Some simple mathematica notebooks used for two generic purposes: calculating useful quantities or experimental rates in the context of ultracold bosonic atoms in optical lattices (bose-hubbard physics), or useful demonstration code for physical effects
Comparison of scattering rates in optical lattices. Involves both a numerical calculation compared to a theory prediction given the assumption of deep traps. This is then compared to experiments in the Li & Rb Experiments for the Greiner Lab at Harvard as there are some published measurements to be compared to.
Estimation of scattering rates in optical lattice with imperfect contrast due to non-unity reflection coefficients of substrate. Additional calculation that comes angle of incidence that determines this reflection from Fresnel coefficients. Contrast, DC offsets, and scattering rate estimtes based upon power and angle of incidence in notebook.
Description of scaling laws for particle number fluctuations and particle number entropy in finite, fixed particle number bose-hubbard systems at infinite temperature. This also distinguishes between scaling of of system size and sub-system size and what type of general formulation one should expect. In general this notebook should give some insight on how to make some generalizations about the thermal expectation of a bose-hubbard system and derive some simple scaling laws from it. Some distinguishing factors between many- and single-particle differences are mentioned towards end of notebook.
This provides the classical intuition for the classical hall effect that can be transferred to integer quantum hall effect.
This notebook draws a comparison between the density matrix approach and projective measurements of an atom from spontaneous emission of a photon. This monte-carlo approach and density matrix approach should overlap in the limit of many averages of the random sampling of the atom.
