Stationary states in a quantum gravity model

A model theory for quantized gravity is discussed where only selected degrees of freedom are quantized. The concept of stationary states is introduced. It is shown that the Planck length arises as a lower bound to the space-time length scale in a natural way.     

Subject index to volume 37

A number of new effects is predicted, which appear under resonant interaction between light and gas. The velocity distribution of the total number of particles (excited and unexcited) varies due to the increase in the cross section under excitation. This leads to uneven energy distribution between the translational degrees of freedom and, as a result, to anisotropy of pressure, temperature, and to thermal flows which result in the appearance of a density and temperature gradient in the stationary state.     

Influence functionals in deep inelastic reactions

It is suggested that the concept of influence functionals introduced by Feynman and Vernon could be applied to the study of deep inelastic reactions among heavy ions if the coupling between the relative motion and the internal degrees of freedom has a separable form as suggested by Hofmann and Siemens.     

Calculation of the velocity of a molecular gas slipping over a sphere with regard to accommodation coefficients

The velocity of molecular gas slipping over a spherical surface is calculated by exact analytical methods including the accommodation coefficients for the first two moments of the distribution function. An extension of the BGK approach to the Boltzmann kinetic model for the case of rotational degrees of freedom is used as the basic equation.     

考虑转动能的一维/二维Boltzmann-Rykov模型方程数值算法

研究考虑转动能的Boltzmann-Rykov模型方程,基于转动自由度对气体分子速度分布函数矩积分,引入约化速度分布函数,应用离散速度坐标法与数值积分技术,将气体运动论模型方程化为在离散速度坐标点处关于三个约化速度分布函数的联立方程组.应用拓展计算流体力学有限差分方法,数值计算考虑转动自由度的双原子气体一维、二维Boltzmann模型方程,得到高、低Knudsen数一维激波管内流动和二维竖直平板绕流问题的流场,分析验证考虑转动能的Boltzmann-Rykov模型方程全流域统一算法求解一维/二维气体流动问题的可靠性.结果表明,气体稀薄程度与分子内自由度对流场具有较大影响,且Knudsen数较高的稀薄气体流动呈现严重的非平衡流动特点.     

The energy method for analyzing the piezoelectric electroacoustic transducers

The energy method of calculating the properties of piezoelectric electroacoustic transducers is considered. The Lagrangian of an electroacoustic transducer as a system performing multiple energy conversions is introduced. The Euler equations describing operation of a transducer with many mechanical degrees of freedom are derived from the least action principle. The corresponding multicontour equivalent circuit of the transducer is introduced. For the particular case of a transducer having one mechanical degree of freedom the governing equations are obtained by applying the Energy Conservation Law, and equivalent circuit with one mechanical branch also introduced. Application of the energy method is illustrated with examples of the pulsating spherical transducer as the one degree of freedom system and the multimode cylindrical transducer comprised of circular rings as the system with multiple degrees of freedom. Advantages of the method for application with electroacoustic transducers are summarized.     

THE COMPOSITE PARTICLE REPRESENTATION THEORY: (I) The Composite Particle Representation Transformation

A generalization of the quantum mechanical representation transformation is presented, in this paper. It is shown that, as an important example, the Boson-expansion method, commonly employed in nuclear physics, corresponds to such a .generalized transformation. Using this generalization, we were able to construct a special representation called the "Composite Particle Representation". In the composite. particle representation, the composite particle degrees of freedom are included, as well as the original particle degrees of freedom. The former is introduced in order that the motion of certain particle clusters can be described as separate entities in a many-body system. This representation is shown to be exactly equivalent to the usual quantum mechanical .representation which .includes only the original particle degrees of freedom. Many applications of this theory are expected, in particular in the study of hadrons.from the quark point of view and the Interacting Boson Mode1 in nuclei.     

A translational heat-bath model for foreign gas broadening of spectral lines—I. Variational methods

A new formalism of Green's functions is used for discussing foreign gas broadening of atomic spectral lines. In the present work, the translational degrees of freedom are separated from the internal degrees of freedom by a translational heat-bath model. The conditions of a heat bath, weak and binary collisions lead to a Lorentzian line shape in the center of the line and to a rapid decay of the line wings. For weak interaction potentials, a new explicit expression for line broadening, which demonstrates this behaviour, is obtained.     

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.     

The role of macroinstrument and microinstrument and of observable quantities in the new conception of thermodynamics

In the first part of the paper, we introduce the concept of observable quantities associated with a macroinstrument measuring the density and temperature and with a microinstrument determining the radius of a molecule and its free path length, and also the relationship between these observable quantities. The concept of the number of degrees of freedom, which relates the observable quantities listed above, is generalized to the case of low temperatures. An analogy between the creation and annihilation operators for pairs (dimers) and the creation and annihilation operators for particles (molecules) is carried out. A generalization of the concept of a Bose condensate is introduced for classical molecules as an analog of an ideal liquid (without attraction). The negative pressure in the liquid is treated as holes (of exciton type) in the density of the Bose condensate. The phase transition gas-liquid is calculated for an ideal gas (without attraction). A comparison with experimental data is carried out. In the other part of the paper, we introduce the concept of new observable quantity, namely, of a pair (a dimer), as a result of attraction between nearest neighbors. We treat in a new way the concepts of Boyle temperature T _B (as the temperature above which the dimers disappear) and of the critical temperature T _c (below which the trimers and clusters are formed). The equation for the Zeno line is interpreted as the relation describing the dependence of the temperature on the density at which the dimers disappear. We calculate the maximal density of the liquid and also the maximal density of the holes. The law of corresponding states is derived as a result of an observation by a macrodevice which cannot distinguish between molecules of distinct gases, and a comparison of theoretical and experimental data is carried out.     

Models for incommensurate phases in crystals withPcmn symmetry

A discussion is given of the relation between different models for systems with incommensurate phases. Moreover, a generalisation of such models is introduced, which shows an alternative explanation for similar phase diagrams. To get this one may vary the range of the interactions and the numbers of degrees of freedom per site.Another generalization involves coupling to elastic degrees of freedom. Such a coupling may change the type of the incommensurate phase transition.     

Old mathematical errors in statistical physics

In this paper, we discuss the following questions of quantum statistics: (1) the absence of Bose condensate in ideal Bose gas in the two-dimensional and one-dimensional case; (2) the concentration of the Bose condensate in an ideal Bose gas at the lowest level of the spectrum of the Schrödinger operator. In classical statistics, we discuss the discrepancy between the notion of Boltzman-Maxwell ideal gas with the notion of saturated vapor. The appearance of clusters requires the complete revision of the Clayperon equation as an equation depending on the number of degrees of freedom. For the new ideal gas and the ideal virtual liquid, we describe the phase transition of the first kind by specifying the concept of negative pressure for ideal virtual liquids.     

Formation of the phase composition of nonequilibrium samples prepared by rapid solidification of oxide melts

The number of phases in an equilibrium system p composed of t components is constrained by the Gibbs phase rule, which can be written as f = t + n − p − r, where f is the number of degrees of freedom; n is the number of thermodynamic parameters, determining the conditions of the system; and r is the number of compositional restrictions. To formally apply the Gibbs phase rule to such objects, the concept of a system with negative degrees of freedom was introduced in [1]. Their existence is related to the incorrect estimate of the aforementioned system parameters or the kinetic hindrance of the processes in the sample.     

Exponentially Long Equilibrium Times in a One-Dimensional Collisional Model of Classical Gas

Around 1900, J. H. Jeans suggested that the abnormal specific heats observed in diatomic gases, specifically the lack of contribution to the heat capacity from the internal vibrational degrees of freedom, in apparent violation of the equipartition theorem, might be caused by the large separation between the time scale for the vibration and the time scale associated with a typical binary collision in the gas. We consider here a simple 1D model and show how, when these time scales are well separated, the collisional dynamics is constrained by a many- particle adiabatic invariant. The effect is that the collisional energy exchanges betgween the translational and the vibrational degrees of freedom are slowed down by an exponential factor (as Jeans conjectured). A metastable situation thus occurs, in which the fast vibrational degrees of freedom effectively do not contribute to the specific heat. Hence, the observed freezing out of the vibrational degrees of freedom could in principle be explained in terms of classical mechanics. We discuss the phenomenon analytically, on the basis of an approximation introduced by Landau and Teller (1936) for a related phenomenon, and estimate the time scale for the evolution to statistical equilibrium. The theoretical analysis is supported by numerical examples.     

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.     

Cumulative author index of Volumes 351 to 360

The dynamic evolution of granular gases is fundamentally different from molecular gases due to the energy loss during collisions. Nevertheless techniques of kinetic theory are useful in a regime, when the granular particles are moving rapidly and the gas is sufficiently dilute. In these lecture notes we analyse in detail the collision of two rough particles which is inelastic due to incomplete normal and tangential restitution as well as Coulomb friction. Based on the Walton model a time evolution operator for the many particle system is introduced, a formalism which is well suited for simple approximations. We discuss free cooling of granular particles with particular emphasis on the exchange of energy between rotational and translational degrees of freedom.     

Light-induced stationary gas flows

A new effect is described: macroscopic flows occur under specific conditions along the walls of a cuvette in gas excited resonantly with a plane light wave from the ground state. The effect is the result of the light-induced energy redistribution between the translational degrees of freedom.     

Quantum key distribution on composite photons, polarization qutrits

Polarization states of a photon are the most natural degrees of freedom for encoding classical information bits. The two-dimensional space of states associated with polarization degrees of freedom of the photon is insufficient for many problems of information transfer with quantum states. We propose to use the polarization degrees of freedom of composite states of photons (polarization qutrits) for secret cryptographic key distribution.     

Charge distribution in a Kondo-correlated quantum dot

We report on direct measurement of charge and its distribution in a Kondo correlated quantum dot (QD). A noninvasive potential-sensitive detector, in proximity with a QD, reveals that, although the conductance of the QD is significantly enhanced as it enters the Kondo regime, the average charge remains unaffected. This demonstrates the separation between spin and charge degrees of freedom. We find, however, under certain conditions, an abrupt redistribution of charge in the QD, taking place with an onset of Kondo correlation. This suggests a correlation between the spin and charge degrees of freedom.     

Spectral features of a nematic liquid crystal consisting of biaxial molecules with internal rotation

Expressions for the components of the optical permittivity tensor of a nematic liquid crystal consisting of biaxial π-conjugated molecules with a conformational degree of freedom (internal rotation) are obtained. A relationship between the intensity and dichroism of absorption bands in isotropic and nematic phases and the parameters of conformational, orientational, and mixed conformational and orientational orders of the molecules is established. A distribution function for the molecules is obtained that takes into account the mutual correlation of their conformational and orientational degrees of freedom. The effect of this correlation on the above-noted order parameters, the dichroism of the absorption bands, and the dependence of the measured oscillator strengths of molecular transitions on the character and degree of orientational order of biaxial molecules is studied. On the basis of comparison with experimental data, the relative role of different terms in the distribution function that are responsible for the correlation between the conformational and orientational degrees of freedom of the molecules is ascertained.