DOA Estimation Based on Sparse Representation of the Fractional Lower Order Statistics in Impulsive Noise

This paper is mainly to deal with the problem of direction of arrival(DOA) estimations of multiple narrow-band sources impinging on a uniform linear array under impulsive noise environments. By modeling the impulsive noise as α-stable distribution, new methods which combine the sparse signal representation technique and fractional lower order statistics theory are proposed. In the new algorithms, the fractional lower order statistics vectors of the array output signal are sparsely represented on an overcomplete basis and the DOAs can be effectively estimated by searching the sparsest coefficients. To enhance the robustness performance of the proposed algorithms,the improved algorithms are advanced by eliminating the fractional lower order statistics of the noise from the fractional lower order statistics vector of the array output through a linear transformation. Simulation results have shown the effectiveness of the proposed methods for a wide range of highly impulsive environments.

A Scheme for Simulation of Quantum Gates by Abelian Anyons

Anyons can be used to realize quantum computation, because they are two-level systems in two dimensions. In this paper, we propose a scheme to simulate single-qubit gates and CNOT gate using Abelian anyons in the Kitaev model. Two pairs of anyons （six spins） are used to realize single-qubit gates, while ten spins are needed for the CNOT gate. Based on these quantum gates, we show how to realize the Grover algorithm in a two-qubit system.

Exact Solution of a New Class of Bariev Model

The exact solution of a new type of Bariev Hamiltonian constructed with particles which obeys generalized exchange statistics in one dimension is studied in the framework of coordinate Bethe ansatz method. The energy spectrum and the related Bethe ansatz equations are obtained.

Extremes of Shepp statistics for fractional Brownian motion

Define the incremental fractional Brownian field with parameter H ∈ （0, 1） by ZH（τ, s） = BH（s-＋τ） - BH（S）, where BH（s） is a fractional Brownian motion with Hurst parameter H ∈ （0, 1）. We firstly derive the exact tail asymptoties for the maximum MH＊（T） = max（τ,s）∈[a,b]×[0,T] ZH（τ, s）/τH of the standardised fractional Brownian motion field, with any fixed 0 〈 a 〈 b 〈 ∞ and T 〉 0; and we, furthermore, extend the obtained result to the ease that T is a positive random variable independent of {BH（s）, s ≥ 0}. As a by-product, we obtain the Gumbel limit law for MH＊r（T） as T →∞.

Pauli Paramagnetic Susceptibility of an Ideal Anyon Gas within Haldane Fractional Exclusion Statistics

The finite-temperature Pauli paramagnetic susceptibility of a three-dimensional ideal anyon gas obeying Haldane fractional exclusion statistics is studied analytically.Different from the result of an ideal Fermi gas,the susceptibility of an ideal anyon gas depends on a statistical factor g in Haldane statistics model.The low-temperature and high-temperature behaviors of the susceptibility are investigated in detail.The Pauli paramagnetic susceptibility of the two-dimensional ideal anyons is also derived.It is found that the reciprocal of the susceptibility has the similar factorizable property which is exhibited in some thermodynamic quantities in two dimensions.

Intermediate symmetric construction of transformation between anyon and Gentile statistics

Gentile statistics describes fractional statistical systems in the occupation number representation.Anyon statistics researches those systems in the winding number representation.Both of them are intermediate statistics between Bose–Einstein and Fermi–Dirac statistics.The second quantization of Gentile statistics shows a lot of advantages.According to the symmetry requirement of the wave function and the property of braiding,we give the general construction of transformation between anyon and Gentile statistics.In other words,we introduce the second quantization form of anyons in an easier way.This construction is a correspondence between two fractional statistics and gives a new description of anyon.Basic relations of second quantization operators,the coherent state and Berry phase are also discussed.