Chemical potential for the Bose gases in a one-dimensional harmonic trap

Liu, T G; Niu, Meng; Liu, Q H

doi:10.1088/0143-0807/31/3/l01

Cited by 2 publications

(1 citation statement)

References 3 publications

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“…After the experimental realization of Bose-Einstein condensates (BEC) in harmonic confinements in 1995, quantum statistics for the bosonic or fermionic linear harmonic oscillators has received renewed theoretical interest partly because they provide experimentally controllable BECs of the nonuniform thermodynamic systems [2,11,15,16]). Well-established theorems and relations for the uniform systems can not be used without justification.…”

Section: Introductionmentioning

confidence: 99%

Crossover from Quantum to Boltzmann Statistics for Free Particles in a Single Harmonic Trap

et al. 2011

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With invoking analytical formulae in number theory and numerical calculations, we calculate the number of microstates in microcanonical ensemble for free particles in a single harmonic trap which in whole space defines a thermodynamic system but not a spatially homogeneous one. Once the number of excitation quanta m is larger than the square of the particle number N 2 as m O(N 2 ) when N 1, the number of microcanonical microstates for an ideal, harmonically trapped Bose or Fermi gas gradually converge to the Boltzmann microcanonical microstates for the classical particles with a proper consideration of the indistinguishability.

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Section: Introductionmentioning

confidence: 99%

Crossover from Quantum to Boltzmann Statistics for Free Particles in a Single Harmonic Trap

et al. 2011

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Application of oil and dye flow visualization in incompressible turbomachinery flows

et al. 2022

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Flow visualization is one of many available tools in experimental fluid mechanics and is used from the primary stages of fluid mechanics research in order to identify the physical sizes and locations of the flow features under consideration. Most of the fluids used in engineering applications are transparent (water, air, etc) and flow visualization techniques are used in order to make their flow patterns visible. Simple flow visualization experiments are relatively inexpensive and they can be easily implemented providing with a first feeling of the characteristics of the flow domain. Subsequently, flow visualization techniques are of great applicability in complex flow fields and especially in turbomachinery applications where the flow is characterized by three dimensional and secondary flow patterns. In general, fluid motion can be visualized by surface flow visualization, by particle tracer methods or by optical methods. The former flow visualization technique reveals the streamlines of fluid flows around a solid surface. In this paper flow visualization techniques applied in two different cases of experimental testing (fans in crossflow and cascade experiment) are presented. In both cases, the mixture of paint was prepared using a highly volatile light mineral or heavy machine oil of viscosities of approximately 100cP and 200cP, respectively, together with very fine pigments of Titanium Dioxide (TiO2) or fluorescein sodium in various colors. After the preparation of the mixture, a homogenous thin film was applied onto the whole plate surface by painting it with a soft brush. The air stream which flows over the surface of the plate, modifies the concentration and the homogeneity of the oil film, according to the flow conditions very close to the wall. The film was dried by the airflow and photographed for further consideration while the time taken for drying depended on the wind tunnel velocity as well as, on the pigmentation of the mixture. Successful and un-successful flow visualization tests are herein presented while each case is respectively commented as far as the mixtures, the proportions used and the application onto the rigs are concerned.

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Chemical potential for the Bose gases in a one-dimensional harmonic trap

Cited by 2 publications

References 3 publications

Crossover from Quantum to Boltzmann Statistics for Free Particles in a Single Harmonic Trap

Crossover from Quantum to Boltzmann Statistics for Free Particles in a Single Harmonic Trap

Application of oil and dye flow visualization in incompressible turbomachinery flows

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