Fermi gas in harmonic oscillator potentials

Assuming the validity of grand canonical statistics, we study the properties of a spin-polarized Fermi gas in harmonic traps. Universal forms of Fermi temperature $T_F$, internal energy $U$ and the specific heat per particle of the trapped Fermi gas are calculated as a {\it function} of particle number, and the results compared with those of infinite number particles.Comment: 8 pages, 1 figure, LATE

Studies on Temperature and Strain Sensitivities of a Few-mode Critical Wavelength Fiber Optic Sensor

This paper studied the relationship between the temperature/strain wavelength sensitivity of a fiber optic in-line Mach-Zehnder Interferometer (MZI) sensor and the wavelength separation of the measured wavelength to the critical wavelength (CWL) in a CWL-existed interference spectrum formed by interference between LP01 and LP02 modes. The in-line MZI fiber optic sensor has been constructed by splicing a section of specially designed few-mode fiber (FMF), which support LP01 and LP02 modes propagating in the fiber, between two pieces of single mode fiber. The propagation constant difference, Δβ, between the LP01 and LP02 modes, changes non-monotonously with wavelength and reaches a maximum at the CWL. As a result, in sensor operation, peaks on the different sides of the CWL then shift in opposite directions, and the associated temperature/strain sensitivities increase significantly when the measured wavelength points become close to the CWL, from both sides of the CWL. A theoretical analysis carried out has predicted that with this specified FMF sensor approach, the temperature/strain wavelength sensitivities are governed by the wavelength difference between the measured wavelength and the CWL. This conclusion was seen to agree well with the experimental results obtained. Combining the wavelength shifts of the peaks and the CWL in the transmission spectrum of the SFS structure, this study has shown that this approach forms the basis of effective designs of high sensitivity sensors for multi-parameter detection and offering a large measurement range to satisfy the requirements needed for better industrial measurements

Exploiting Cognitive Structure for Adaptive Learning

Adaptive learning, also known as adaptive teaching, relies on learning path recommendation, which sequentially recommends personalized learning items (e.g., lectures, exercises) to satisfy the unique needs of each learner. Although it is well known that modeling the cognitive structure including knowledge level of learners and knowledge structure (e.g., the prerequisite relations) of learning items is important for learning path recommendation, existing methods for adaptive learning often separately focus on either knowledge levels of learners or knowledge structure of learning items. To fully exploit the multifaceted cognitive structure for learning path recommendation, we propose a Cognitive Structure Enhanced framework for Adaptive Learning, named CSEAL. By viewing path recommendation as a Markov Decision Process and applying an actor-critic algorithm, CSEAL can sequentially identify the right learning items to different learners. Specifically, we first utilize a recurrent neural network to trace the evolving knowledge levels of learners at each learning step. Then, we design a navigation algorithm on the knowledge structure to ensure the logicality of learning paths, which reduces the search space in the decision process. Finally, the actor-critic algorithm is used to determine what to learn next and whose parameters are dynamically updated along the learning path. Extensive experiments on real-world data demonstrate the effectiveness and robustness of CSEAL.Comment: Accepted by KDD 2019 Research Track. In Proceedings of the 25th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining (KDD'19

Lie bialgebras of generalized Witt type

In a paper by Michaelis a class of infinite-dimensional Lie bialgebras containing the Virasoro algebra was presented. This type of Lie bialgebras was classified by Ng and Taft. In this paper, all Lie bialgebra structures on the Lie algebras of generalized Witt type are classified. It is proved that, for any Lie algebra $W$ of generalized Witt type, all Lie bialgebras on $W$ are coboundary triangular Lie bialgebras. As a by-product, it is also proved that the first cohomology group $H^1(W,W \otimes W)$ is trivial.Comment: 14 page

Quantum simulation of artificial Abelian gauge field using nitrogen-vacancy center ensembles coupled to superconducting resonators

We propose a potentially practical scheme to simulate artificial Abelian gauge field for polaritons using a hybrid quantum system consisting of nitrogen-vacancy center ensembles (NVEs) and superconducting transmission line resonators (TLR). In our case, the collective excitations of NVEs play the role of bosonic particles, and our multiport device tends to circulate polaritons in a behavior like a charged particle in an external magnetic field. We discuss the possibility of identifying signatures of the Hofstadter "butterfly" in the optical spectra of the resonators, and analyze the ground state crossover for different gauge fields. Our work opens new perspectives in quantum simulation of condensed matter and many-body physics using hybrid spin-ensemble circuit quantum electrodynamics system. The experimental feasibility and challenge are justified using currently available technology.Comment: 6 papes+supplementary materia