On Dunkl-Bose-Einstein Condensation in Harmonic Traps
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arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866917764456775680 |
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| author | Hocine, A. Hamil, B. Merabtine, F. Lütfüoğlu, B. C. Benarous, M. |
| author_facet | Hocine, A. Hamil, B. Merabtine, F. Lütfüoğlu, B. C. Benarous, M. |
| contents | The use of the Dunkl derivative, which is defined by a combination of the difference-differential and reflection operator, allows the classification of the solutions according to even and odd solutions. Recently, we considered the Dunkl formalism to investigate the Bose-Einstein condensation of an ideal Bose gas confined in a gravitational field. In this work, we address a similar problem and examine an ideal Bose gas trapped by a three-dimensional harmonic oscillator within the Dunkl formalism. To this end, we derive an analytic expression for the critical temperature of the N particle system, discuss its value at large-N limit and finally derive and compare the ground state population with the usual case result. In addition, we explore two thermal quantities, namely the Dunkl-internal energy and the Dunkl-heat capacity functions. The Wigner parameter of the Dunkl formalism can be successfully used to obtain a better agreement between experimental and theoretical results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_10891 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On Dunkl-Bose-Einstein Condensation in Harmonic Traps Hocine, A. Hamil, B. Merabtine, F. Lütfüoğlu, B. C. Benarous, M. Quantum Gases Statistical Mechanics High Energy Physics - Theory The use of the Dunkl derivative, which is defined by a combination of the difference-differential and reflection operator, allows the classification of the solutions according to even and odd solutions. Recently, we considered the Dunkl formalism to investigate the Bose-Einstein condensation of an ideal Bose gas confined in a gravitational field. In this work, we address a similar problem and examine an ideal Bose gas trapped by a three-dimensional harmonic oscillator within the Dunkl formalism. To this end, we derive an analytic expression for the critical temperature of the N particle system, discuss its value at large-N limit and finally derive and compare the ground state population with the usual case result. In addition, we explore two thermal quantities, namely the Dunkl-internal energy and the Dunkl-heat capacity functions. The Wigner parameter of the Dunkl formalism can be successfully used to obtain a better agreement between experimental and theoretical results. |
| title | On Dunkl-Bose-Einstein Condensation in Harmonic Traps |
| topic | Quantum Gases Statistical Mechanics High Energy Physics - Theory |
| url | https://arxiv.org/abs/2308.10891 |