EXPONENT BEHAVIORS OF SINGLE MODE LASER SYSTEM WITH SATURABLE ABSORBER NEAR THRESHOLD

In this letter we discuss the exponent behaviors near a threshold of single mode laser system in the presence of a saturable absorber. Four threshold exponents, β,δ,γ and α, and four threshold amplitudes B,D,г and A are obtained. They obey the generalized scaling laws of z=4.     

Non-equilibrium phase transition of the fully frustrated square lattice Coulomb gas model

The non-equilibrium phase transitions of the fullyfrustrated (f = 1/2) square lattice Coulomb gas (CG) modeldriven by external electrical fields are studied in the frameworkof the short-time dynamic scaling approach. The criticaltemperature T_c, the static and dynamic critical exponents2β/ν, ν, and z are obtained for several smalldriving fields. The results show that T_c decreases with theincrease of electric field, and 2β/ν and z arestrongly dependent on the external electric field. Interestingly,contrary to the equilibrium case, in the presence of smallelectric field, the calculated exponent ν is close to that inpure 2D Ising model, which provides numerical evidence thatexternal electric field may change the universality class of thef = 1/2 CG system.     

Transitions to Equilibrium State in Classical φ4 Lattice

Statistical behavior of a classical φ⁴ Hamiltonian lattice is investigated from microscopic dynamics. The largest Lyapunov exponent and entropies are considered for manifesting chaos and equipartition behaviors of the system. It is found, for the first time, that for any large while finite system size there exist two critical couplings for the transitions to equipartitions, and the scaling behaviors of these lower and upper critical couplings vs. the system size are numerically obtained.     

Critical Behaviors and Finite-Size Scaling of Principal Fluctuation Modes in Complex Systems

Complex systems consisting of N agents can be investigated from the aspect of principal fluctuation modes of agents. From the correlations between agents, an N×N correlation matrix C can be obtained. The principal fluctuation modes are defined by the eigenvectors of C. Near the critical point of a complex system, we anticipate that the principal fluctuation modes have the critical behaviors similar to that of the susceptibity. With the Ising model on a two-dimensional square lattice as an example, the critical behaviors of principal fluctuation modes have been studied. The eigenvalues of the first 9 principal fluctuation modes have been invesitigated. Our Monte Carlo data demonstrate that these eigenvalues of the system with size L and the reduced temperature t follow a finite-size scaling form λ_n(L, t)=L^γ/ν f_n(tL^1/ν), where γ is critical exponent of susceptibility and ν is the critical exponent of the correlation length. Using eigenvalues λ₁, λ₂ and λ₆, we get the finite-size scaling form of the second moment correlation length ξ(L, t)=Lξ(tL^1/ν). It is shown that the second moment correlation length in the two-dimensional square lattice is anisotropic.     

全局耦合网络上的两种类集团的聚集-湮没反应动力学

利用Monte-Carlo模拟研究了全局耦合网络上扩散限制的不可逆聚集-湮没过程的动力学行为. 在系统中, 同种类集团相遇, 将发生聚集反应; 不同种类的集团相遇, 则发生部分湮没反应. 模拟结果表明:1) 当两种粒子初始浓度相等时, 系统长时间演化后, 集团浓度c(t)和粒子浓度g(t)呈现幂律形式, c(t)～t^{- α}和g(t)～t^-β, 其中幂指数α 和β 满足α=2β 的关系, 且α=2/(2 + q); 集团大小分布随时间的演化满足标度律, a_kt)=k^-τt^-ω\varPhi (k/t^z), 其中τ≈-1.27q, ω≈(3 + 1.27q)/(2 + q), z=α/2=1/(2 + q); 2) 当两种粒子初始浓度不相等时, 系统经长时间演化后, 初始浓度较小的种类完全湮没, 而初始浓度较大的那个种类的集团浓度c_A(t)仍具有幂律形式, c_A(t)～t^-α, 其中α=1/(1+q), 其集团大小分布随时间的演化也满足标度律, 标度指数为τ≈-1.27q, ω≈(2 + 1.27q)/(1 + q)和z=α=1/(1 + q). 模拟结果与已报道的理论分析结果相符得很好.     

Development of particle multiplicity distributions using a general form of the grand canonical partition function

Various phenomenological models of particle multiplicity distributions are discussed using a general form of a unified model which is based on the grand canonical partition function and Feynman's path integral approach to statistical processes. These models can be written as special cases of a more general distribution which has three control parameters which are a,x,z. The relation to these parameters to various physical quantities are discussed. A connection of the parameter a with Fisher's critical exponent τ is developed. Using this grand canonical approach, moments, cumulants and combinants are discussed and a physical interpretation of the combinants are given and their behavior connected to the critical exponent τ. Various physical phenomena such as hierarchical structure, void scaling relations, Koba–Nielson–Olesen or KNO scaling features, clan variables, and branching laws are shown in terms of this general approach. Several of these features which were previously developed in terms of the negative binomial distribution are found to be more general. Both hierarchical structure and void scaling relations depend on the Fisher exponent τ. Applications of our approach to the charged particle multiplicity distribution in jets of L3 and H1 data are given.     

Electroproduction of π from C leading to low-lying residual states in B

Energy distributions of π⁺ produced from ¹²C by electrons of total energy 195 MeV were measured at various angles. The results show large contributions from transitions leaving the residual nucleus in the ground (1⁺), first (2⁺) excited state and states at around 4.5 MeV. The angular distributions of ¹²C(γ, π⁺)¹²B leading to these residual states are deduced from the energy distributions by the unfolding method with the virtual photon theory. Theoretical results with the Helm model and the shell model are compared with the experimental results. Their relative shapes are in good agreement. A better agreement in the absolute value is found for the theoretical results which include the final-state interaction estimated with a pion optical potential. The surface production model shows better agreement with the experimental (γ, π⁺) cross sections than the volume production model.     

颗粒尺寸分散度对颗粒体系力学和几何结构特性的影响

利用颗粒离散元方法, 研究了由2048个光滑颗粒组成的体系在各向同性压缩条件下, 颗粒尺寸分散度s对颗粒体系力学和几何结构特性的影响. 结果表明: 配位数、剪切模量、静态结构因子以及取向序关联函数等都随分散度的变化而变化, 而力的累积分布不受分散度的影响. 其中, 单分散体系(亦即s=0)的静态结构因子在低波数区域(亦即低k)遵从幂律标度S(k)∝0.2k^-4/3, 各分散度下取向序关联函数峰值符合e指数变化规律g₆(r)∝ae^-r/ξ₆, 其中序关联长度ξ₆随分散度s增大而减小. 关键词： 颗粒物质 尺寸分散度 结构因子 取向序关联     

Non-equilibrium critical phenomena and phase transitions into absorbing states

This review addresses recent developments in non-equilibrium statistical physics. Focusing on phase transitions from fluctuating phases into absorbing states, the universality class of directed percolation is investigated in detail. The survey gives a general introduction to various lattice models of directed percolation and studies their scaling properties, field-theoretic aspects, numerical techniques, as well as possible experimental realizations. In addition, several examples of absorbing-state transitions which do not belong to the directed percolation universality class will be discussed. As a closely related technique, we investigate the concept of damage spreading. It is shown that this technique is ambiguous to some extent, making it impossible to define chaotic and regular phases in stochastic non-equilibrium systems. Finally, we discuss various classes of depinning transitions in models for interface growth which are related to phase transitions into absorbing states.     

The (p, t) and (p, τ) reactions on O at 39.8 MeV

Differential cross sections have been measured at forward angles for (p, t) and (p, τ) transitions from ¹⁷O to the ⁻ ground states and lowest-energy ⁻ states in the ¹⁵O and ¹⁵N mirror nuclei. The data are compared with DWBA calculations using simple single-particle and single-hole wave functions. When the (p, t) and (p, τ) transitions are considered separately, the calculated and experimental ratios of the ⁻ integrated cross sections to the ⁻ integrated cross sections agree to within 30 %; however, the ratios of (p, τ) cross sections to the mirror state (p, t) cross sections are calculated to be about twice as large as actually measured. This experimentally observed reduction of the (p, τ) cross section relative to the (p, t) cross section can possibly be attributed to interference between the S = 0 and S = 1 components of the (p, τ) transitions.     

Influence of saturable absorber on critical phenomenon analogies in single mode laser driven by external coherent field

The influence of the existence of absorbing atoms in a laser cavity on the critical exponents of abrupt transitions between steady states in the system of single mode onephoton laser driven by an external coherent field is discussed. An isolated threshold when ,and a kind of threshold when, where is the pump parameter of the absorbing atoms, is obtained. The asymptotic forms of the families of potential functions for the system near these threshold are also found. The well-known scaling hypothesis in the general homogeneous function form is shown to be a characteristic of these asymptotic families. Four threshold exponents, , , and and four threshold amplitudes,B, D, andA, near each of these thresholds, are obtained. The threshold exponents near each threshold obey the scaling laws of critical phenomena, while the corresponding amplitudes obey the definite relations between exponents and amplitudes.     

Scaling properties of eden clusters in three and four dimensions

We study the scaling properties of noise reduced Eden clusters in three and four dimensions for variant B in the strip geometry. We find that the width W for large times behaves as a(s)g(L/s^d−1), where L is the width of the strip, s the noise reduction parameter, d the dimension of space, and a(s) a decreasing function of s, g is a scaling function with the property g(u)→1/2 as u→0 and g(u)u^x as u→∞, where χ is the roughness exponent. This scaling result leads to a new way of determining χ. In 3 dimensions, our numerical values for χ support a recent conjecture by Kim and Kosterlitz: χ = 2/(d + 2), and contradict all the former analytical conjectures. In 4 dimensions, we cannot distinguish between the conjectures of Kim and Kosterlitz and the conjecture of Wolf and Kertész, because large crossovers and finite size effects make the measurement of the exponents difficult.     

Calogero-Moser and Toda systems for twisted and untwisted affine Lie algebras

The elliptic Calogero-Moser Hamiltonian and Lax pair associated with a general simple Lie algebra G are shown to scale to the (affine) Toda Hamiltonian and Lax pair. The limit consists in taking the elliptic modulus τ and the Calogero-Moser couplings m to infinity, while keeping fixed the combination M = m e^iδθτ for some exponent δ. Critical scaling limits arise when 1/δ equals the Coxeter number or the dual Coxeter number for the untwisted and twisted Calogero-Moser systems respectively; the limit consists then of the Toda system for the affine Lie algebras G⁽¹⁾ and (G⁽¹⁾)^V. The limits of the untwisted or twisted Calogero-Moser system, for δ less than these critical values, but non-zero, consists of the ordinary Toda system, while for δ = 0, it consists of the trigonometric Calogero-Moser systems for the algebras G and G^V respectively.     

Critical behavior of thermal relaxation near a breakdown point

At a composition far above the percolation threshold, the resistance of a composite sample increases with time due to Joule heating as a constant current of a sufficiently large value is passed through the sample. If the current is less than a certain breakdown current (I(b)) the resistance eventually reaches a steady value with a characteristic relaxation time tau(h). The latter diverges with current I as tau(h) approximately (1-I(2)/I(2)(b))(-z). The value of the exponent z displays large fluctuations leading to unusual scaling of the relaxation time. It is shown that the results lead to important conclusions about the nature of breakdown phenomena.     

Scaling predictions for thermodynamical properties of finite-size liquid systems

The notion of spatial limitation of a system undergoing critical phenomena and phase transitions is presented. The scaling formulae for the singular part of the fluctuation free energy and correlation length for spatially limited liquid systems are analyzed. The conducted research supports the conclusion that reducing of the volume's size leads, after the decreasing of the correlation length, to decreasing of the susceptibility χ, which is equivalent to isothermal compressibility β_T for one-component liquid.     

RADIATIVE DECAY J/ψ→γη′ IN PERTURBATIVE QCD

The deccy rate of J/ψ→γη^′ is calculated by using the light-cone wave function of the flavor singlet pseudoscalar. The result is reasonably in agreement with the experiment.     

Exponent inequalities in dynamical systems

In this Letter, we derive exponent inequalities relating the dynamic exponent z to the steady state exponent Γ for a general class of stochastically driven dynamical systems. We begin by deriving a general exact inequality, relating the response function and the correlation function, from which the various exponent inequalities emanate. We then distinguish between two classes of dynamical systems and obtain different and complementary inequalities relating z and Γ. The consequences of those inequalities for a wide set of dynamical problems, including critical dynamics and Kardar-Parisi-Zhang-like problems, are discussed.     

Critical Behavior of Ising Model with Long Range Correlated Quenched Impurities

The theoretic renormalization-group approach is applied to the study of the critical behavior of the ddimensional Ising model with long-range correlated quenched impurities, which has a power-like correlations r^-(d-p). The asymptotic scaling law is studied in the framework of the expansion in e = 4 - d. In d ~ 4, the dynamic exponent z .is calculated up to the second order in p with ρ= O(ε^1/2). The shape function is obtained in one-loop calculation. When d = 4, the logarithmic corrections to the critical behavior are found. The finite size effect on the order parameter relaxation rate is also studied.