整数自旋粒子的方程和波函数

从高自旋态的Bargmann-Wigner方程出发,建立了整数自旋粒子的运动方程,通过求解方程得到了一套整数自旋粒子波函数,并建立了等效Largrange形式.     

Thermodynamics of one-dimensional nonlinear lattices

Analytic equations were obtained for the thermodynamic parameters of one-dimensional lattices of particles with the Toda and Morse interaction potentials in a canonical Gibbs ensemble. For the same systems, equations were derived for molecular dynamics simulations of thermodynamic processes. Stochastic differential equations were solved with simulating the thermostat by Langevin sources with random forced. Analytic equations for thermodynamic parameters (energy, temperature, and pressure) excellently coincided with molecular dynamics simulation results. The kinetics of system relaxation to the thermodynamic equilibrium state was analyzed. The advantages of simulating the physical properties of systems in a canonical compared with microcanonical ensemble were demonstrated.     

Theory of formation of second-phase particles as a result of diffusive saturation of solid solutions

A complete system of canonical equations, which describes the precipitation of new-phase particles as a result of diffusive saturation, is formulated. An asymptotic solution of this system of equations with respect to time is obtained in the general form. The volume of the precipitated new phase and the motion of the boundary of a two-phase region at a given point in the crystal is found for sufficiently large times to be independent of the nucleation mechanism and of the mechanism of mass to the particles of the precipitated phase.     

Canonical solutions of variational problems and canonical equations of mechanics

The canonical (non-parametric) solutions of the variational problems for integral functionals are considered and the canonical solutions of variational problems of mechanics in Minkowski spaces are derived. By combining the variational principles of least action, flow, and hyperflow canonically invariant equations for the energy-momentum variable are obtained. From these equations the equations for the action and wave functions as a general solution of the combined variational problems of mechanics are derived. These equations are applicable for describing different types of particles and interactions and are summarized within the approach of general relativity.     

Wave functions in geometric quantization

A geometrical way is described to associate quantum states in the sense of geometric quantization to wave functions in the quantum mechanical sense for each relativistic elementary particle. Explicit computations are made in a number of cases: Klein-Gordon and Dirac equations, neutrino and antineutrino Weyl equations, and very general cases of massive and massless particles of arbitrary spin. In this later case one is led in a canonical way to Penrose wave equations.     

General nonlocal diffusion–convection mean field models: Nonexistence of global solutions

We consider model equations for the self-consistent field for interacting particles which feature general diffusion operators in canonical and microcanonical setting. A result on the nonexistence of solutions defined globally in time is proved.     

Relativistic kinetic equations for inelastically interacting particles in a gravitational field

The relativistic canonical formalism is used to construct the kinetic equations for a gas in a gravitational field, whose particles interact with one another via numerous inelastic collisions. Boltzmann's H-theorem is proved for T-invariant interactions.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 19–23, August, 1983.     

Infinitely divisible distribution functions of class L and the Lee-Yang theorem

It is shown that the free-energy density of a large class of ferromagnets satisfying the Lee-Yang property is to be connected with the limit characteristic function of a suitably renormalized sum of independent and non-identically distributed random variables. Using the canonical representation formulae of such characteristic functions, various chains of inequalities are derived for the Ursell functions.     

The motion of a classical spinning particle in a Riemann-Cartan space-time

A consistent set of equations of motion for classical charged particles with spin and magnetic dipole moment in a Riemann-Cartan space-time is generated from a constrained Lagrangian formalism. The equations avoid the spurious free helicoidal solutions and at the same time conserve the canonical condition of normalization of the 4-velocity. The 4-velocity and the mechanical moment are parallel in this theory, where the condition of orthogonality between spin and 4-velocity is treated as a nonholonomic constraint. A generalized BMT precession equation is obtained as one of the results of the formalism.     

Anti-gravitation

The possibility of a symmetry between gravitating and anti-gravitating particles is examined. The properties of the anti-gravitating fields are defined by their behavior under general diffeomorphisms. The equations of motion and the conserved canonical currents are derived, and it is shown that the kinetic energy remains positive whereas the new fields can make a negative contribution to the source term of Einstein's field equations. The interaction between the two types of fields is naturally suppressed by the Planck scale.     

Foundations of the fluctuation theory of adsorption on microcrystalline particles

Fundamentals of the equilibrium fluctuation theory of adsorption of molecules on microcrystalline particles taking into account the atomic structure of nonuniform surfaces were developed. The importance of taking into account the discrete character of adsorption centers in constructing adsorption isotherm equations was demonstrated. This changes the type of the mathematical apparatus in the search for a maximum distribution function term in a grand canonical ensemble: instead of differential derivatives, symmetrized difference derivatives should be used. The fluctuation theory of adsorption was generalized to ideal multicomponent mixtures of molecules. Adsorption isotherm equations for multicomponent mixtures on uniform and nonuniform surfaces taking into account limited sizes of the surface of various microcrystal faces and fluctuation contributions were obtained. The equations describe the influence of equilibrium fluctuations on adsorption isotherms for adsorbent particles of all sizes, from nanometric to macroscopic. An analysis of the equations showed that the influence of fluctuations was strongest at low coverages for each microcrystal face. The simplest case of taking fluctuations into account in the presence of contributions of lateral interactions in the mean field approximation was discussed.     

Kinetic equation with exact charge conservation.

A kinetic master equation for multiplicity distributions is formulated for charged particles which are created or destroyed only in pairs due to the conservation of their Abelian charge. It allows one to study time evolution of the multiplicity distributions in a relativistic many-body system with arbitrary average particle multiplicities. It is shown to reproduce the equilibrium results for both canonical (rare particles) and grand canonical (abundant particles) systems. For canonical systems, the equilibrium multiplicity is much lower and the relaxation time is much shorter than the naive extrapolation from grand canonical results. Implications for chemical equilibration in heavy-ion collisions are also discussed.     

Brownian particles with long- and short-range interactions

We develop the kinetic theory of Brownian particles with long- and short-range interactions. Since the particles are in contact with a thermal bath fixing the temperature T, they are described by the canonical ensemble. We consider both overdamped and inertial models. In the overdamped limit, the evolution of the spatial density is governed by the generalized mean field Smoluchowski equation including a mean field potential due to long-range interactions and a generically nonlinear barotropic pressure due to short-range interactions. This equation describes various physical systems such as self-gravitating Brownian particles (Smoluchowski-Poisson system), bacterial populations experiencing chemotaxis (Keller-Segel model) and colloidal particles with capillary interactions. We also take into account the inertia of the particles and derive corresponding kinetic and hydrodynamic equations generalizing the usual Kramers, Jeans, Euler and Cattaneo equations. For each model, we provide the corresponding form of free energy and establish the H-theorem and the virial theorem. Finally, we show that the same hydrodynamic equations are obtained in the context of nonlinear mean field Fokker-Planck equations associated with generalized thermodynamics. However, in that case, the nonlinear pressure is due to the bias in the transition probabilities from one state to the other leading to non-Boltzmannian distributions while in the former case the distribution is Boltzmannian but the nonlinear pressure arises from the two-body correlation function induced by the short-range potential of interaction. As a whole, our paper develops connections between the topics of long-range interactions, short-range interactions, nonlinear mean field Fokker-Planck equations and generalized thermodynamics. It also justifies from a kinetic theory based on microscopic processes, the basic equations that were introduced phenomenologically to describe self-gravitating Brownian particles, chemotaxis and colloidal suspensions with attractive interactions.     

Going to 10 TPa: The Calculated Hugoniots for Cu,Ta, and Mo

The Hugoniot equations of state for shock compressed Cu, Ta, and Mo are calculated at pressures up to 4 TPa and then up to 10 TPa are obtained by extrapolation. The calculations are parameter-free in that the cold part of the Helmholtz free-energy is calculated using the first-principles full-potential linearized augmented plane wave method within the generalized gradient approximation, the thermal contribution to the Helmholtz free-energy due to the lattice oscillations is calculated using the recently developed classical mean-field potential approach, and that due to the thermal electrons is calculated using the one-dimensional numerical integration. The calculated results agree with the existing experimental values very well.     

Quantal Poincaré-Cartan Integral Invariant for Field Theory

On the basis of the phase-space generating function of Green function for a system with a regular/singular Lagrangian, the quantal Poincaré-Cartan integral invariant (PCII) for field theory is derived. This PCII is equivalent to the quantal canonical equations. For this case in which the Jacobian of the transformation does not equalto unity, the quantal PCII can still be derived. This case is different from the quantal first Noether theorem. The quantal PCII connected with canonical equations and canonical transformation is also discussed.     

Hamilton's principle,covariant Hamiltonian,and canonical formalism in four and five dimensions

A discussion of the 1950s and 1960s on the existence of an explicit covariant canonical formalism is renewed. A new point of view is introduced where Hamilton's principle, based on the existence of a Hamiltonian, is postulated independently from the Lagrange formalism. The Hamiltonian is determined by transformation properties and dimensional considerations. The variation of the action without constraints leads to an explicit covariant canonical formalism and correct equations of motion. The introduction of the charge as a fifth momentum gives rise to a reformulation of classical relativistic point mechanics as a five-dimensionalU(1) gauge theory with a theoretically invisible extra dimension. A generalization to other gauge groups is given. The inversion of the proper time is introduced as a new particle-antiparticle symmetry that allows one to show that in the five-dimensional classical theory all particles have positive energy.