原子核费密多体系统平均场近似的推广

本文应用先前得到的序参量——统计格林函数耦合方程组,对于原子核多费密子体系,系统地导出了它的平均场近似,Hartree-Fock近似和无规相位近似。并求出了相应近似下系统热力学势的明显表达式。本文的讨论也适用于处于平衡或非平衡定常态的其他多体系统。 关键词：     

Nonuniversality of Critical Exponents in a Fractional Quenched Kardar–Parisi–Zhang Equation

In this article we address the problem of the depinning transition for driven interfaces in random media. We introduce a fractional Kardar–Parisi–Zhang equation with quenched noise, in which the normal diffusion term is replaced by a fractional Laplacian accounting for long-range interactions through quenched disorder. The critical values of the external driving force and nonlinear term coefficient evidently depend on the system size at the depinning transition. For a fixed value of the external driving force, the fractional order much determines the value of the nonlinear term coefficient that leads to a depinned interface. Near the depinning threshold, the critical exponent obtained numerically is nonuniversal, and weakly depends on the fractional order.     

Factorization of correlation functions and the replica limit of the Toda lattice equation

Exact microscopic spectral correlation functions are derived by means of the replica limit of the Toda lattice equation. We consider both Hermitian and non-Hermitian theories in the Wigner–Dyson universality class (class A) and in the chiral universality class (class AIII). In the Hermitian case we rederive two-point correlation functions for class A and class AIII as well as several one-point correlation functions in class AIII. In the non-Hermitian case the average spectral density of non-Hermitian complex random matrices in the weak non-Hermiticity limit is obtained directly from the replica limit of the Toda lattice equation. In the case of class A, this result describes the spectral density of a disordered system in a constant imaginary vector potential (the Hatano–Nelson model) which is known from earlier work. New results are obtained for the average spectral density in the weak non-Hermiticity limit of a quenched chiral random matrix model at non-zero chemical potential. These results apply to the ergodic or ϵ domain of the quenched QCD partition function at non-zero chemical potential. Our results have been checked against numerical results obtained from a large ensemble of random matrices. The spectral density obtained is different from the result derived by Akemann for a closely related model, which is given by the leading order asymptotic expansion of our result. In all cases, the replica limit of the Toda lattice equation explains the factorization of spectral one- and two-point functions into a product of a bosonic (non-compact integral) and a fermionic (compact integral) partition function. We conclude that the fermionic partition functions, the bosonic partition functions and the supersymmetric partition function are all part of a single integrable hierarchy. This is the reason that it is possible to obtain the supersymmetric partition function, and its derivatives, from the replica limit of the Toda lattice equation.     

ON AN APPROXIMATE FORM OF THE COUPLED EQUATIONS OF THE ORDER PARAMETER WITH THE WEAK ELECTROMAGNETIC FIELD FOR THE IDEAL SUPERCONDUCTOR

A simplified derivation of the macroscopic electrodynamic equations of Umezawa, Hancini et al. for superconductors is given in the framework of the closed time path Green's functions (CTPGF)using generalized Ward-Takahashi identities. It is shown that the forms of the equations obtained are the same for both thermoe quilibrium and nonequilibrium stationary states provided the electromagnetic field is weak and its effect on the modulus of the order parameter can be neglected. The statistical behavior of the states is completely specified in the equations by parameters which can be calculated by the method of CTPGF.     

闭路格林函数中的相互作用绘景

本文证明了闭路格林函数中所引入的相互作用绘景应是Incoming相互作用绘景,微扰展开也是在这个意义上进行的。 关键词：     

时间反演对称和非平衡统计定常态(Ⅰ)

本文是作者从微观量子统计理论出发应用微观可逆性原理讨论非平衡统计定常态普遍性质的第一部份。文中给出了非平衡量子统计格林函数(闭路格林函数)在定常态上关于时间反演对称的表达方式。把生成泛函技术和时间反演对称结合起来,得到了具有时间反演对称性的非平衡统计定常态上统计格林函数和顶点函数所满足的时间反演对称关系。 关键词：     

Quenched master fields

We derive an exact algebraic (master) equation for the euclidean master field of any large-N matrix theory, including quantum chromodynamics. The master equation is the quenched Langevin equation. The master field, a translationally covariant function of (uniform) random momenta and (gaussian) random noise, is easily constructed in perturbation theory.     

The Random Average Process and Random Walk in a Space-Time Random Environment in One Dimension

We study space-time fluctuations around a characteristic line for a one-dimensional interacting system known as the random average process. The state of this system is a real-valued function on the integers. New values of the function are created by averaging previous values with random weights. The fluctuations analyzed occur on the scale n ^1/4, where n is the ratio of macroscopic and microscopic scales in the system. The limits of the fluctuations are described by a family of Gaussian processes. In cases of known product-form invariant distributions, this limit is a two-parameter process whose time marginals are fractional Brownian motions with Hurst parameter 1/4. Along the way we study the limits of quenched mean processes for a random walk in a space-time random environment. These limits also happen at scale n ^1/4 and are described by certain Gaussian processes that we identify. In particular, when we look at a backward quenched mean process, the limit process is the solution of a stochastic heat equation.     

Interquark potential with finite quark mass from lattice QCD

We present an investigation of the interquark potential determined from the q ?q Bethe-Salpeter (BS) amplitude for heavy quarkonia in lattice QCD. The q ?q potential at finite quark mass m(q) can be calculated from the equal-time and Coulomb gauge BS amplitude through the effective Schr?dinger equation. The definition of the potential itself requires information about a kinetic mass of the quark. We then propose a self-consistent determination of the quark kinetic mass on the same footing. To verify the proposed method, we perform quenched lattice QCD simulations with a relativistic heavy-quark action at a lattice cutoff of 1/a≈2.1 GeV in a range 1.0≤m(q)≤3.6 GeV. Our numerical results show that the q ?q potential in the m(q)→∞ limit is fairly consistent with the conventional one obtained from Wilson loops. The quark-mass dependence of the q ?q potential and the spin-spin potential are also examined.     

Replica limit of the toda lattice equation

In a recent breakthrough Kanzieper showed that it is possible to obtain exact nonperturbative random matrix results from the replica limit of the corresponding Painlevé equation. In this article we analyze the replica limit of the Toda lattice equation and obtain exact expressions for the two-point function of the Gaussian unitary ensemble and the resolvent of the chiral unitary ensemble. In the latter case both the fully quenched and the partially quenched limit are considered. This derivation explains in a natural way the appearance of both compact and noncompact integrals, the hallmark of the supersymmetric method, in the replica limit of the expression for the resolvent.     

Magnetization of quenched dilute ferromagnets

Bragg-Williams self-consistent mean field theory is extended to the case of random quenched site-dilution. A comparison is made with Monte Carlo results for the triangular lattice. The extension to more general types of quenched disorder is outlined.     

Statics and kinetics at the nematic-isotropic interface in porous media

We extend the random anisotropy nematic spin model to study nematic-isotropic transitions in porous media. A complete phase diagram is obtained. In the limit of relative low randomness the existence of a triple point is predicted. For relatively large randomness we have found a depression in temperature at the transition, together with a first order transition which ends at a tricritical point, beyond which the transition becomes continuous. We use this model to investigate the motion of the nematic-isotropic interface. We assume the system to be isothermal and initially quenched into the metastable régime of the isotropic phase. Using an appropriate form of the free energy density we obtain the domain wall solutions of the time-dependent Ginzburg-Landau equation. We find that including a random field leads to smaller velocity of the interface and to larger interface width. Received 12 November 1998 and Received in final form 15 March 1999     

Depinning transition of the quenched Mullins-Herring equation: A short-time dynamic method

The depinning phase transition of the Mullins-Herring equation with an external driving force and quenched random noise is studied in a short-time dynamic scaling scheme. Besides the critical driving force, all the critical exponents can be accessed, agreeing well with those in long-time steady-state simulations. The finite size effects on the critical exponents are also discussed. It is found that reasonable results can be achieved with a relatively small system, which highlights the advantage of the present approach.     

自对耦无序分布随机链Potts模型的临界普适性研究

以蒙特卡罗模拟方法对自对耦分布二维随机链q态Potts模型的短时临界行为进行了数值研究.利用初始非平衡演化阶段存在的普适幂指数和有限体积标度行为，数值模拟了在不同形式随机分布时q＝3和q＝8态Potts模型磁临界指数η和动力学临界指数z.计算结果发现η不依赖于自对偶无序分布的具体形式， 从而以数值方法给出了一个关于淬火掺杂自旋系统的临界普适行为的验证. 关键词： 随机链Potts模型 动力学蒙特卡罗模拟 临界普适性     

Remarks concerning the derivation and the expansion of the master equation

The present work consist of two parts: In the first part we apply the method of quasilinearization to the differential equation describing the time development of the quantum-mechanical probability density. In this way we derive the master equation without resorting to perturbation theory. In the second part of the paper, for a general form of the master equation which is an integro-differential equation, we test the accuracy of the Fokker-Planck approximation with the help of a solvable model. Then we study an alternative way of reducing the integro-differential equation to a partial differential equation. By expanding the transition probability W(q, q′), and the distribution function in terms of a complete set of functions, we show that for certain forms of W(q, q′), the master equation can be transformed exactly to partial differential equations of finite order.     

Critical behaviour of random compressible magnets

The critical properties of a compressible random magnet are studied using renormalization group methods. Then-component orderparameter is coupled to quenched disorder and to the elastic fluctuations of the anisotropic solid. It is shown, that the critical behaviour of a compressible random magnet is in general the same as that of a random magnet on a rigid lattice. However, if the specific heat exponent of the ideal magnet is positive and the disorder is sufficiently weak, a macroscopic instability may prevent the system in reaching the critical point. The resulting first-order transition may be preceded by pseudocritical behaviour characteristic to pure compressible magnets. The effect of random magnetic fields on the critical properties of compressible magnets is also discussed.     

Dynamics of Non- interacting System with Long-Range Correlated Quenched Impurities

The theoretic renormalization group approach is applied to the study of the critical behavior of non-interacting system with long-range correlated quenched impurities, which has a power-like correlations r-(d-ρ). Totwo-loop order, the asymptotic scaling laws and the critical exponents are studied in the frame of a double (ε, ρ)expansion with ρ of order ε = 4 - d. In d ＜ 4, it is argued that the initial slip exponent θ = 0 together with the dynamicexponent z ＜ 2 is exact in this kind of random system.     

Recurrence and Higher Ergodic Properties for Quenched Random Lorentz Tubes in Dimension Bigger than Two

We consider the billiard dynamics in a non-compact set of ℝ ^d that is constructed as a bi-infinite chain of translated copies of the same d-dimensional polytope. A random configuration of semi-dispersing scatterers is placed in each copy. The ensemble of dynamical systems thus defined, one for each global realization of the scatterers, is called quenched random Lorentz tube. Under some fairly general conditions, we prove that every system in the ensemble is hyperbolic and almost every system is recurrent, ergodic, and enjoys some higher chaotic properties.     

自洽的关联渗流问题

本文用实空间重整化群方法处理有粹灭关联的渗流系统。我们选择最近邻短程序α为关联参量。对于关联的几率我们做了自洽的处理。在二维我们的结果表明只有一个非平庸的物理不动点,关联在无序渗流点附近是个无用参量,这与其他的关联渗流模型一致。 关键词：