied such as in quantum mechanics. |
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IOS2206.article-1071 |
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Universitas Indonesia |
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51 |
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library:university library |
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Perpustakaan Universitas Indonesia |
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492 |
| collection |
MAKARA of Science Series |
| repository_id |
2206 |
| city |
KOTA DEPOK |
| province |
JAWA BARAT |
| repoId |
IOS2206 |
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2016-09-24T00:14:09Z |
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2016-09-24T00:20:37Z |
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17.60897 |