Refined Simulations of the Reaction Front for Diffusion-Limited Two-Species Annihilation in One Dimension

Extensive simulations are performed of the diffusion-limited reaction A$+$B$\to 0$ in one dimension, with initially separated reagents. The reaction rate profile, and the probability distributions of the separation and midpoint of the nearest-neighbour pair of A and B particles, are all shown to exhibit dynamic scaling, independently of the presence of fluctuations in the initial state and of an exclusion principle in the model. The data is consistent with all lengthscales behaving as $t^{1/4}$ as $t\to\infty$. Evidence of multiscaling, found by other authors, is discussed in the light of these findings.Comment: Resubmitted as TeX rather than Postscript file. RevTeX version 3.0, 10 pages with 16 Encapsulated Postscript figures (need epsf). University of Geneva preprint UGVA/DPT 1994/10-85

Critical Temperature of a Trapped Bose Gas: Mean-Field Theory and Fluctuations

We investigate the possibilities of distinguishing the mean-field and fluctuation effects on the critical temperature of a trapped Bose gas with repulsive interatomic interactions. Since in a direct measurement of the critical temperature as a function of the number of trapped atoms these effects are small compared to the ideal gas results, we propose to observe Bose-Einstein condensation by adiabatically ramping down the trapping frequency. Moreover, analyzing this adiabatic cooling scheme, we show that fluctuation effects can lead to the formation of a Bose condensate at frequencies which are much larger than those predicted by the mean-field theory.Comment: 4 pages of ReVTeX and 3 figures. Submitted to Physical Review

The Mystery of the Ramsey Fringe that Didn't Chirp

We use precision microwave spectroscopy of magnetically trapped, ultra-cold 87Rb to characterize intra- and inter-state density correlations. The cold collision shifts for both normal and condensed clouds are measured. The results verify the presence of the sometimes controversial "factors of two", in normal-cloud mean-field energies, both within a particular state and between two distinct spin species. One might expect that as two spin species decohere, the inter-state factor of two would revert to unity, but the associated frequency chirp one naively expects from such a trend is not observed in our data.Comment: Proceedings of the 18th International Conference on Atomic Physics (ICAP 2002

Decoherence-driven Cooling of a Degenerate Spinor Bose Gas

We investigate the relationship between the coherence of a partially Bose-condensed spinor gas and its temperature. We observe cooling of the normal component driven by decoherence as well the effect of temperature on decoherence rates.Comment: 4 pages, 2 figure

The Reaction-Diffusion Front for A+B→∅A+B \to\emptyset in One Dimension

We study theoretically and numerically the steady state diffusion controlled reaction $A+B\rightarrow\emptyset$, where currents $J$ of $A$ and $B$ particles are applied at opposite boundaries. For a reaction rate $\lambda$, and equal diffusion constants $D$, we find that when $\lambda J^{-1/2} D^{-1/2}\ll 1$ the reaction front is well described by mean field theory. However, for $\lambda J^{-1/2} D^{-1/2}\gg 1$, the front acquires a Gaussian profile - a result of noise induced wandering of the reaction front center. We make a theoretical prediction for this profile which is in good agreement with simulation. Finally, we investigate the intrinsic (non-wandering) front width and find results consistent with scaling and field theoretic predictions.Comment: 11 pages, revtex, 4 separate PostScript figure

Normal-superfluid interaction dynamics in a spinor Bose gas

Coherent behavior of spinor Bose-Einstein condensates is studied in the presence of a significant uncondensed (normal) component. Normal-superfluid exchange scattering leads to a near-perfect local alignment between the spin fields of the two components. Through this spin locking, spin-domain formation in the condensate is vastly accelerated as the spin populations in the condensate are entrained by large-amplitude spin waves in the normal component. We present data evincing the normal-superfluid spin dynamics in this regime of complicated interdependent behavior.Comment: 5 pages, 4 fig

Current Educational Publications

Current Educational Publications: The Place of Intelligence Among Human Endowments; A Royal Road in Number Wor

Ground State Asymptotics of a Dilute, Rotating Gas

We investigate the ground state properties of a gas of interacting particles confined in an external potential in three dimensions and subject to rotation around an axis of symmetry. We consider the so-called Gross-Pitaevskii (GP) limit of a dilute gas. Analyzing both the absolute and the bosonic ground state of the system we show, in particular, their different behavior for a certain range of parameters. This parameter range is determined by the question whether the rotational symmetry in the minimizer of the GP functional is broken or not. For the absolute ground state, we prove that in the GP limit a modified GP functional depending on density matrices correctly describes the energy and reduced density matrices, independent of symmetry breaking. For the bosonic ground state this holds true if and only if the symmetry is unbroken.Comment: LaTeX2e, 37 page

Diffusion-controlled annihilation A+B→0A + B \to 0 with initially separated reactants: The death of an AA particle island in the BB particle sea

We consider the diffusion-controlled annihilation dynamics $A+B\to 0$ with equal species diffusivities in the system where an island of particles $A$ is surrounded by the uniform sea of particles $B$. We show that once the initial number of particles in the island is large enough, then at any system's dimensionality $d$ the death of the majority of particles occurs in the {\it universal scaling regime} within which $\approx 4/5$ of the particles die at the island expansion stage and the remaining $\approx 1/5$ at the stage of its subsequent contraction. In the quasistatic approximation the scaling of the reaction zone has been obtained for the cases of mean-field ($d \geq d_{c}$) and fluctuation ($d < d_{c}$) dynamics of the front.Comment: 4 RevTex pages, 1 PNG figure and 1 EPS figur