Zamolodchikov-Faddeev algebra in 2-component anyons

We investigate Wilczeck's mutual fractional statistical model at the field- theoretical level. The effective Hamiltonian for the particles is derived by the canonical procedure, whereas the commutators of the anyonic excitations are proved to obey the Zamolodchikov-Faddeev algebra. Cases leading to well known statistics as well as Laughlin's wave function are discussed.Comment: Preprint of Nankai Institute of Mathematics, Chin

GHZ States, Almost-Complex Structure and Yang--Baxter Equation (I)

Recent study suggests that there are natural connections between quantum information theory and the Yang--Baxter equation. In this paper, in terms of the generalized almost-complex structure and with the help of its algebra, we define the generalized Bell matrix to yield all the GHZ states from the product base, prove it to form a unitary braid representation and present a new type of solution of the quantum Yang--Baxter equation. We also study Yang-Baxterization, Hamiltonian, projectors, diagonalization, noncommutative geometry, quantum algebra and FRT dual algebra associated with this generalized Bell matrix.Comment: 17 pages, late

Reproduction numbers and the expanding fronts for a diffusion-advection SIS model in heterogeneous time-periodic environment

This paper deals with a simplified SIS model, which describes the transmission of the disease in time-periodic heterogeneous environment. To understand the impact of spatial heterogeneity of environment and small advection on the persistence and eradication of an infectious disease, the left and right free boundaries are introduced to represent the expanding fronts. The basic reproduction numbers $R_0^D$ and $R_0^F(t)$, which depends on spatial heterogeneity, temporal periodicity and advection, are introduced. A spreading-vanishing dichotomy is established and sufficient conditions for the spreading and vanishing of the disease are given. The asymptotic spreading speeds for the left and right fronts are also presented.Comment: 14 page

Susceptibility and Group Velocity in a Fully Quantized Model For Electromagnetically Induced Transparency

We have developed a fully quantized model for EIT in which the decay rates are taken into account. In this model, the general form of the susceptibility and group velocity of the probe laser we obtained are operators. Their expectation value and fluctuation can be obtained on the Fock space. Furthermore the uncertainty of the group velocity under very weak intensity of the controlling laser and the uncertainty relation between the phase operator of coupling laser and the group velocity are approximately given. Considering the decay rates of various levels, we may analyze the probe laser near resonance in detail and calculate the fluctuation in both absorption and dispersion. We also discuss how the fully quantized model reduces to a semiclassical model when the mean photon numbers of the coupling laser is getting large.Comment: 10 pages, 3 figures, Submitted to Phys.Lett.

The John Theorem for Simplex

In this paper, we give a description of the John contact points of a regular simplex. We prove that the John ellipsoid of any simplex is ball if and only if this simplex is regular and that the John ellipsoid of a regular simplex is its inscribed ball.Comment: 8 page

More about the doubling degeneracy operators associated with Majorana fermions and Yang-Baxter equation

A new realization of doubling degeneracy based on emergent Majorana operator $\Gamma$ presented by Lee-Wilczek has been made. The Hamiltonian can be obtained through the new type of solution of Yang-Baxter equation, i.e. $\breve{R}(\theta)$-matrix. For 2-body interaction, $\breve{R}(\theta)$ gives the "superconducting" chain that is the same as 1D Kitaev chain model. The 3-body Hamiltonian commuting with $\Gamma$ is derived by 3-body $\breve{R}_{123}$-matrix, we thus show that the essence of the doubling degeneracy is due to $[\breve{R}(\theta), \Gamma]=0$. We also show that the extended $\Gamma'$-operator is an invariant of braid group $B_N$ for odd $N$. Moreover, with the extended $\Gamma'$-operator, we construct the high dimensional matrix representation of solution to Yang-Baxter equation and find its application in constructing $2N$-qubit Greenberger-Horne-Zeilinger state for odd $N$.Comment: 12 pages, 1 figure

Subspace Clustering Based Tag Sharing for Inductive Tag Matrix Refinement with Complex Errors

Annotating images with tags is useful for indexing and retrieving images. However, many available annotation data include missing or inaccurate annotations. In this paper, we propose an image annotation framework which sequentially performs tag completion and refinement. We utilize the subspace property of data via sparse subspace clustering for tag completion. Then we propose a novel matrix completion model for tag refinement, integrating visual correlation, semantic correlation and the novelly studied property of complex errors. The proposed method outperforms the state-of-the-art approaches on multiple benchmark datasets even when they contain certain levels of annotation noise.Comment: 4 page

On a conjecture of Stanley depth of squarefree Veronese ideals

In this paper, we partially confirm a conjecture, proposed by Cimpoea\c{s}, Keller, Shen, Streib and Young, on the Stanley depth of squarefree Veronese ideals $I_{n,d}$. This conjecture suggests that, for positive integers $1 \le d \le n$, \sdepth (I_{n,d})= \lfloor \binom{n}{d+1}/\binom{n}{d} \rfloor+d. Herzog, Vladoiu and Zheng established a connection between the Stanley depths of quotients of monomial ideals and interval partitions of certain associated posets. Based on this connection, Keller, Shen, Streib and Young recently developed a useful combinatorial tool to analyze the interval partitions of the posets associated with the squarefree Veronese ideals. We modify their ideas and prove that if $1 \le d \le n \le (d+1) \lfloor \frac{1+\sqrt{5+4d}}{2}\rfloor+2d$, then \sdepth (I_{n,d})= \lfloor \binom{n}{d+1}/\binom{n}{d} \rfloor+d. We also obtain \lfloor \frac{d+\sqrt{d^2+4(n+1)}}{2} \rfloor \le \sdepth(I_{n,d}) \le \lfloor \binom{n}{d+1}/\binom{n}{d} \rfloor+d for $n > (d+1) \lfloor \frac{1+\sqrt{5+4d}}{2}\rfloor+2d$. As a byproduct of our construction, We give an alternative proof of Theorem $1.1$ in $[13]$ without graph theory.Comment: 11 pages; Theorem 1.2 has been changed due to a gap in the previous versio

Localization condition for two-level systems

The dynamics of two-level systems in an external periodic field are investigated in general. The necessary conditions of localization are obtained through analysing the time-evolving matrix. It is found that localization is possible if not only is the dynamics of the system periodic, but also its period is the same as that of the external potential. A model system in a periodic $\delta$-function potential is studied thoroughly.Comment: Preprint ( reprint ) of Nankai Institute of Mathematics. For hard copy, write to Prof. Mo-lin GE directly. Do not send emails to this computer account pleas

Quasi-calssical approach to two-level systems with dissipation

The quantum dynamics of two-level systems under classical oscillator heat bath is mapped to the classical one of a charged particle under harmonic oscillator potential plus a magnetic field in a plane. The behavior of eigenstates and tunneling and localization are studied in detail. The broken symmetry condition and Langevin-like dissipative equation of motion are obtained. Some special dynamic features are considered.Comment: Preprint ( reprint ) of Nankai Institute of Mathematics. For hard copy, write to Prof. Mo-lin GE. Do not send emails to this computer accoun