Current Distribution and Random Matrix Ensembles for an Integrable Asymmetric Fragmentation Process

We calculate the time-evolution of a discrete-time fragmentation process in which clusters of particles break up and reassemble and move stochastically with size-dependent rates. In the continuous-time limit the process turns into the totally asymmetric simple exclusion process (only pieces of size 1 break off a given cluster). We express the exact solution of the master equation for the process in terms of a determinant which can be derived using the Bethe ansatz. From this determinant we compute the distribution of the current across an arbitrary bond which after appropriate scaling is given by the distribution of the largest eigenvalue of the Gaussian unitary ensemble of random matrices. This result confirms universality of the scaling form of the current distribution in the KPZ universality class and suggests that there is a link between integrable particle systems and random matrix ensembles.     

A Note on the Bethe Ansatz Solution of the Supersymmetric t-J Model

The three different sets of Bethe ansatz equations describing the Bethe ansatz solution of the supersymmetric t-J model are known to be equivalent. Here we give a new, simplified proof of this fact which relies on the properties of certain polynomials. We also show that the corresponding transfer matrix eigenvalues agree.     

Spinon statistics in integrable spin-S Heisenberg chains

The spectrum of the integrable spin-S Heisenberg chains is completely characterized in terms of spinons. In the continuum limit they form a quasi-particle basis to the higher level SU(2) Wess-Zumino-Witten (WZW) models. Enumerating the spinon states in finite systems we obtain effective single particle distribution functions for these objects which generalize Haldane's generalized exclusion principle to quasi-particles with non-Abelian exchange statistics.     

序参量守恒的反铁磁分子晶体的非线性集体激发

采用双子格模型和相干态表示，考虑磁－声子耦合作用和磁子间的相互作用，研究了序参量守恒的一维反铁磁分子晶体ＣｅＡｓ在外磁场存在下的非线性集体激发特性，并求了孤立子能量、质量和自旋的空间组态，给出在一维序参量守恒的反铁磁分子晶体ＣｅＡｓ中出现的非线性磁子局域特性。     

Stepwise Gauge Equivalence of Differential Operators

In this paper, we study the relation between the notion of gauge equivalence and solutions of certain systems of nonlinear partial differential equations. This relation is based on stepwise gauge equivalence.__________Translated from Matematicheskie Zametki, vol. 77, no. 6, 2005, pp. 917–929.Original Russian Text Copyright ©2005 by S. P. Khekalo.     

Three-dimensional cytoplasmic calcium propagation with boundaries

Ca²⁺plays an important role in cell signal transduction.Its intracellular propagation is the most basic process of Ca²⁺signaling,such as calcium wave and double messenger system.In this work,with both numerical simulation and mean field ansatz,the three-dimensional probability distribution of Ca²⁺,which is read out by phosphorylation,is studied in two scenarios with boundaries.The coverage of distribution of Ca²⁺is found at an order of magnitude ofμm,which is consistent with experimental observed calcium spike and wave.Our results suggest that the double messenger system may occur in the ER-PM junction to acquire great efficiency.The buffer effect of kinase is also discussed by calculating the average position of phosphorylations and free Ca²⁺.The results are helpful to understand the mechanism of Ca²⁺signaling.     

REMABKS ON THE STRUCTURE OF EVOLUTION EQUATIONS

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Exact solution of the XXX Gaudin model with generic open boundaries

The XXX Gaudin model with generic integrable open boundaries specified by the most general non-diagonal reflecting matrices is studied. Besides the inhomogeneous parameters, the associated Gaudin operators have six free parameters which break the U(1)$U\left(1\right)$-symmetry. With the help of the off-diagonal Bethe ansatz, we successfully obtained the eigenvalues of these Gaudin operators and the corresponding Bethe ansatz equations.     

Hyperkähler metric and GMN ansatz on focus–focus fibrations

In this paper, we study the hyperkähler metric and practise GMN’s construction of hyperkähler metric on focus–focus fibrations. We explicitly compute the action–angle coordinates on the local model of focus–focus fibrations, and show its semi-global invariant should be harmonic to admit a compatible holomorphic 2-form. Then we study the canonical semi-flat metric on it. After the instanton correction, finally we are able to get a reconstruction of the generalized Ooguri–Vafa metric.