Nonequilibrium Wetting

When a nonequilibrium growing interface in the presence of a wall is considered a nonequilibrium wetting transition may take place. This transition can be studied through Langevin equations or discrete growth models. In the first case, the Kardar-Parisi-Zhang equation, which defines a very robust universality class for nonequilibrium moving interfaces, with a soft-wall potential is considered. While in the second, microscopic models, in the corresponding universality class, with evaporation and deposition of particles in the presence of hard-wall are studied. Equilibrium wetting is related to a particular case of the problem, it corresponds to the Edwards-Wilkinson equation with a potential in the continuum approach or to the fulfillment of detailed balance in the microscopic models. In this review we present the analytical and numerical methods used to investigate the problem and the very rich behavior that is observed with them.     

Construction of the mass velocity profile for a rarefied molecular gas entrained by a rotating sphere taking into account thermophysical parameters of the gas

The problem of a sphere rotating in a molecular gas is solved in the isothermal approximation. The expression for the velocity of a rarefied molecular gas entrained by a sphere rotating in it is derived for sliding flow conditions taking into account the second-order correction in the Knudsen number. A generalization of the Boltzmann kinetic equation in the BGK model to the case of rotational degrees of freedom of gas molecules is used as the basic equation. The diffusive reflection model is employed as the microscopic boundary condition on the surface of the sphere. It is shown that this approach makes it possible to take into account the dependence of the gas velocity on the Prandtl number and gas temperature.     

An Investigation of Relativistic Microscopic Optical Potential in Terms of Relativistic Brueckner-Bethe-Goldstone Equation

Relativistic microscopic optical potential of nucleon-nucleus is derived from the relativistic Brueckner-Bethe-Goldstone (RBBG) equation.The complex effective mass of a nucleon is determined by a fit to 200MeV p-⁴⁰Ca scattering data.The relativistic microscopic optical potentials with this effective mass are obtained from RBBG for p-¹⁶O,⁴⁰Ca,⁹⁰Zr and ²⁰⁸Pb scattering in energy range from 160 to 180MeV.The microscopic optical potential is used to study the proton-⁴⁰Ca scattering problem at 200MeV.The results,such as defferential cross section,analyzing power and spin rotation function are compared with those calculated from phenomenological relativistic optical potential.     

Properties of quark matter in a new quasiparticle model with QCD running coupling

The running of the QCD coupling in the effective mass causes thermodynamic inconsistency problem in the conventional quasiparticle model. We provide a novel treatment which removes the inconsistency by an effective bag constant. The chemical potential dependence of the renormalization subtraction point is constrained by the Cauchy condition in the chemical potential space. The stability and microscopic properties of strange quark matter are then studied within the completely self-consistent quasiparticle model, and the obtained equation of state of quark matter is applied to the investigation of strange stars. It is found that our improved model can describe well compact stars with mass about two times the solar mass, which indicates that such massive compact stars could be strange stars.     

On linearized hydrodynamic modes in statistical physics

We formulate the linearized generalized Boltzmann equation as an (asymmetric) eigenvalue problem. This problem has five eigenvalues which tend to zero when the uniformity parameter tends to zero: to second order in this parameter, they correspond to damped sound (two modes), diffusing shear flow (two modes), and diffusing entropy flow (one mode). The microscopic expressions deduced from these results for the transport coefficients agree with the correlation-function formulas. Moreover, the corresponding eigenfunctions are explicitly displayed to lowest order in the uniformity parameter: they are microscopic analogs, in terms ofone-particle distribution functions, of the well-known linearized hydrodynamic modes of macroscopic physics. All results are established to all orders in the interactions.     

Harmonic approximation to small amplitude nuclear vibrations

We present a microscopic treatment of many body correlations for small amplitude nuclear vibrations in the harmonic approximation. Although this approximation will be valid only within discussed limits, it leads to a very simple generalized form of the usual RPA matrix equation     

Exact Scaling Functions for One-Dimensional Stationary KPZ Growth

We determine the stationary two-point correlation function of the one-dimensional KPZ equation through the scaling limit of a solvable microscopic model, the polynuclear growth model. The equivalence to a directed polymer problem with specific boundary conditions allows one to express the corresponding scaling function in terms of the solution to a Riemann–Hilbert problem related to the Painlevé II equation. We solve these equations numerically with very high precision and compare our, up to numerical rounding exact, result with the prediction of Colaiori and Moore⁽¹⁾ obtained from the mode coupling approximation.     

On the balance laws of extended thermodynamics (ET) for non-ideal gases

The conservation laws of mass and momentum and the equations of balance of momentum flux and energy flux as well as the higher order balance laws are derived by means of the modified Klimontovich kinetic equation for non-ideal gases. The effect of the body forces and inertial forces during the persistence of a collision is taken into account in order to have the balance laws valid for general frames of reference. The sequence of macroscopic quantities appearing in the balance equations is decomposed into convective and non-convective parts and this decomposition is explained on the basis of statistical mechanics. A problem of symmetry or non-symmetry of tensors associated with the presence of interactions between microscopic particles is discussed from a molecular point of view. Explicit expressions for the energy density, the pressure, the pressure tensor, the heat flux and the other expressions characteristic for ET are given in terms of microscopic variables.     

The KdV-Burgers equation in speed gradient viscous continuum model

Based on the microscopic two velocity difference model, a macroscopic model called speed viscous continuum model is developed to describe traffic flow. The relative velocities are added to the motion equation, which leads to viscous effects in continuum model. The viscous continuum model overcomes the backward travel problem, which exists in many higher-order continuum models. Nonlinear analysis shows that the density fluctuation in traffic flow leads to density waves. Near the onset of instability, a small disturbance could lead to solitons described by the Korteweg-de Vries-Burgers (KdV-Burgers) equation, which is seldom found in other traffic flow models, and the soliton solution is derived.     

A Boltzmann Equation Approach to the Dynamics of the Simple Piston

The evolution of a simple piston under a constant external force is investigated from a microscopic approach. Using Boltzmann's equation and simplifying assumptions it is shown that the system evolves towards equilibrium according to the macroscopic laws of thermodynamics: entropy production is positive and Onsager's relations are verified near equilibrium. Numerical simulations are presented which show that the evolution takes place in two stages: first a deterministic approach to the equilibrium position and then a stochastic motion around the equilibrium position. It also shows that the damping is not correctly described with these simplifying assumptions and a quantitative explanation of this effect remains an open problem.     

Macroscopic Time Evolution and MaxEnt Inference for Closed Systems with Hamiltonian Dynamics

MaxEnt inference algorithm and information theory are relevant for the time evolution of macroscopic systems considered as problem of incomplete information. Two different MaxEnt approaches are introduced in this work, both applied to prediction of time evolution for closed Hamiltonian systems. The first one is based on Liouville equation for the conditional probability distribution, introduced as a strict microscopic constraint on time evolution in phase space. The conditional probability distribution is defined for the set of microstates associated with the set of phase space paths determined by solutions of Hamilton’s equations. The MaxEnt inference algorithm with Shannon’s concept of the conditional information entropy is then applied to prediction, consistently with this strict microscopic constraint on time evolution in phase space. The second approach is based on the same concepts, with a difference that Liouville equation for the conditional probability distribution is introduced as a macroscopic constraint given by a phase space average. We consider the incomplete nature of our information about microscopic dynamics in a rational way that is consistent with Jaynes’ formulation of predictive statistical mechanics, and the concept of macroscopic reproducibility for time dependent processes. Maximization of the conditional information entropy subject to this macroscopic constraint leads to a loss of correlation between the initial phase space paths and final microstates. Information entropy is the theoretic upper bound on the conditional information entropy, with the upper bound attained only in case of the complete loss of correlation. In this alternative approach to prediction of macroscopic time evolution, maximization of the conditional information entropy is equivalent to the loss of statistical correlation, and leads to corresponding loss of information. In accordance with the original idea of Jaynes, irreversibility appears as a consequence of gradual loss of information about possible microstates of the system.     

The dynamic natures of microscopic particles described by nonlinear Schrödinger equation

There are a lot of difficulties and troubles in quantum mechanics, when the linear Schrödinger equation is used to describe microscopic particles. Thus, we here replace it by a nonlinear Schrödinger equation to investigate the properties and rule of microscopic particles. In such a case we find that the motion of microscopic particle satisfies classical rule and obeys the Hamiltonian principle, Lagrangian and Hamilton equations. We verify further the correctness of these conclusions by the results of nonlinear Schrödinger equation under actions of different externally applied potential. From these studies, we see clearly that rules and features of motion of microscopic particle described by nonlinear Schrödinger equation are greatly different from those in the linear Schrödinger equation, they have many classical properties, which are consistent with concept of corpuscles. Thus, we should use the nonlinear Schrödinger equation to describe microscopic particles.     

Mode coupling from linear and nonlinear kinetic equations

The calculation of mode coupling contributions to equilibrium time correlation functions from the nonlinear Boltzmann equation is reconsidered. It is suggested that the use of a nonlinear kinetic equation is not appropriate in this context, but instead such calculations should be reinterpreted in terms of the Klimontovich equation for the microscopic phase space density. For hard spheres the Klimontovich equation is formally similar to the nonlinear Boltzmann equation, and this similarity is exploited to explain the successful calculation of mode coupling effects from the latter. The relationship of the Klimontovich formulation to the linear ring approximation is also established.     

Uncertainty features of microscopic particles described by nonlinear Schrüdinger equation

The uncertainty relationship between position and momentum of the microscopic particles is calculated by nonlinear quantum theory in which the states of the particles are described by a nonlinear Schrüdinger equation. The results show that the uncertainty relation differs from that in the quantum mechanics and has a minimum value in this case. This means that the position and momentum of the particles could be determined simultaneously to a certain degree, which could be caused by the wave–corpuscle duality of the microscopic particles described by the nonlinear Schrüdinger equation.     

Rarefied molecular gas flow near the rotating cylindrical surface

An exact analytic solution of the problem of the right circular cylinder in a rarefied molecular gas is constructed in the isothermal approximation. An expression for the velocity of a rarefied molecular gas entrained by the cylinder rotated therein is obtained in the regime of a flow with slip accounting for the second-order correction in terms of the Knudsen number. A generalization of the BGK model of the Boltzmann kinetic equation accounting for the rotational degrees of freedom of gas molecules is used as the governing equation, and the diffuse reflection model is used as a microscopic boundary condition on the cylinder surface. The given approach is shown to enable the consideration of the gas flow dependence on the Prandtl number and the gas temperature.     

Quark cluster model and the R-matrix theory treatment of NN scattering

A microscopic quark cluster model has been developed for six-quark states consisting of two s³ quark clusters. The consequences of channel nonorthogonality and existence of Pauliforbidden states are investigated explicitly by solving the eigenvalue problem of the resonating group method (RGM) kernel. Since the RGM kernels needed are all available, the form of the six-quark states given in this paper is very suited to detailed RGM calculations. A rigorous treatment based on the R-matrix theory has been carried out to obtain NN phase shifts. The spin-spin term of the quark-quark interaction favors states of higher color-spin symmetry. This explains the larger change caused by the hidden color states in the ³S₁ phase shifts than in the ¹S₀ phase shifts. Phase shifts calculated with inclusion of the delta and hidden color states are still too repulsive. It is pointed out that there arises a subtle problem in adding the one-boson exchange potential by hand to the RGM equation.     

Kinetic ising model study of phase separation in binary alloys

The decomposition of binary alloys after a sudden quench below the critical temperature of unmixing is studied on a microscopic basis, using a stochastic model analog to the Kawasaki spin exchange Ising model. For interactions of long range the model reduces to the standard phenomenological equation. We relate this nonlinear equation to our recent treatment of the time-dependent Ginzburg-Landau theory, and calculate the nonequilibrium relaxation functions. For interactions of short range we present some computer simulations. As example, we treat a 55×55 square lattice, with a gradient in the chemical potential. Details are given for the relaxation process, which is a coarsening at the initial stage of the decomposition, while later the gradient produces a more macroscopic phase separation.     

光子的态矢量函数

从广义Schr?dinger方程出发，在三个充分必要的量子化条件规范下，得到了一个新颖的光子一维态矢量函数，除了光子的能量和动量特征以外，它还包含有光子的角动量属性，完整地描述了光子作为量子力学中相对论自由粒子的行为.对一维光子态矢量函数的分析不仅定义了描述光子行为的微观参量——概率幅和相位，而且将这些微观参量与光束的宏观偏振联系了起来，具体剖析了一个人们一直感到困惑的偏振问题，得到了圆满的解释. 关键词： 光子态矢量函数 概率幅 相位 偏振     

概率波和非概率波

对于把克莱因-戈尔登方程当作是玻色子的方程的看法提出异议,认为它是所有微观粒子均要满足的方程,但它却不能成为任何一类粒子的波动方程.提出了克-戈方程中包含着概率和非概率两类波的概念,认为概率波还要遵从一个对时和空都是一阶导数的方程,这才是粒子的波动方程.不同种类粒子性质的不同则体现在他们概率波类型的不同上.