26,994 research outputs found
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 , internal energy 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
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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 of generalized Witt type, all Lie bialgebras on are
coboundary triangular Lie bialgebras. As a by-product, it is also proved that
the first cohomology group 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
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