Disappearance of time integrals of exact memory functions in time-convolution generalized master equations

Memory functions in time-convolution Generalized Master Equations (GME) for probabilities of finding a general system (interacting by a general coupling with a true thermodynamic bath) in individual states are considered without resorting to any approximation. After taking the thermodynamic bath limit, time integrals from zero to infinite times of the memories are considered. It is argued that these integrals entering, e.g., the usual naive Markov approximation converting GME the Pauli master (PME) equations are exactly zero. This implies long-time tails of memories (unobtainable by perturbational expansions) and slower-than-exponential long-time asymptotics of relaxation.     

Tree-level breaking of SU(2)×U(1) in general SUGRA theories

It is shown that SU(2)×U(1) can be broken at the tree level, without the occurrence of global potential minima that break U(1)_e.m., in supergravity models that are more general than those proposed by Nilles, Srednicki and Wyler. The study comprises an analysis of models with a general soft supersymmetry-breaking structure as well as those of the Hall-Lykken-Weinberg type.     

Lyapunov Spectrum of Asymptotically Sub-additive Potentials

For general asymptotically sub-additive potentials (resp. asymptotically additive potentials) on general topological dynamical systems, we establish some variational relations between the topological entropy of the level sets of Lyapunov exponents, measure-theoretic entropies and topological pressures in this general situation. Most of our results are obtained without the assumption of the existence of unique equilibrium measures or the differentiability of pressure functions. Some examples are constructed to illustrate the irregularity and the complexity of multifractal behaviors in the sub-additive case and in the case that the entropy map is not upper-semi continuous.     

Nonlinear Dynamical Stability of Newtonian Rotating and Non-rotating White Dwarfs and Rotating Supermassive Stars

We prove general nonlinear stability and existence theorems for rotating star solutions which are axi-symmetric steady- state solutions of the compressible isentropic Euler-Poisson equations in 3 spatial dimensions. We apply our results to rotating white dwarf and high density supermassive (extreme relativistic) stars, stars which are in convective equilibrium and have uniform chemical composition. Also, we prove nonlinear dynamical stability of non-rotating white dwarfs with general perturbation without any symmetry restrictions. This paper is a continuation of our earlier work ([26]).     

相对论修正对麦克斯韦-玻耳兹曼分布律的影响

在本文中,分别推导了低速情形（E≈m0c^2＋p^2/2m0）和一般情形（E=√p^2c^2＋m0^2c^4）下考虑相对论修正的动量分布表达式和速率分布表达式,发现低速情形下修正后的动量分布形式与不考虑修正的动量分布在形式上一致,而速率分布形式发生了改变;对一般情形的动量分布函数和速率分布函数进行了数值模拟并对结果进行了必要讨论．我们发现当β减少时整个动量分布曲线向大动量区域延伸,当β较大,即温度较低使得p〈1时,一般情形将近似为低速情形．     

Are there basic laws of quantum information processing?

We prove within the quantum formalism without reduction postulate that the no-cloning theorem and the principle of no-increasing of entanglement (in a bit weaker formulations) are equivalent. We argue that the result is a manifestation of more general principles governing quantum information processing analogous to the thermodynamical laws.     

Classical unified fields: Physical space

We develop a general unified theory of classical mechanics and classical electromagnetism in a gravitational field on Friedman-Schöuten space-time (FSS). In this formalism (i) local equations of a charged fluid in an electromagnetic field are the same as in classical mechanics, (ii) local equations for a moving charged fluid are the same as in electromagnetism, (iii) the path of a charged particle under gravity and electromagnetism is a geodesic of the four-dimensional FSS, and (iv) the strong equivalence principle and a nonzero torsion coexist without conflict.     

Short Thermionic-Cathode Discharge in Alkaline-Earth Metal Vapor

A short (without a positive column) Knudsen thermionic discharge initiated in barium and strontium vapor has been investigated. It has been shown that the behavior of these discharges and their formation mechanism, effective heating of the plasma electrons by a cathode electron beam, are, in general, similar to the discharge in cesium.     

On the general form of the Beltrami equation and Papkovich's solution of the axially symmetrical problem of the classical theory of elasticity

The paper shows the connection between the general form of the Beltrami equation of compatibility, which had already been derived by the author, and the form given for it in orthogonal curvilinear coordinates by Lurye (para 2, 3).Some of the properties of Papkovich's general solution of the axially symmetrical problem (without body forces) of the theory of elasticity and its relation to the Finzi-Krutkov solution are discussed so as to supplement to a certain extent the paper of Trenin (para 4, 5, 6).     

Solving the Schrödinger equation of atoms and molecules without analytical integration based on the free iterative-complement-interaction wave function

A local Schr?dinger equation (LSE) method is proposed for solving the Schr?dinger equation (SE) of general atoms and molecules without doing analytic integrations over the complement functions of the free ICI (iterative-complement-interaction) wave functions. Since the free ICI wave function is potentially exact, we can assume a flatness of its local energy. The variational principle is not applicable because the analytic integrations over the free ICI complement functions are very difficult for general atoms and molecules. The LSE method is applied to several 2 to 5 electron atoms and molecules, giving an accuracy of 10(-5) Hartree in total energy. The potential energy curves of H2 and LiH molecules are calculated precisely with the free ICI LSE method. The results show the high potentiality of the free ICI LSE method for developing accurate predictive quantum chemistry with the solutions of the SE.     

A general method for constructing curved traversable wormholes in (2+1)-dimensional spacetime

We develop a general method for constructing curved traversable wormholes in (2+1)-dimensional spacetime, by generating surfaces of revolution around smooth curves. Application of this method to a straight line gives the usual spherically symmetric wormholes. The physics behind (2+1)-d curved traversable wormholes is discussed based on solutions to the Einstein field equations when the tidal force is zero. The Einstein field equations are found to reduce to one equation whereby the mass-energy density varies linearly with the Ricci scalar, which signifies that our (2+1)-d curved traversable wormholes are supported by dust of ordinary and exotic matter without radial tension nor lateral pressure. With this, two examples of (2+1)-d curved traversable wormholes: the helical wormhole and the catenary wormhole, are constructed and we show that there exist geodesics through them supported by non-exotic matter. This general method is applicable to our (3+1)-d spacetime.     

Perturbation to Lie Symmetry and Adiabatic Invariants for General Holonomic Mechanical Systems

Based on the concept of adiabatic invariant, the perturbation to the Lie symmetry and adiabatic invariants for general holonomic mechanical systems are studied. The exact invariants induced directly from the Lie symmetry of the system without perturbation are given. The perturbation to the Lie symmetry is discussed and the adiabatic invariants that have the different form from that in [Act. Phys. Sin. 55 (2006) 3236 (in Chinese)] of the perturbed system, are obtained.     

Decay of the false vacuum at finite temperature

In this paper we study kinetics of the first-order phase transitions in gauge theories with spontaneous symmetry breaking. A general theory of the decay of the metastable phase (false vacuum) at a finite temperature is developed. A number of concrete examples are considered, which will make it possible to study kinetics of phase transitions in a wide class of theories without complicated computer calculations.     

Perturbation to Lie Symmetry and Adiabatic Invariants for General Holonomic Mechanical Systems

Based on the concept of adiabatic invariant, the perturbation to the Lie symmetry and adiabatic invariants for general holonomic mechanical systems are studied. The exact invariants induced directly from the Lie symmetry of the system without perturbation are given. The perturbation to the Lie symmetry is discussed and the adiabatic invariants that have the different form from that in [Act. Phys. Sin. 55 (2006) 3236 (in Chinese)] of the perturbed system, are obtained.     

Disturbance-Observer-Based U-Control (DOBUC) for Nonlinear Dynamic Systems

U-model, which is a control-oriented model set with the property of generally facilitate nonlinearity dynamic inversion/cancellation, has been introduced to the Disturbance Observer-Based control (DOBC) methods to improve the performance of the nonlinear systems in this paper. A general DOB based U-Control (DOBUC) framework is proposed to improve the disturbance attenuation capability of U-controller for both linear and nonlinear systems combined with (based on) the U-model-based dynamic inversion which expands the classical linear disturbance observer control to general nonlinear systems. The proposed two-step DOBUC design procedures in which the design of DOB and U-controller are totally independent and separated, enables the establishment of global exponential stability without being subject to disturbances and uncertainties. Comparative simulation experiments with Nonlinear DOBC in controlling Wind Energy Conversion Systems (WECS) and Permanent Magnet Synchronous Motors (PMSM) demonstrated the proposed method.     

Planar dielectric grating diffraction theories

Various planar dielectric grating diffraction theories are reviewed for the case of a general sinusoidal permittivity planar grating with slanted fringes and plane wave incidence at an arbitrary angle. Exact formulations without approximations (rigorous coupled-wave analysis and rigorous modal analysis) are developed first. Then, using a series of fundamental assumptions, rigorous theory is shown to reduce to the various approximate theories in the appropriate limits. The implications of these fundamental assumptions are discussed.     

Scale-free networks via attaching to random neighbors

Preferential attachment is considered one of the key factors in the formation of scale-free networks. However, complete random attachment without a preferential mechanism can also generate scale-free networks in nature, such as protein interaction networks in cells. This article presents a new scale-free network model that applies the following general mechanisms: (i) networks expand continuously by the addition of new vertices, and (ii) new vertices attach to random neighbors of random vertices that are already well connected. The proposed model does not require global-based preferential strategies and utilizes only the random attachment method. Theoretical analysis and numerical simulation results denote that the proposed model has steady scale-free network characteristics, and random attachment without a preferential mechanism may generate scale-free networks.     

Novel methods for finding general forms of new multi-soliton solutions to (1+1)-dimensional KdV equation and (2+1)-dimensional Kadomtsev–Petviashvili (KP) equation

In this paper, two novel methods used to solve (1+1) and (2+1)-dimensional completely integrable equations are proposed. The methods are applied to handle the KdV and Kadomtsev–Petviashvili (KP) equations with variable coefficients, and the general forms of new multi-soliton solutions are formally obtained, respectively. In addition, the new multi-soliton solution is suitable to two different type KP equations. Comparing with the Hirota’s method, the results show that new methods are straightforward handling the KdV and KP equations without conjecturing the transformation and good in dealing the equations with variable coefficients.     

Cosmological models with constant deceleration parameter and bulk viscous mode

Recently Berman and Gomide have presented cosmological models with a constant deceleration parameter in general relativity without assuming a specific equation of state. It is shown that these models are equivalent to those with bulk viscosity. Some general remarks are made on the former models, including implications for violations of causality.     

Derivation of the Bosonic Part of the Electroweak Chiral Lagrangian from a General Underlying Technicolor Theory

Bosonic part of SU(2)L U(1)Y effective chiral Lagrangian for electroweak symmetry breaking is derived from an underlying technicolor theory with no approximation. The underlying theory is assumed to be the most general gauge theory without fundamental scalars. A condensate is required to exist in the theory which breaks SU(2)L U(1)Y dynamically to U(1)em and the anomaly of the theory caused by gauge interaction must be cancelled. The formulation offers general definitions in terms of underlying theory for the low energy constants in effective chiral Lagrangian.``