多量子位Heisenberg模型中纠缠的时间演化特性

研究了多量子位Heisenberg模型中纠缠的时间演化特性, 并给出了平均纠缠度〈C〉和多体纠缠度Q的解析表达式. 结果发现无论是对〈C〉还是对Q随着时间t的不断增长, 它们均先线性的增大, 而后达到一近似稳定状态, 并绕一平衡值做无规则的上下震荡. 若进一步考察N〈C〉则还可以发现, 纠缠上下震荡的平衡值与Heisenberg链的长度几乎无关, 而仅由它们的次近邻耦合常数J决定.     

Effects of impurity on the entanglement of the three-qubit Heisenberg XXX spin chain

We investigate the entanglement of the three-qubit Heisenberg XXX chain in the presence of impurity and obtain the analytical expressions of the concurrence C. It is found that for impurity entanglement, C appears only when J ₁ > J for J > 0, and J ₁ > 0 for J < 0, and in these two regions C increases with the increase of J ₁, so is the critical temperature T _c. When J ₁ ≫ | J |, C reaches its maximum value 0.5 and T _c reaches the asymptotic value T _c = 3.41448J ₁. For entanglement between the normal lattices, C appears only when J > 0 and −2J < J ₁ < J, and initially increases with the increase of J ₁ and arrives at the maximum value C _max = (e^4J/T −3)/(e^4J/T + 3) before it decays to zero gradually, so is the critical temperature T _c with, however, the maximum value T _cmax = 4J/In3. Supported by the Natural Science Research Project of Shaanxi Province (Grant No. 2004A15)     

Smooth solutions for a stochastic hydrodynamical equation in Heisenberg paramagnet

In this article, we consider a stochastic hydrodynamical equation in Heisenberg paramagnet driven by additive noise. We prove the existence and uniqueness of smooth solutions to this equation with difference method.     

Ostrowski type inequalities on H-type groups

The main aim of this paper is to establish an Ostrowski type inequality on H-type groups using the L^∞ norm of the horizontal gradient. The work has been motivated by the work of Anastassiou and Goldstein in [G.A. Anastassiou, J.A. Goldstein, Higher order Ostrowski type inequalities over Euclidean domains, J. Math. Anal. Appl. 337 (2008) 962-968].     

Local Theory of Primitive Theta Functions

We study primitive theta functions, which were first introduced by Shintani, in a purely local setting. We investigate a metaplectic representation of U(1) acting on the space of local primitive theta functions and give its explicit irreducible decomposition. As a by-product, we give a new proof of epsilon dichotomy for (U(1),U(1)).     

Heat kernel analysis on infinite-dimensional Heisenberg groups

We introduce a class of non-commutative Heisenberg-like infinite-dimensional Lie groups based on an abstract Wiener space. The Ricci curvature tensor for these groups is computed and shown to be bounded. Brownian motion and the corresponding heat kernel measures, {νt}_t>0, are also studied. We show that these heat kernel measures admit: (1) Gaussian like upper bounds, (2) Cameron-Martin type quasi-invariance results, (3) good Lp-bounds on the corresponding Radon-Nikodym derivatives, (4) integration by parts formulas, and (5) logarithmic Sobolev inequalities. The last three results heavily rely on the boundedness of the Ricci tensor.     

Absolute continuity of Wasserstein geodesics in the Heisenberg group

In this paper we answer to a question raised by Ambrosio and Rigot [L. Ambrosio, S. Rigot, Optimal mass transportation in the Heisenberg group, J. Funct. Anal. 208 (2) (2004) 261-301] proving that any interior point of a Wasserstein geodesic in the Heisenberg group is absolutely continuous if one of the end-points is. Since our proof relies on the validity of the so-called Measure Contraction Property and on the fact that the optimal transport map exists and the Wasserstein geodesic is unique, the absolute continuity of Wasserstein geodesic also holds for Alexandrov spaces with curvature bounded from below.     

Multipartite Entanglement in Heisenberg Model

The effects of anisotropy and magnetic field on multipartite entanglement of ground state in Heisenberg XY model are investigated. The multipartite entanglement increases as a function of the inverse strength of the external field when the degree of anisotropy is finite. There are two peaks when the degree of anisotropy is γ=±1. When the degree of anisotropy increases further, the multipartite entanglement will decrease and tend to a constant. The threshold of the inverse strength of the external field for generating multipartite entanglement generally decreases with the increasing of qubits.