Exact solution of the two-axis countertwisting Hamiltonian for the half-integer JJ case

Bethe ansatz solutions of the two-axis countertwisting Hamiltonian for any (integer and half-integer) $J$ are derived based on the Jordan-Schwinger (differential) boson realization of the $SU(2)$ algebra after desired Euler rotations, where $J$ is the total angular momentum quantum number of the system. It is shown that solutions to the Bethe ansatz equations can be obtained as zeros of the extended Heine-Stieltjes polynomials. Two sets of solutions, with solution number being $J+1$ and $J$ respectively when $J$ is an integer and $J+1/2$ each when $J$ is a half-integer, are obtained. Properties of the zeros of the related extended Heine-Stieltjes polynomials for half-integer $J$ cases are discussed. It is clearly shown that double degenerate level energies for half-integer $J$ are symmetric with respect to the $E=0$ axis. It is also shown that the excitation energies of the `yrast' and other `yrare' bands can all be asymptotically given by quadratic functions of $J$, especially when $J$ is large.Comment: LaTex 12 pages, 3 figures. Major cosmetic type revision. arXiv admin note: text overlap with arXiv:1609.0558

Exact solution of the two-axis countertwisting Hamiltonian

It is shown that the two-axis countertwisting Hamiltonian is exactly solvable when the quantum number of the total angular momentum of the system is an integer after the Jordan-Schwinger (differential) boson realization of the SU(2) algebra. Algebraic Bethe ansatz is used to get the exact solution with the help of the SU(1,1) algebraic structure, from which a set of Bethe ansatz equations of the problem is derived. It is shown that solutions of the Bethe ansatz equations can be obtained as zeros of the Heine-Stieltjes polynomials. The total number of the four sets of the zeros equals exactly to $2J+1$ for a given integer angular momentum quantum number $J$, which proves the completeness of the solutions. It is also shown that double degeneracy in level energies may also occur in the $J\rightarrow\infty$ limit for integer $J$ case except a unique non-degenerate level with zero excitation energy.Comment: LaTex 10 pages. Version to appear in Annals of Physic

The Heine-Stieltjes correspondence and a new angular momentum projection for many-particle systems

A new angular momentum projection for systems of particles with arbitrary spins is formulated based on the Heine-Stieltjes correspondence, which can be regarded as the solutions of the mean-field plus pairing model in the strong pairing interaction G ->Infinity limit. Properties of the Stieltjes zeros of the extended Heine-Stieltjes polynomials, of which the roots determine the projected states, and the related Van Vleck zeros are discussed. The electrostatic interpretation of these zeros is presented. As examples, applications to n nonidentical particles of spin-1/2 and to identical bosons or fermions are made to elucidate the procedure and properties of the Stieltjes zeros and the related Van Vleck zeros. It is shown that the new angular momentum projection for n identical bosons or fermions can be simplified with the branching multiplicity formula of U(N) supset O(3) and the special choices of the parameters used in the projection. Especially, it is shown that the solutions for identical bosons can always be expressed in terms of zeros of Jacobi polynomials. However, unlike non-identical particle systems, the n-coupled states of identical particles are non-orthogonal with respect to the multiplicity label after the projection.Comment: 14 pages LaTeX with no figur

Quantum phase transitional patterns in the SD-pair shell model

Patterns of shape-phase transition in the proton-neutron coupled systems are studied within the $SD$-pair shell model. The results show that some transitional patterns in the $SD$-pair shell model are similar to the $U(5)-SU(3)$, $U(5)-SO(6)$ transitions with signatures of the critical point symmetry of the interacting boson model.Comment: 13 pages, 7 figure

Current State of the Digital Deception Studies in IS

Digital deceptions exist on the Internet in various forms and for different purposes. The purpose of this study is to understand the current state of the digital deception research in IS discipline. Based on our review and analysis of the selected digital deception articles published in IS journals and conference proceedings, we discussed various perspectives of digital deceptions, such as the media, types of deception, deceivers, motivations, and victims. The results of our study indicate that deception phenomena are severely under-researched in IS discipline. The study provides suggestions for future research

Efficient chain structure for high-utility sequential pattern mining

High-utility sequential pattern mining (HUSPM) is an emerging topic in data mining, which considers both utility and sequence factors to derive the set of high-utility sequential patterns (HUSPs) from the quantitative databases. Several works have been presented to reduce the computational cost by variants of pruning strategies. In this paper, we present an efficient sequence-utility (SU)-chain structure, which can be used to store more relevant information to improve mining performance. Based on the SU-Chain structure, the existing pruning strategies can also be utilized here to early prune the unpromising candidates and obtain the satisfied HUSPs. Experiments are then compared with the state-of-the-art HUSPM algorithms and the results showed that the SU-Chain-based model can efficiently improve the efficiency performance than the existing HUSPM algorithms in terms of runtime and number of the determined candidates

FRIOD: a deeply integrated feature-rich interactive system for effective and efficient outlier detection

In this paper, we propose an novel interactive outlier detection system called feature-rich interactive outlier detection (FRIOD), which features a deep integration of human interaction to improve detection performance and greatly streamline the detection process. A user-friendly interactive mechanism is developed to allow easy and intuitive user interaction in all the major stages of the underlying outlier detection algorithm which includes dense cell selection, location-aware distance thresholding, and final top outlier validation. By doing so, we can mitigate the major difficulty of the competitive outlier detection methods in specifying the key parameter values, such as the density and distance thresholds. An innovative optimization approach is also proposed to optimize the grid-based space partitioning, which is a critical step of FRIOD. Such optimization fully considers the high-quality outliers it detects with the aid of human interaction. The experimental evaluation demonstrates that FRIOD can improve the quality of the detected outliers and make the detection process more intuitive, effective, and efficient