两种典型转换条件下的二次谐波系统在浑沌态下的光子统计

分别在好腔和坏腔两种典型的谐波转换条件下,数值分析了调制泵浦作用下的二次谐波产生系统的浑沌动力学行为.运用文献1给出的方法,在新的条件下研究了系统在浑沌态下的光子统计,结果表明仍为超Poisson分布,而且在某些情况下,浑沌态光场的光子数相对涨落甚至比热光场的光子数相对涨落还要大.最后得出了普遍性的结论;二次谐波系统在浑沌态下的光子统计为形式丰富多样的超Poisson分布,浑沌光场是一种强度高、涨落大的光场.     

The ergodicity of a class of almost Anosov systems

In this paper, we prove that some volume-preserving almost Anosov systems are ergodic if they are essentially accessible. The key idea is that there are stable and unstable manifolds with uniform size on the orbits of the hyperbolic points for these systems.     

Ergodicity of stochastic 2D Navier–Stokes equation with Lévy noise

In this paper we deal with the 2D Navier-Stokes equation perturbed by a Lévy noise force whose white noise part is non-degenerate and that the intensity measure of Poisson measure is σ-finite. Existence and uniqueness of invariant measure for this equation is obtained, two main properties of the Markov semigroup associated with this equation are proved. In other words, strong Feller property and irreducibility hold in the same space.     

Discontinuous Condensation Transition and Nonequivalence of Ensembles in a Zero-Range Process

We study a zero-range process where the jump rates do not only depend on the local particle configuration, but also on the size of the system. Rigorous results on the equivalence of ensembles are presented, characterizing the occurrence of a condensation transition. In contrast to previous results, the phase transition is discontinuous and the system exhibits ergodicity breaking and metastable phases. This leads to a richer phase diagram, including nonequivalence of ensembles in certain phase regions. The paper is motivated by results from granular clustering, where these features have been observed experimentally. An erratum to this article can be found at     

Exponential mixing for stochastic PDEs: the non-additive case

We establish a general criterion which ensures exponential mixing of parabolic stochastic partial differential equations (SPDE) driven by a non additive noise which is white in time and smooth in space. We apply this criterion on two representative examples: 2D Navier–Stokes (NS) equations and Complex Ginzburg–Landau (CGL) equation with a locally Lipschitz noise. Due to the possible degeneracy of the noise, Doob theorem cannot be applied. Hence, a coupling method is used in the spirit of Kuksin and Shirikyan (J. Math. Pures Appl. 1:567–602, 2002) and Mattingly (Commun. Math. Phys. 230:421–462, 2002). Previous results require assumptions on the covariance of the noise which might seem restrictive and artificial. For instance, for NS and CGL, the covariance operator is supposed to be diagonal in the eigenbasis of the Laplacian and not depending on the high modes of the solutions. The method developed in the present paper gets rid of such assumptions and only requires that the range of the covariance operator contains the low modes.     

Computational Bayesian Analysis of Hidden Markov Models

Abstract

Versions of the Gibbs Sampler are derived for the analysis of data from hidden Markov chains and hidden Markov random fields. The principal new development is to use the pseudolikelihood function associated with the underlying Markov process in place of the likelihood, which is intractable in the case of a Markov random field, in the simulation step for the parameters in the Markov process. Theoretical aspects are discussed and a numerical study is reported.     

Stochastic Quantization of the Two-Dimensional Polymer Measure

We prove that there exists a diffusion process whose invariant measure is the two-dimensional polymer measure ν _g . The diffusion is constructed by means of the theory of Dirichlet forms on infinite-dimensional state spaces. We prove the closability of the appropriate pre-Dirichlet form which is of gradient type, using a general closability result by two of the authors. This result does not require an integration by parts formula (which does not hold for the two-dimensional polymer measure ν _g ) but requires the quasi-invariance of ν _g along a basis of vectors in the classical Cameron—Martin space such that the Radon—Nikodym derivatives (have versions which) form a continuous process. We also show the Dirichlet form to be irreducible or equivalently that the diffusion process is ergodic under time translations. Accepted 16 April 1998     

含瞬时态、具有突变率的广义生-灭Q-矩阵(I)

研究含瞬时态、具有突变率的广义生-灭拟q-矩阵,给出易于验证的Q过程存在性准则,并构造出全部Q过程和全部诚实Q过程,证明了不需附加任何条件,所有诚实Q过程都是常返的,给出诚实Q过程是遍历的充要条件,并求出其遍历测度,以及证明了不存在可配称Q过程.最后给出两个例子以说明我们的结果易于验证.