Mean-field theory of Feshbach-resonant interactions in 85Rb condensates

Recent Feshbach-resonance experiments with 85Rb Bose-Einstein condensates have led to a host of unexplained results: dramatic losses of condensate atoms for an across-resonance sweep of the magnetic field, a collapsing condensate with a burst of atoms emanating from the remnant condensate, increased losses for decreasing interaction times, and coherent oscillations between remnant and burst atoms. Using a simple yet realistic mean-field model, we find that rogue dissociation, molecular dissociation to noncondensate atom pairs, is strongly implicated as the physical mechanism responsible for these observations.     

Optical detection of fractional particle number in an atomic Fermi-Dirac gas

We study theoretically a Fermi-Dirac atomic gas in a one-dimensional optical lattice coupled to a coherent electromagnetic field with a topologically nontrivial soliton phase profile. We argue that the resulting fractional eigenvalues of the particle number operator can be detected via light scattering. This could be a truly quantum mechanical measurement of particle number fractionalization in a dilute atomic gas.     

Walsh's Brownian Motion-Type of Extensions

Let (X _t ) be a rotation invariant Feller process on the state space F R²{} consisting of finite number of rays, meeting at 0. We study a certain class of possible strong Markov extensions of (X _t ) to F ,{} given the corresponding radial extension to [0, ). A well-known example is the class of Walsh's Brownian motions, in the case where (X _t ) is the Brownian motion on F. It turns out that while the symmetric extension of Walsh's Brownian motion-type always exists, the non-symmetric extension exists iff (X _t ), roughly speaking, does not jump from one ray to another before hitting 0.     

Unique representation in number systems and L codes

An algorithm is presented for deciding whether or not the representation according to a given number system is unique.     

Determination of antimony in geochemical samples by graphite furnace atomic absorption spectrometry using different matrix modifiers

Determination of antimony by graphite furnace atomic absorption spectrometry using five different matrix modifiers, viz. nitric acid, copper, nickel, molybdenum and palladium, together with L'vov platform was studied. Without matrix modification, antimony was lost in a 1.2-M HCl solution when the thermal pretreatment temperature exceeded 700°C. By using 1.4 M HNO₃ or $\text{1μg}\text{20μl}$ copper solution the thermal pretreatment temperature could be increased up to 900°C. The matrix modification with $\text{2μg}\text{20μl}$ palladium, $\text{4μg}\text{20μl}$ molybdenum, or $\text{20μg}\text{20μl}$ nickel allowed the use of 1300°C as the pretreatment temperature. The best results were obtained with palladium when its concentration exceeded $\text{0.8μg}\text{20μl}$. Chemical interferences were studied with standard solutions spiked with different metal chlorides. The severe interference caused by iron chloride was avoided with ascorbic acid (2.5 %, $\text{w}\text{v}$). The method was tested on some geochemical reference samples.     

Variational principles for differential equations with symmetries and conservation laws

This research was supported in part by NSF grant DMS 91-00674     

4-Aryl-8-hydroxyquinolines from 4-chloro-8-tosyloxyquinoline using a Suzuki-Miyaura cross-coupling approach

4-Chloro-8-tosyloxyquinoline was successfully cross-coupled with various arylboronic acids in anhydrous Suzuki-Miyaura conditions. The protective tosyl group was stable during the anhydrous coupling. The use of tosyl protection in association with anhydrous Suzuki-Miyaura reaction conditions allows the use of commercially available but relative inert 5-chloro-8-hydroxyquinoline for the synthesis of 5-phenyl-8-hydroxyquinoline. Deprotection could easily be made by using suitable nucleophiles to afford the final 5-phenyl and 4-aryl-8-hydroxyquinolines in high yields. Under acidic conditions the tosyloxy group is sufficiently stable to allow selective further modification of acid labile functional groups.