5,493 research outputs found
On preconditioned SSOR methods for the linear complementarity problem
In this paper, we consider the preconditioned iterative methods for solving the linear complementarity problem associated with an M-matrix. Two preconditioned SSOR methods for solving the linear complementarity problem are proposed. The convergence of the proposed methods are analyzed, and the comparison results are derived. The comparison results show that the proposed preconditioned SSOR methods accelerate the convergent rate of the SSOR method. Numerical experiments verify the theory results
Josephson dynamics of a spin-orbit coupled Bose-Einstein condensate in a double well potential
We investigate the quantum dynamics of an experimentally realized spin-orbit
coupled Bose-Einstein condensate in a double well potential. The spin-orbit
coupling can significantly enhance the atomic inter-well tunneling. We find the
coexistence of internal and external Josephson effects in the system, which are
moreover inherently coupled in a complicated form even in the absence of
interatomic interactions. Moreover, we show that the spin-dependent tunneling
between two wells can induce a net atomic spin current referred as spin
Josephson effects. Such novel spin Josephson effects can be observable for
realistically experimental conditions.Comment: 8 page
A Framework of Fuzzy Diagnosis
Fault diagnosis has become an important component in intelligent systems, such as intelligent control systems and intelligent eLearning systems. Reiter's diagnosis theory, described by first-order sentences, has been attracting much attention in this field. However, descriptions and observations of most real-world situations are related to fuzziness because of the incompleteness and the uncertainty of knowledge, e. g., the fault diagnosis of student behaviors in the eLearning processes. In this paper, an extension of Reiter's consistency-based diagnosis methodology, Fuzzy Diagnosis, has been proposed, which is able to deal with incomplete or fuzzy knowledge. A number of important properties of the Fuzzy diagnoses schemes have also been established. The computing of fuzzy diagnoses is mapped to solving a system of inequalities. Some special cases, abstracted from real-world situations, have been discussed. In particular, the fuzzy diagnosis problem, in which fuzzy observations are represented by clause-style fuzzy theories, has been presented and its solving method has also been given. A student fault diagnostic problem abstracted from a simplified real-world eLearning case is described to demonstrate the application of our diagnostic framework
Superfluid and magnetic states of an ultracold Bose gas with synthetic three-dimensional spin-orbit coupling in an optical lattice
We study ultracold bosonic atoms with the synthetic three-dimensional
spin-orbit (SO) coupling in a cubic optical lattice. In the superfluidity
phase, the lowest energy band exhibits one, two or four pairs of degenerate
single-particle ground states depending on the SO-coupling strengths, which can
give rise to the condensate states with spin-stripes for the weak atomic
interactions. In the deep Mott-insulator regime, the effective spin Hamiltonian
of the system combines three-dimensional Heisenberg exchange interactions,
anisotropy interactions and Dzyaloshinskii-Moriya interactions. Based on Monte
Carlo simulations, we numerically demonstrate that the resulting Hamiltonian
with an additional Zeeman field has a rich phase diagram with spiral, stripe,
vortex crystal, and especially Skyrmion crystal spin-textures in each xy-plane
layer. The obtained Skyrmion crystals can be tunable with square and hexagonal
symmetries in a columnar manner along the z axis, and moreover are stable
against the inter-layer spin-spin interactions in a large parameter region.Comment: 9 pages, 4 figures; title modified, references and discussions added;
accepted by PR
Quantum simulation of exotic PT-invariant topological nodal loop bands with ultracold atoms in an optical lattice
Since the well-known PT symmetry has its fundamental significance and
implication in physics, where PT denotes the combined operation of
space-inversion P and time-reversal T, it is extremely important and intriguing
to completely classify exotic PT-invariant topological metals and to physically
realize them. Here we, for the first time, establish a rigorous classification
of topological metals that are protected by the PT symmetry using KO-theory. As
a physically realistic example, a PT-invariant nodal loop (NL) model in a 3D
Brillouin zone is constructed, whose topological stability is revealed through
its PT-symmetry-protected nontrivial Z2 topological charge. Based on these
exact results, we propose an experimental scheme to realize and to detect
tunable PT-invariant topological NL states with ultracold atoms in an optical
lattice, in which atoms with two hyperfine spin states are loaded in a
spin-dependent 3D OL and two pairs of Raman lasers are used to create
out-of-plane spin-flip hopping with site-dependent phase. Such a realistic
cold-atom setup can yield topological NL states, having a tunable ring-shaped
band-touching line with the two-fold degeneracy in the bulk spectrum and
non-trivial surface states. The states are actually protected by the combined
PT symmetry even in the absence of both P and T symmetries, and are
characterized by a Z2-type invariant (a quantized Berry phase). Remarkably, we
demonstrate with numerical simulations that (i) the characteristic NL can be
detected by measuring the atomic transfer fractions in a Bloch-Zener
oscillation; (ii) the topological invariant may be measured based on the
time-of-flight imaging; and (iii) the surface states may be probed through
Bragg spectroscopy. The present proposal for realizing topological NL states in
cold atom systems may provide a unique experimental platform for exploring
exotic PT-invariant topological physics.Comment: 11 pages, 6 figures; accepted for publication in Phys. Rev.
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