The mesoscopic effects in the quantum trapped gases of the Bose atoms constitute
the main subject of the present thesis. These effects are the most difficult for
the theoretical analysis in the quantum statistical physics since they can’t be seen by
neither a standard quantum mechanics of the simple microscopic systems of one or
very few atoms nor a standard statistical physics of the macroscopic systems that are
infinite in the bulk (thermodynamic) limit.
Most of the experiments on the cold quantum gases performed in the last decade,
starting from the first demonstration of BEC in 1995, involve the mesoscopic systems
of a finite number of atoms. The mesoscopic effects should manifest themselves most
clearly and easily near a critical temperature of BEC; however, they could be observed
also above and below the critical temperature.
Here I study the quantum and thermal fluctuations of the Bose-Einstein condensate
(BEC) in a box with the periodic boundary conditions under a particle-number
constraint. The above constraint is the only reason for the BEC and is crucial for the
mesoscopic effects in the BEC fluctuations, especially in the vicinity of the critical
temperature in the Bose gas.
I employ the particle-number conserving operator formalism of Girardeau and
Arnowitt introduced in 1959 to analyze the canonical ensemble fluctuations. I present
analytical formulas and numerical calculations for the central moments of the ground
state occupation fluctuations in an ideal Bose gas in a box with a mesoscopic number of particles.
I present the analysis of the BEC statistics both on a temperature at a fixed
number of particles and on a number of particles at a fixed temperature. Both analyses
are valid for the purpose of understanding the important mesoscopic effects near the
critical temperature. I emphasize the non-Gaussian nature of the fluctuations.
The presented formalism can be generalized to the case of a weakly interacting
Bose gas in a box in the framework of the Bogoliubov approximation. The work in
this direction is in progress but is not included in the present thesis.
| Identifer | oai:union.ndltd.org:tamu.edu/oai:repository.tamu.edu:1969.1/ETD-TAMU-3040 |
| Date | 15 May 2009 |
| Creators | Dorfman, Konstantin Evgenievich |
| Contributors | Kocharovsky, Vitaly V. |
| Source Sets | Texas A and M University |
| Language | en_US |
| Detected Language | English |
| Type | Book, Thesis, Electronic Thesis, text |
| Format | electronic, application/pdf, born digital |
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