Metastability for a Stochastic Dynamics with a Parallel Heat Bath Updating Rule

We consider the problem of metastability for a stochastic dynamics with a parallel updating rule with single spin rates equal to those of the heat bath for the Ising nearest neighbors interaction. We study the exit from the metastable phase, we describe the typical exit path and evaluate the exit time. We prove that the phenomenology of metastability is different from the one observed in the case of the serial implementation of the heat bath dynamics. In particular we prove that an intermediate chessboard phase appears during the excursion from the minus metastable phase toward the plus stable phase.     

Sharp Asymptotics for Fixation Times in Stochastic Population Genetics Models at Low Mutation Probabilities

This article describes new models in population genetics that extend the neutral Wright–Fisher model by including strong selection and mutation. Fixation times are studied in the limit of small mutation probabilities within the framework of Markov chains with rare transitions. The main result outlines the role of the discrete geometry of the fitness landscape and provides a mean for estimating the expected number of generations for an individual with better fitness value to appear. Some connections to evolutionary algorithms are discussed as well.     

Sharp Spectral Asymptotics and Weyl Formula for Elliptic Operators with Non-smooth Coefficients

The aim of this paper is to give the Weyl formula for eigenvalues of self-adjoint elliptic operators, assuming that first-order derivatives of the coefficients are Lipschitz continuous. The approach is based on the asymptotic formula of Hörmander"s type for the spectral function of pseudodifferential operators having Lipschitz continuous Hamiltonian flow and obtained via a regularization procedure of nonsmooth coefficients.     

Stochastic Dynamics on Hypergraphs and the Spatial Majority Rule Model

This article starts by introducing a new theoretical framework to model spatial systems which is obtained from the framework of interacting particle systems by replacing the traditional graphical structure that defines the network of interactions with a structure of hypergraph. This new perspective is more appropriate to define stochastic spatial processes in which large blocks of vertices may flip simultaneously, which is then applied to define a spatial version of the Galam’s majority rule model. In our spatial model, each vertex of the lattice has one of two possible competing opinions, say opinion 0 and opinion 1, as in the popular voter model. Hyperedges are updated at rate one, which results in all the vertices in the hyperedge changing simultaneously their opinion to the majority opinion of the hyperedge. In the case of a tie in hyperedges with even size, a bias is introduced in favor of type 1, which is motivated by the principle of social inertia. Our analytical results along with simulations and heuristic arguments suggest that, in any spatial dimensions and when the set of hyperedges consists of the collection of all n×?×n blocks of the lattice, opinion 1 wins when n is even while the system clusters when n is odd, which contrasts with results about the voter model in high dimensions for which opinions coexist. This is fully proved in one dimension while the rest of our analysis focuses on the cases when n=2 and n=3 in two dimensions.     

A Lower Bound for the Wehrl Entropy of Quantum Spin with Sharp High-Spin Asymptotics

A lower bound for the Wehrl entropy of a single quantum spin is derived. The high-spin asymptotics of this bound coincides with Liebs conjecture up to, but not including, terms of first and higher order in the inverse spin quantum number. The result presented here may be seen as complementary to the verification of the conjecture in cases of lowest spin by Schupp [Commun. Math. Phys. 207, 481 (1999)]. The present result for the Wehrl-entropy is obtained from interpolating a sharp norm bound that also implies a sharp lower bound for the so-called Rényi-Wehrl entropy with certain indices that are evenly spaced by half of the inverse spin quantum number.     

并行化光滑分子动力学方法及其与分子动力学的耦合

提出光滑分子动力学方法(SMD)的并行化计算方法,编制光滑分子动力学以及光滑分子动力学-分子动力学(SMD-MD)耦合的并行程序,并分析铜纳米单晶的单向拉伸和带裂纹板的拉伸问题.光滑分子动力学在分子动力学基础上引入背景网格,在背景网格点上求解运动方程,由此将控制MD临界时间步长的因素化为背景网格单元尺寸,扩大可用的时间积分步长,缩短总计算时间.通过单晶拉伸和带裂纹板拉伸等较大规模问题的计算,验证方法的正确性.与传统分子动力学相比,SMD和SMD-MD耦合方法可以节约计算时间.     

A Spatial Stochastic Model for Virus Dynamics

We introduce a spatial stochastic model for virus dynamics. We show that if the death rate of infected cells increases too fast with the virus load the virus dies out. This is in sharp contrast with what happens in the (non-spatial deterministic) basic model for virus dynamics. AMS 1991 Subject Classification: 60K35     

理解随机过程分子动力学中的真实/虚拟动力学

Molecular dynamics with the stochastic process provides a convenient way to compute structural and thermodynamic properties of chemical, biological, and materials systems. It is demonstrated that the virtual dynamics case that we proposed for the Langevin equation[J. Chem. Phys. 147, 184104 (2017)] in principle exists in other types of stochastic thermostats as well. The recommended "middle" scheme[J. Chem. Phys. 147, 034109 (2017)] of the Andersen thermostat is investigated as an example. As shown by both analytic and numerical results, while the real and virtual dynamics cases approach the same plateau of the characteristic correlation time in the high collision frequency limit, the accuracy and efficiency of sampling are relatively insensitive to the value of the collision frequency in a broad range. After we compare the behaviors of the Andersen thermostat to those of Langevin dynamics, a heuristic schematic representation is proposed for understanding efficient stochastic thermostatting processes with molecular dynamics.     

A Gentle Stochastic Thermostat for Molecular Dynamics

We discuss a dynamical technique for sampling the canonical measure in molecular dynamics. We present a method that generalizes a recently proposed scheme (Samoletov et al., J. Stat. Phys. 128:1321–1336, 2007), and which controls temperature by use of a device similar to that of Nosé dynamics, but adds random noise to improve ergodicity. In contrast to Langevin dynamics, where noise is added directly to each physical degree of freedom, the new scheme relies on an indirect coupling to a single Brownian particle. For a model with harmonic potentials, we show under a mild non-resonance assumption that we can recover the canonical distribution. In spite of its stochastic nature, experiments suggest that it introduces a relatively weak perturbative effect on the physical dynamics, as measured by perturbation of temporal autocorrelation functions. The kinetic energy is well controlled even in the early stages of a simulation.     

Stochastic Event-Driven Molecular Dynamics

A novel Stochastic Event-Driven Molecular Dynamics (SEDMD) algorithm is developed for the simulation of polymer chains suspended in a solvent. SEDMD combines event-driven molecular dynamics (EDMD) with the Direct Simulation Monte Carlo (DSMC) method. The polymers are represented as chains of hard-spheres tethered by square wells and interact with the solvent particles with hard-core potentials. The algorithm uses EDMD for the simulation of the polymer chain and the interactions between the chain beads and the surrounding solvent particles. The interactions between the solvent particles themselves are not treated deterministically as in EDMD, rather, the momentum and energy exchange in the solvent is determined stochastically using DSMC. The coupling between the solvent and the solute is consistently represented at the particle level retaining hydrodynamic interactions and thermodynamic fluctuations. However, unlike full MD simulations of both the solvent and the solute, in SEDMD the spatial structure of the solvent is ignored. The SEDMD algorithm is described in detail and applied to the study of the dynamics of a polymer chain tethered to a hard-wall subjected to uniform shear. SEDMD closely reproduces results obtained using traditional EDMD simulations with two orders of magnitude greater efficiency. Results question the existence of periodic (cycling) motion of the polymer chain.     

Vlasov Scaling for Stochastic Dynamics of Continuous Systems

We describe a general derivation scheme for the Vlasov-type equations for Markov evolutions of particle systems in continuum. This scheme is based on a proper scaling of corresponding Markov generators and has an algorithmic realization in terms of related hierarchical chains of correlation functions equations. Several examples of realization of the proposed approach in particular models are presented.     

Parallel Dynamics of Hopfield Network with Self-coupling Terms

The parallel dynamics of Hopfield network with self-coupling terms is calculated by an analytical approach with probability theory. The explicit formulas obtained for the first two steps of evolu tion of main overlap are in good agreement with computer simulations.     

Stochastic Model of Microtubule Dynamics

We introduce a continuous time stochastic process on strings made of two types of particle, whose dynamics mimics that of microtubules in a living cell. The long term behaviour of the system is described in terms of the velocity v of the string end. We show that v is an analytic function of its parameters and study its monotonicity properties. We give a complete characterisation of the phase diagram of the model and derive several criteria of the growth (\(v>0\)) and the shrinking (\(v<0\)) regimes of the dynamics.     

Dynamics of Entanglement of Qutrit-Qutrit States with Stochastic Dephasing

The effect of stochastic dephasing on the dynamics of entanglement of qutrit-qutrit states is investigated by using negativity and bound entanglement defined with realignment criterion. From the analysis, we find that the time evolution of quantum free entanglement and bound entanglement depends on the fluctuations of the stochastic variables and the parameters of the particular initial states of concern. Our results imply that some qutrits states display both distillability sudden death and entanglement sudden death, while some states do not display distillability sudden death but onlyentanglement sudden death.     

Gibbsian Dynamics and Invariant Measures for Stochastic Dissipative PDEs

We present a general strategy for proving ergodicity for stochastically forced nonlinear dissipative PDEs. It consists of two main steps. The first step is the reduction to a finite dimensional Gibbsian dynamics of the low modes. The second step is to prove the equivalence between measures induced by different past histories using Girsanov theorem. As applications, we prove ergodicity for Ginzburg–Landau, Kuramoto–Sivashinsky and Cahn–Hilliard equations with stochastic forcing.     

Quantum Zeno Dynamics Through Stochastic Protocols

Quantum measurements play a crucial role in quantum mechanics since they perturb, unavoidably and irreversibly, the state of the measured quantum system. More extremely, the constant observation of a quantum system can even freeze its dynamics to a subspace, effectively truncating the Hilbert space of the system. It represents the quantum version of the famous flying arrow Zeno paradox, and is called quantum Zeno dynamics. In general, it can be obtained by applying frequent consecutive quantum measurements that are equally spaced in time. Here, we introduce time disorder in the measurement sequence, and analytically investigate how this temporal stochasticity may affect the confinement probability of the system in the subspace. As main result, we then exploit how different dissipative and coherent Zeno protocols can be generalized to this stochastic scenario. Finally, our analytical predictions are numerically tested on a paradigmatic spin chain where we find a trade‐off between a probabilistic scheme with high fidelity (compared to perfect subspace dynamics) and a deterministic one with a slightly lower fidelity, moving further steps towards new schemes of Zeno‐based control for future quantum technologies.     

基于分区域耦合的随机并行梯度下降自适应光学

基于随机并行梯度下降(SPGD)方法的自适应光学(AO)系统通过直接优化系统的性能评价函数来控制波前校正器以补偿光束中存在的波前畸变。为了提高这种无模型优化自适应光学系统的收敛速度, 提出了基于分区域耦合的新方法以改进传统随机并行梯度下降自适应光学系统的工作方式。将波前校正器光学孔径分成多块子区域, 每块子区域对应着的所有驱动器作为一个整体控制单元, 从形式上可以得到一个空间分辨率较低的分区域波前校正器。该校正器与原校正器同步工作, 并采用随机并行梯度下降算法对同一个性能评价函数进行优化, 从而构成了双校正器的耦合工作结构。对256单元分立活塞式波前校正器建立了自适应成像系统的数值模型, 结果表明这种分区域耦合的随机并行梯度下降自适应光学系统比传统随机并行梯度下降自适应光学系统具有更快的收敛速度和更好的渐近态。