Evidence for correlated states in a cluster of bosons with Rashba spin-orbit coupling

We study the ground state properties of spin-half bosons subjected to the Rashba spin-orbit coupling in two dimensions. Due to the enhancement of the low energy density of states, it is expected that the effect of interaction becomes more important. After reviewing several possible ideal condensed states, we carry out an exact diagonalization calculation for a cluster of the bosons in the presence of strong spin-orbit coupling on a two-dimensional disk and reveal strong correlations in its ground state. We derive a low-energy effective Hamiltonian to understand how states with strong correlations become energetically more favorable than the ideal condensed states.Comment: 23 pages, 6 figure

Mott-Superfluid Transition for Spin-Orbit Coupled Bosons in One-Dimensional Optical Lattices

We study the effects of spin-orbit coupling on the Mott-superfluid transition of bosons in a one-dimensional optical lattice. We determine the strong coupling magnetic phase diagram by a combination of exact analytic and numerical means. Smooth evolution of the magnetic structure into the superfluid phases are investigated with the density matrix renormalization group technique. Novel magnetic phases are uncovered and phase transitions between them within the superfluid regime are discussed. Possible experimental detection are discussed.Comment: 5 pages, 4 figure

The Effects of Organic Products on Conventional Products and Retailer Assortment Planning

The rapid growth in organic products has posed a major challenge to conventional retailer assortment planning. On the one hand, conventional retailers, driven by the relatively high margins of organic products, have increased organic product offerings. On the other hand, the shelf space for conventional retailers has remained the same, with newly opened stores much smaller in sizes. Therefore, retailers need to carefully manage their conventional product assortments to harvest the benefit of offering and increasing organic product assortments. In order to manage the assortment efficiently, conventional retailers need to understand how organic products would affect their existing products, consumers, and supply chain relationships. From the two essays that comprise this dissertation, the first essay aims to explain how organic products would affect retailers’ conventional assortments, as well as how supply chain power would shift the connection between organic assortments and conventional assortment. The second essay estimates the substitution effect between organic products and conventional products, and how consumers choose between organic and conventional products while multiple other product attributes also present. Research questions proposed in the essays are answered by statistical analysis of difference-in-difference analysis, instrumental variable regressions, and structural estimations on retailer scanner panel data that contains weekly product sales over a 4-year time horizon. Our findings suggest that a market expansion effect due to the introduction and expansion of organic products outweighs the operational costs for increasing both organic and conventional assortments. However, the supply chain power structure between retailers and manufacturers as well as retailer shelf space constraints will shift the relationship between organic and conventional assortments. We also find that consumers are more price-sensitive in organic products, and organic condition, product style, and seller attributes are all highly influential in shaping consumers’ purchasing decisions