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Statistical, Nonlinear, and Soft Matter Physics Commons™
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Full-Text Articles in Statistical, Nonlinear, and Soft Matter Physics
Numerical Analysis Of Bose-Einstein Condensation In A Three-Dimensional Harmonic Oscillator Potential, Martin K. Ligare
Numerical Analysis Of Bose-Einstein Condensation In A Three-Dimensional Harmonic Oscillator Potential, Martin K. Ligare
Faculty Journal Articles
Bose–Einstein condensation is the anomalous accumulation of particles in the ground state of a system of bosons, when compared with the population in a system of particles obeying classical statistics. I use undergraduate-level statistical mechanics and a symbolic algebra computer program to study the occupation numbers of the energy levels of a finite number of noninteracting particles confined in a three-dimensional harmonic oscillator potential. I also calculate the heat capacity of the gas. The harmonic oscillator potential simplifies the calculations and approximates the conditions of the recent experiments achieving Bose–Einstein condensation in laser-cooled alkali vapors.
Applying Binomial Statistics To Weighted Monte Carlo, Sue Ellen Mccloskey, William C. Hall, Wilfred J. Braithwaite
Applying Binomial Statistics To Weighted Monte Carlo, Sue Ellen Mccloskey, William C. Hall, Wilfred J. Braithwaite
Journal of the Arkansas Academy of Science
Weighted Monte Carlo calculations requiring a uniform sampling of the problem-space can suffer from diminished statistical significance because many, if not most, of the randomly-chosen sampling points contribute only slightly to the desired result. Their contribution is reduced in size due the variable-size of the weighting terms. In contrast, none of the randomly-chosen points which are favored by variable size weighting terms will have their statistical significance enhanced beyond that of just one random point in the Monte Carlo sampling. A Monte Carlo analysis was used in earlier work to verify both Gauss' Law and Newton's Shell Theorem. Both examples …