Critical behaviours of contact near phase transitions

A central quantity of importance for ultracold atoms is contact, which measures two-body correlations at short distances in dilute systems. It appears in universal relations among thermodynamic quantities, such as large momentum tails, energy, and dynamic structure factors, through the renowned Tan relations. However, a conceptual question remains open as to whether or not contact can signify phase transitions that are insensitive to short-range physics. Here we show that, near a continuous classical or quantum phase transition, contact exhibits a variety of critical behaviors, including scaling laws and critical exponents that are uniquely determined by the universality class of the phase transition and a constant contact per particle. We also use a prototypical exactly solvable model to demonstrate these critical behaviors in one-dimensional strongly interacting fermions. Our work establishes an intrinsic connection between the universality of dilute many-body systems and universal critical phenomena near a phase transition.Comment: Final version published in Nat. Commun. 5:5140 doi: 10.1038/ncomms6140 (2014

Optimality of feedback control for qubit purification under inefficient measurement

A quantum system may be purified, i.e., projected into a pure state, faster if one applies feedback operations during the measurement process. However, the existing results suggest that such an enhancement is only possible when the measurement efficiency exceeds 0.5, which is difficult to achieve experimentally. We address the task of finding the global optimal feedback control for purifying a single qubit in the presence of measurement inefficiency. We use the Bloch vector length, a more physical and practical quantity than purity, to assess the quality of the state, and employ a backward-iteration algorithm to find the globally optimal strategy. Our results show that a speedup is available for quantum efficiencies well below 0.5, which opens the possibility of experimental implementation in existing systems

Adoption of e-commerce by the agri-food sector in China: the case of Minyu e-commerce company

In recent years, increasing numbers of smallholders in developing countries such as China have begun to sell agricultural products directly to consumers via online shops using a third-party trade platform. It is increasingly clear that e-commerce has become a new and effective way to help smallholders gain access to the market. The investigation of agricultural e-commerce practices has a significant role in helping to understand the development of the agri-food sector in China. This teaching case provides an example of adopting e-commerce in the interaction and trading activities between participants in the food sector through a typical agricultural products e-commerce company in China, Minyu E-commerce. Particularly, the case analyzes the business model evolution through the ecosystem life cycle at the company. This case can be used to teach graduate/postgraduate students in agricultural business, MBA and executive programmes about the agri-food e-commerce business model