Lattices of Quantum Automata

We defined and studied three different types of lattice-valued finite state quantum automata (LQA) and four different kinds of LQA operations, discussed their advantages, disadvantages, and various properties. There are four major results obtained in this paper. First, no one of the above mentioned LQA follows the law of lattice value conservation. Second, the theorem of classical automata theory, that each nondeterministic finite state automaton has an equivalent deterministic one, is not necessarily valid for finite state quantum automata. Third, we proved the existence of semilattices and also lattices formed by different types of LQA. Fourth, there are tight relations between properties of the original lattice l and those of the l-valued lattice formed by LQA.     

鼓泡床内气固两相流的变尺度格子气模拟

基于格子气自动机的建模思想,建立气固两相流的变尺度格子气模型,用微观层次的气固作用规则描述两相流的宏观行为.二维流场空间被离散成两层不同尺度的正六边形网格,固体颗粒和气体粒子分别在各自的网格上运动;在格子气自动机基本规则基础上设计气固相作用规则和附加演化规则;确定模型宏观物理量的统计计算方法,并根据相似原理建立模型物理量与真实物理量之间的转换关系.用建立的模型对鼓泡床内气固流动行为进行模拟,通过比较发现,变尺度格子气模型的模拟结果与文献中的实验结果和双流体模型的模拟结果吻合较好,且平均相对误差更小,表明建模方法的正确性和模型的有效性.     

热声发动机的格子气模拟

在传统的9-bit格子气模型中引入了温度区的概念,并应用于热声发动机的模拟研究.利用改进后的格子气模型,模拟了热声谐振管中的自激振荡和二维温度场的分布及温度随时间的演化过程,同时,对热声板叠的长度和在声场中的位置对声幅的影响也进行了数值研究,所得结果对板叠的优化设计是有价值的.通过对模拟和实验结果的比较,验证了热声机格子气模型的有效性,表明格子气方法适用于热声模拟.     

Around Multicolour Disordered Lattice Gas

We consider a system of multicolour disordered lattice gas, following closely the (monocolour) introduced by Faggionato and Martinelli^(3,4). We study the projection on the monocolour system and we derive an estimate of the closeness between grand canonical and canonical Gibbs measures. AMS Classification: Primary: 60K35, 82C20, 82C22     

Efficiency of Classical and Quantum Games Equilibria

Nash equilibria and correlated equilibria of classical and quantum games are investigated in the context of their Pareto efficiency. The examples of the prisoner’s dilemma, battle of the sexes and the game of chicken are studied. Correlated equilibria usually improve Nash equilibria of games but require a trusted correlation device susceptible to manipulation. The quantum extension of these games in the Eisert–Wilkens–Lewenstein formalism and the Frąckiewicz–Pykacz parameterization is analyzed. It is shown that the Nash equilibria of these games in quantum mixed Pauli strategies are closer to Pareto optimal results than their classical counter-parts. The relationship of mixed Pauli strategies equilibria and correlated equilibria is also studied.     

Effects of Field Orientation on the Driven Lattice Gas

Steady states of the driven lattice gas (DLG) on triangular, hexagonal and square lattices with the field at several fixed orientations to the principal lattice vectors were studied by Monte Carlo simulation. In most cases a strong field suppressed change to a low-temperature ordered phase. On each lattice, one field orientation that caused nonequilibrium ordering was identified. On triangular and hexagonal lattices, dependence of energy and anisotropy on field strength was studied at those orientations. Anisotropic ordering along the field developed at intermediate temperatures under weak fields. Partial ordering along the field persisted to low temperature under strong fields.     

Weakly Regular Quantum Grammars and Asynchronous Quantum Automata

In this paper, we define weakly regular quantum grammars (WRQG), regular quantum grammars (RQG), asynchronous quantum automata (AQA) and synchronous quantum automata (SQA). Moreover, we investigate the relationships between quantum languages generated by weakly quantum regular grammars and by asynchronous quantum automata. At the mean time, we discuss the relationships between regular quantum grammars and synchronous quantum automata. This work is supported by National Science Foundation of China (Grant No. 10571112) and 973 Program of China (No. 2002CB312200).     

Return Probability of Quantum and Correlated Random Walks

The analysis of the return probability is one of the most essential and fundamental topics in the study of classical random walks. In this paper, we study the return probability of quantum and correlated random walks in the one-dimensional integer lattice by the path counting method. We show that the return probability of both quantum and correlated random walks can be expressed in terms of the Legendre polynomial. Moreover, the generating function of the return probability can be written in terms of elliptic integrals of the first and second kinds for the quantum walk.     

Quantum Pushdown Automata

Quantum automata are mathematical models for quantum computing. We analyze the existing quantum pushdown automata, propose a q quantum pushdown automata (qQPDA), and partially clarify their connections. We emphasize some advantages of our qQPDA over others. We demonstrate the equivalence between qQPDA and another QPDA. We indicate that qQPDA are at least as powerful as the QPDA of Moore and Crutchfield with accepting words by empty stack. We introduce the quantum languages accepted by qQPDA and prove that every -q quantum context-free language is also an -q quantum context-free language for any (0, 1) and (0, 1).     

Fluctuation Dissipation Equation for Lattice Gas with Energy

In this paper we introduce a lattice gas with energy, and obtain the fluctuation dissipation equation for it. The system has two conserved quantities, the number of particles and the total energy. Once the fluctuation dissipation equation is established, the hydrodynamic limit is easily deduced from it by using the methods found in ref. 1 for this model.     

Discrete Green's Function for Lattice Random Walk

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Discrete Green's Function for Lattice Random Walk

A lattice random walk model based on particles scattering on discrete lattice of homogenous space is introduced. The discrete Green's function (DFG) for two-dimensional and three-dimensional lattice random walk of photon is found and proved by mathematical induction. The convolution theorem of photon lattice random walk is presented. They can be used with the method of images to calculate the photon density distribution in semi-infinite and finite slab homogenous turbid media such as tissue.     

Lattice Gas with Finite-Range Interaction Under Gravity

Existence of a phase separation is proved for a classical lattice gas with finite-range pair potential under the action of a weak gravitational field.     

Pumping Lemma for Quantum Automata

Not all lattice-valued quantum automata possess the pumping property in its strict form. However the pumping lemma can be generalized, and all lattice-valued quantum automata possess the generalized pumping property.     

On the Lowest Energy Nucleation Path in a Supersaturated Lattice Gas

A lattice gas with non-conserved spin flip dynamics (of both non-Glauber and Glauber types) is considered at TT _c , the critical temperature. For arbitrary supersaturation, S, a general expression for the inverse of the nucleation rate along the lowest energy path is derived. The exponential part is identical to the one by Neves and Schonmann [Commun. Math. Phys. 137:20 (1991)]. The preexponential can be expressed in terms of elliptic theta-functions for small S, and in the limits, respectively, of ST/ or ST/ (– being the nearest-neighbor interaction energy), elementary versions of the general expression are further obtained. The preexponential has a smooth component, as well as small-scale modulations which are approximately periodic in the inverse supersaturation. For ST/, the smooth part is proportional to , in contrast to the zero-T limit where it is linear in S. The latter limit becomes apparent only at extremely low temperatures which are cubic in S.     

Kink movements and percolation in the binary additive cellular automaton

We show that under the Bernoulli initial condition two kinks in the cellular automaton (CA) 18/256 will annihilate each other with probability one. It turns out that there is an equivalent statement in terms of percolation in the simple binary additive CA. Namely, under the Bernoulli initial condition, l's do not percolate in the binary additive CA.     

Sharp Phase Boundaries for a Lattice Flux Line Model

We consider a model of nonintersecting flux lines in a rectangular region on the lattice ^d , where each flux line is a non-isotropic self-avoiding random walk constrained to begin and end on the boundary of the region. The thermodynamic limit is reached through an increasing sequence of such regions. We prove the existence of several distinct phases for this model, corresponding to different regimes for the flux line density—a phase with zero density, a collection of phases with maximal density, and at least one intermediate phase. The locations of the boundaries of these phases are determined exactly for a wide range of parameters. Our results interpolate continuously between previous results on oriented and standard nonoriented self-avoiding random walks.     

Phase Transitions in a Driven Lattice Gas with Anisotropic Interactions

The Ising lattice gas, with its well known equilibrium properties, displays a number of surprising phenomena when driven into nonequilibrium steady states. We study such a model with anisotropic interparticle interactions (J _||J ), using both Monte Carlo simulations and high temperature series techniques. Under saturation drive, the shift in the transition temperature can be both positive and negative, depending on the ratio J _||/J ! For finite drives, both first- and second-order transitions are observed. Some aspects of the phase diagram can be predicted by investigating the two-point correlation function at the first nontrivial order of a high-temperature series expansion.     

Evolution of Matter Wave Interference of Bose-Condensed Gas in a 2D Optical Lattice

We investigate the average particle-number distribution of the atoms in the combined potential of 2D optical lattices and 3D harmonic magnetic trap based on the Gross-Pitaevskii equation. After the combined potential is switched off, and only the optical lattice is switched off, we give the analytical results of the wavefunction of the Bosecondensed gas at any time t by using a propagator method. For both disk-shaped and cigar-shaped Bose-condensed gas,we discuss the evolution process of the central and side peaks of the interference pattern.