Simulating an Anomalous Prediction of the Boltzmann Equation

Undergraduate Honors Thesis

Citations

Citeable URL: https://scholar.colorado.edu/concern/undergraduate_honors_theses/r207tq01m

Abstract

There is an anomalous prediction of the Boltzmann equation that monopole motion in an isotropic and harmonic potential will not damp. We have implemented a modification to our Time-Averaged Orbiting Potential (TOP) Trap, which we call the zzTOP Trap. Although this modification allows us to reach unprecedented levels of isotropy, it is still not perfectly isotropic. There are several methods of proving that the monopole motion in isotropic and harmonic potentials is undamped, but there are no analytic descriptions of monopole motion in slightly anharmonic and slightly anisotropic potentials. To this end, I have programmed a semi-classical Monte Carlo simulation to numerically predict dynamics of the monopole motion in slightly arbitrary potentials. In this thesis I will discuss Boltzmann’s prediction, introduce monopole and quadrupole motion, and describe and validate the simulation. Then I will investigate monopole and quadrupole shape oscillations in isotropic and harmonic potentials, anisotropic and harmonic potentials, and slightly anharmonic potentials. Finally I will compare dynamics of these motions from the simulation with results we have observed in our experiment.

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