Exponential Convergence Rates of Second Quantization Semigroups and Applications

Exponential convergence rates in the $L^2$-tail norm and entropy are characterized for the second quantization semigroups by using the corresponding base Dirichlet form. This supplements the well known result on the $L^2$-exponential convergence rate of second quantization semigroups. As applications, birth-death type processes on Poisson spaces and the path space of L\'evy processes are investigated.Comment: 20 page

Demystify the mixed-parity pairing of attractive fermions with spin-orbit coupling in optical lattice

The admixture of spin-singlet and spin-triplet pairing states in superconductors can be typically induced by breaking spatial inversion symmetry. Employing the {\it numerically exact} auxiliary-field Quantum Monte Carlo method, we study such mixed-parity pairing phenomena of attractive fermions with Rashba spin-orbit coupling (SOC) in two-dimensional optical lattice at finite temperature. We systematically demystify the evolution of the essential pairing structure in both singlet and triplet channels versus the temperature, fermion filling, SOC and interaction strengths, via computing the condensate fraction and pair wave function. Our numerical results reveal that the singlet channel dominates in the fermion pairing and the triplet pairing has relatively small contribution to the superfluidity for physically relevant parameters. In contrast to the singlet channel mainly consisted of the on-site Cooper pairs, the triplet pairing has plentiful patterns in real space with the largest contributions from several nearest neighbors. As the SOC strengh increases, the pairing correlation is firstly enhanced and then suppressed for triplet pairing while it's simply weakened in singlet channel. We have also obtained the Berezinskii-Kosterlitz-Thouless transition temperatures through the finite-size analysis of condensate fraction. Our results can serve as quantitative guide for future optical lattice experiments as well as accurate benchmarks for theories and other numerical methods.Comment: 14 pages, 11+5 figure

Semantic lifting and reasoning on the personalised activity big data repository for healthcare research

The fast growing markets of smart health monitoring devices and mobile applications provide opportunities for common citizens to have capability for understanding and managing their own health situations. However, there are many challenges for data engineering and knowledge discovery research to enable efficient extraction of knowledge from data that is collected from heterogonous devices and applications with big volumes and velocity. This paper presents research that initially started with the EC MyHealthAvatar project and is under continual improvement following the project’s completion. The major contribution of the work is a comprehensive big data and semantic knowledge discovery framework which integrates data from varied data resources. The framework applies hybrid database architecture of NoSQL and RDF repositories with introductions for semantic oriented data mining and knowledge lifting algorithms. The activity stream data is collected through Kafka’s big data processing component. The motivation of the research is to enhance the knowledge management, discovery capabilities and efficiency to support further accurate health risk analysis and lifestyle summarisation