Magnetic Feshbach resonances in collisions of non-magnetic closed-shell 1Σ^1Σ molecules

Magnetic Feshbach resonances play a central role in experimental research of atomic gases at ultracold temperatures, as they allow one to control the microscopic interactions between ultracold atoms by tuning an applied magnetic field. These resonances arise due to strong hyperfine interactions between the unpaired electron and the nuclear magnetic moment of the alkali metal atoms. A major thrust of current research is to create an ultracold gas of diatomic alkali-metal molecules in the ground rovibrational state of the ground electronic $^1\Sigma$ state. Unlike alkali metal atoms, $^1\Sigma$ diatomic molecules have no unpaired electrons. However, the hyperfine interactions of molecules may give rise to magnetic Feshbach resonances. We use quantum scattering calculations to study the possible width of these resonances. Our results show that the widths of magnetic Feshbach resonances in ultracold molecule-molecule collisions for $^1\Sigma$ molecules may exceed 1 milliGauss, rendering such resonances experimentally detectable. We hope that this work will stimulate the experimental search of these resonances

Rotational predissociation of extremely weakly bound atom-molecule complexes produced by Feshbach resonance association

We study the rotational predissociation of atom - molecule complexes with very small binding energy. Such complexes can be produced by Feshbach resonance association of ultracold molecules with ultracold atoms. Numerical calculations of the predissociation lifetimes based on the computation of the energy dependence of the scattering matrix elements become inaccurate when the binding energy is smaller than the energy width of the predissociating state. We derive expressions that represent accurately the predissociation lifetimes in terms of the real and imaginary parts of the scattering length and effective range for molecules in an excited rotational state. Our results show that the predissociation lifetimes are the longest when the binding energy is positive, i.e. when the predissociating state is just above the excited state threshold

Optically induced conical intersections in traps for ultracold atoms and molecules

We show that conical intersections can be created in laboratory coordinates by dressing a parabolic trap for ultracold atoms or molecules with a combination of optical and static magnetic fields. The resulting ring trap can support single-particle states with half-integer rotational quantization and many-particle states with persistent flow. Two well-separated atomic or molecular states are brought into near-resonance by an optical field and tuned across each other with an inhomogeneous magnetic field. Conical intersections occur at the nodes in the optical field

The prospects of sympathetic cooling of NH molecules with Li atoms

We calculate the quartet potential energy surface for Li+NH and use it to calculate elastic and spin-relaxation cross sections for collisions in magnetically trappable spin-stretched states. The potential is strongly anisotropic but spin-relaxation collisions are still suppressed by centrifugal barriers when both species are in spin-stretched states. In the ultracold regime, both the elastic and inelastic cross sections fluctuate dramatically as the potential is varied because of Feshbach resonances. The potential-dependence is considerably reduced at higher energies. The major effect of using an unconverged basis set in the scattering calculations is to shift the resonances without changing their general behaviour. We have calculated the ratio of elastic and spin-relaxation cross sections, as a function of collision energy and magnetic field, for a variety of potential energy surfaces. Most of the surfaces produce ratios that are favorable for sympathetic cooling, at temperatures below about 20 mK

Multichannel Quantum Defect Theory for cold molecular collisions

Multichannel Quantum Defect Theory (MQDT) is shown to be capable of producing quantitatively accurate results for low-energy atom-molecule scattering calculations. With a suitable choice of reference potential and short-range matching distance, it is possible to define a matrix that encapsulates the short-range collision dynamics and is only weakly dependent on energy and magnetic field. Once this has been produced, calculations at additional energies and fields can be performed at a computational cost that is proportional to the number of channels N and not to N^3. MQDT thus provides a promising method for carrying out low-energy molecular scattering calculations on systems where full exploration of the energy- and field-dependence is currently impractical

Production of Ultracold NH Molecules by Sympathetic Cooling with Mg

We show that sympathetic cooling of NH molecules by Mg atoms has a good prospect of success. We carry out calculations on M-changing collisions of NH (3Σ-) molecules in magnetically trappable states with Mg, using a recently calculated potential energy surface. We show that elastic collision rates are much faster than inelastic rates for a wide range of fields at temperatures up to 10 mK and that the ratio increases for lower temperatures and magnetic fields

Extracting complements and substitutes from sales data: a network perspective

The complementarity and substitutability between products are essential concepts in retail and marketing. Qualitatively, two products are said to be substitutable if a customer can replace one product by the other, while they are complementary if they tend to be bought together. In this article, we take a network perspective to help automatically identify complements and substitutes from sales transaction data. Starting from a bipartite product-purchase network representation, with both transaction nodes and product nodes, we develop appropriate null models to infer significant relations, either complements or substitutes, between products, and design measures based on random walks to quantify their importance. The resulting unipartite networks between products are then analysed with community detection methods, in order to find groups of similar products for the different types of relationships. The results are validated by combining observations from a real-world basket dataset with the existing product hierarchy, as well as a large-scale flavour compound and recipe dataset

Minimizing congestion in single-source, single-sink queueing networks

Motivated by the modeling of customer mobility and congestion in supermarkets, we study queueing networks with a single source and a single sink. We assume that walkers traverse a network according to an unbiased random walk, and we analyze how network topology affects the total mean queue size Q, which we use to measure congestion. We examine network topologies that minimize Q and provide proofs of optimality for some cases and numerical evidence of optimality for others. Finally, we present greedy algorithms that add and delete edges from a network to reduce Q, and we apply these algorithms to a supermarket store layout. We find that these greedy algorithms, which typically tend to add edges to the sink node, are able to significantly reduce Q. Our work helps improve understanding of how to design networks with low congestion and to amend networks to reduce congestion