Fluctuation statistics of mesoscopic Bose-Einstein condensates: reconciling the master equation with the partition function to reexamine the Uhlenbeck-Einstein dilemma
The atom fluctuation statistics of an ideal, mesoscopic, Bose-Einstein condensate are investigated from several different perspectives. By generalizing the grand canonical analysis (applied to the canonical ensemble problem), we obtain a self-consistent equation for the mean condensate particle numb...
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my.um.eprints.79332019-10-09T00:48:22Z http://eprints.um.edu.my/7933/ Fluctuation statistics of mesoscopic Bose-Einstein condensates: reconciling the master equation with the partition function to reexamine the Uhlenbeck-Einstein dilemma Ooi, Chong Heng Raymond Svidzinsky, A.A. Jordan, A.N. QC Physics The atom fluctuation statistics of an ideal, mesoscopic, Bose-Einstein condensate are investigated from several different perspectives. By generalizing the grand canonical analysis (applied to the canonical ensemble problem), we obtain a self-consistent equation for the mean condensate particle number that coincides with the microscopic result calculated from the laser master equation approach. For the case of a harmonic trap, we obtain an analytic expression for the condensate particle number that is very accurate at all temperatures, when compared with numerical canonical ensemble results. Applying a similar generalized grand canonical treatment to the variance, we obtain an accurate result only below the critical temperature. Analytic results are found for all higher moments of the fluctuation distribution by employing the stochastic path integral formalism, with excellent accuracy. We further discuss a hybrid treatment, which combines the master equation and stochastic path integral analysis with results obtained based on the canonical ensemble quasiparticle formalism [Kocharovsky , Phys. Rev. A 61, 053606 (2000)], producing essentially perfect agreement with numerical simulation at all temperatures. 2006 Article PeerReviewed Ooi, Chong Heng Raymond and Svidzinsky, A.A. and Jordan, A.N. (2006) Fluctuation statistics of mesoscopic Bose-Einstein condensates: reconciling the master equation with the partition function to reexamine the Uhlenbeck-Einstein dilemma. Physical Review A, 74 (3). ISSN 1050-2947 http://pra.aps.org/abstract/PRA/v74/i3/e032506 10.1103/PhysRevA.74.032506 |
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QC Physics Ooi, Chong Heng Raymond Svidzinsky, A.A. Jordan, A.N. Fluctuation statistics of mesoscopic Bose-Einstein condensates: reconciling the master equation with the partition function to reexamine the Uhlenbeck-Einstein dilemma |
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The atom fluctuation statistics of an ideal, mesoscopic, Bose-Einstein condensate are investigated from several different perspectives. By generalizing the grand canonical analysis (applied to the canonical ensemble problem), we obtain a self-consistent equation for the mean condensate particle number that coincides with the microscopic result calculated from the laser master equation approach. For the case of a harmonic trap, we obtain an analytic expression for the condensate particle number that is very accurate at all temperatures, when compared with numerical canonical ensemble results. Applying a similar generalized grand canonical treatment to the variance, we obtain an accurate result only below the critical temperature. Analytic results are found for all higher moments of the fluctuation distribution by employing the stochastic path integral formalism, with excellent accuracy. We further discuss a hybrid treatment, which combines the master equation and stochastic path integral analysis with results obtained based on the canonical ensemble quasiparticle formalism [Kocharovsky , Phys. Rev. A 61, 053606 (2000)], producing essentially perfect agreement with numerical simulation at all temperatures. |
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Article |
author |
Ooi, Chong Heng Raymond Svidzinsky, A.A. Jordan, A.N. |
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Ooi, Chong Heng Raymond Svidzinsky, A.A. Jordan, A.N. |
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Ooi, Chong Heng Raymond |
title |
Fluctuation statistics of mesoscopic Bose-Einstein condensates: reconciling the master equation with the partition function to reexamine the Uhlenbeck-Einstein dilemma |
title_short |
Fluctuation statistics of mesoscopic Bose-Einstein condensates: reconciling the master equation with the partition function to reexamine the Uhlenbeck-Einstein dilemma |
title_full |
Fluctuation statistics of mesoscopic Bose-Einstein condensates: reconciling the master equation with the partition function to reexamine the Uhlenbeck-Einstein dilemma |
title_fullStr |
Fluctuation statistics of mesoscopic Bose-Einstein condensates: reconciling the master equation with the partition function to reexamine the Uhlenbeck-Einstein dilemma |
title_full_unstemmed |
Fluctuation statistics of mesoscopic Bose-Einstein condensates: reconciling the master equation with the partition function to reexamine the Uhlenbeck-Einstein dilemma |
title_sort |
fluctuation statistics of mesoscopic bose-einstein condensates: reconciling the master equation with the partition function to reexamine the uhlenbeck-einstein dilemma |
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2006 |
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http://eprints.um.edu.my/7933/ http://pra.aps.org/abstract/PRA/v74/i3/e032506 |
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1648736104243789824 |