On a nonlinear recurrent relation

We study the limiting behavior for the solutions of a nonlinear recurrent relation which arises from the study of Navier-Stokes equations. Some stability theorems are also shown concerning a related class of linear recurrent relations.Comment: to appear in Journal of Statistical Physic

Implementation of quantum algorithms with resonant interactions

We propose a scheme for implementing quantum algorithms with resonant interactions. Our scheme only requires resonant interactions between two atoms and a cavity mode, which is simple and feasible. Moreover, the implementation would be an important step towards the fabrication of quantum computers in cavity QED system.Comment: 4 pages, 3 figure

A Novel Scheme for Material Updating in Source Distribution Optimization of Magnetic Devices using Sensitivity Analysis

A novel material updating scheme, which does not require intermediate states of a material used, is presented for source distribution optimization problems. A mutation factor to determine a degree of topological change in the next design stage on the basis of a current layout accelerates the convergence of an objective function. Easy implementation and fast convergence of the scheme are verified using two MRI design problems where current and permanent magnet distributions have been optimized, respectively

Second Quantization and the Spectral Action

We consider both the bosonic and fermionic second quantization of spectral triples in the presence of a chemical potential. We show that the von Neumann entropy and the average energy of the Gibbs state defined by the bosonic and fermionic grand partition function can be expressed as spectral actions. It turns out that all spectral action coefficients can be given in terms of the modified Bessel functions. In the fermionic case, we show that the spectral coefficients for the von Neumann entropy, in the limit when the chemical potential $\mu$ approaches $0,$ can be expressed in terms of the Riemann zeta function. This recovers a result of Chamseddine-Connes-van Suijlekom.Comment: Author list is expanded. The calculations in the new version are extended to two more Hamiltonians. New references adde

Multipartite quantum correlation and entanglement in four-qubit pure states

Based on the quantitative complementarity relations, we analyze thoroughly the properties of multipartite quantum correlations and entanglement in four-qubit pure states. We find that, unlike the three-qubit case, the single residual correlation, the genuine three- and four-qubit correlations are not suited to quantify entanglement. More interestingly, from our qualitative and numerical analysis, it is conjectured that the sum of all the residual correlations may constitute a good measure for the total multipartite entanglement in the system.Comment: 7 pages, 3 figue