Distribution of Equilibrium Free Energies in a Thermodynamic System with Broken Ergodicity

At low temperatures the configurational phase space of a macroscopic complex system （e.g., a spin-glass） of N - 10^23 interacting particles may split into an exponential number Ωs - exp（const × N） of ergodic sub-spaces （thermodynamic states）. It is usually assumed that the equilibrium collective behavior of such a system is determined by its ground thermodynamic states of the minimal free-energy density, and that the equilibrium free energies follow the distribution of exponentied decay. But actually for some complex systems, the equilibrium free-energy values may follow a Gaussian distribution within an intermediate temperature range, and consequently their equilibrium properties are contributed by excited thermodynamic states. Based on this analysis, the re-weighting parameter y in the cavity approach of spin-glasses is easily understood. Depending on the free-energy distribution, the optimal y can either be equal to or be strictly less than the inverse temperature β.     

Self-Consistent Solutions for the Scattering State with Two Free Electrons

Wave functions for the scattering states with two free electrons in the field of an ion core are explicitly calculated by the self-consistent, continuum Hartree–Fock (CHF) theory. Typically, such states are associated with the three-body recombination, collisional ionization and photo-double ionization, but have never been directly studied previously. The calculated continuum orbitals are found to be predominantly of the plane-wave forms, as though the system is translation invariant, in the context of many-body HF theory. The symmetry is mildly broken by the presence of the core ion, at about fifteen-percents level, indicating that the orbitals are largely delocalized and the effect of the core potential is an important but minor perturbation. The properties of channel orthogonality and completeness are preserved by the nearly plane wave forms. To test the validity of this finding and the CHF, the continuum orbitals are used to evaluate the amplitudes for the electron impact ionization, and the amputation procedure, that is crucial in the theory, is also critically re-examined.     

Low-Frequency Behavior of the Spectral Energy Distribution Function of Equilibrium Radiation in a Degenerate Electron Gas

The low-frequency asymptotic behavior of the spectral energy distribution density of equilibrium radiation in a collisionless degenerate electron gas is studied. It is shown that the spatial dispersion in the electron gas permittivity leads to a logarithmic singularity in the spectral density distribution at low frequencies, similar to that we previously obtained for a Maxwellian plasma. In this case, the contribution of low frequencies to the total radiation energy remains finite. The results of the analytical consideration coincide with the numerical calculation.     

On the Distribution of Free Path Lengths for the Periodic Lorentz Gas III

 For r(0,1), let Z _r ={xR ² |dist(x,Z ²)>r/2} and define τ _r (x,v)=inf{t>0|x+tv∂Z _r }. Let Φ _r (t) be the probability that τ _r (x,v)≥t for x and v uniformly distributed in Z _r and §¹ respectively. We prove in this paper that

Modelling Energetic Electrons by a Kappa-Loss-Cone Distribution at Geostationary Orbit

We adopt a recently developed relativistic kappa-loss-cone （KLC） distribution to model energetic electrons energy spectra observed at the geostatlonary orbit in the storm of 3-4 November 1993. The KLU distribution is found to fit well with the observed data from four satellites during different universal times. This suggests that the electron flux obeys the power-law not only at the lower energies but also at the relativistic energies, and the KLU distribution may provide a better understanding of environments in those space plasmas where relativistic electrons are present.     

On the Transversal Diffusion of Electrons in a Gas in an Electric Field

Discrepancies between Monte Carlo and Boltzmann calculations of electron drift and diffusion in gases have recently led some authors to call into question the same definition of diffusion coefficient perpendicular to the electric field. In this paper we report new results which confirm the observed discrepancies but at the same time we will show that the Monte Carlo results are consistent with more rigorous calculations based on theories of higher order than the first.     

The Distribution of the Free Path Lengths in the Periodic Two-Dimensional Lorentz Gas in the Small-Scatterer Limit

We study the free path length and the geometric free path length in the model of the periodic two-dimensional Lorentz gas (Sinai billiard). We give a complete and rigorous proof for the existence of their distributions in the small-scatterer limit and explicitly compute them. As a corollary one gets a complete proof for the existence of the constant term in the asymptotic formula of the KS entropy of the billiard map in this model, as conjectured by P. Dahlqvist.In memory of Walter Philipp     

实际大气中无线光通信的系统差错性能

无线光通信(FSO)系统的性能受大气湍流影响会产生剧烈波动。根据系统和大气参数评估系统差错性能的研究具有现实意义。以大气湍流信道和光电探测模型为基础,使用拟合概率分布替换常用的对数正态分布,建立了FSO系统差错性能的数学仿真模型,改进了湍流条件下系统误码率计算公式,并且进行全天的验证实验。实验结果显示,光强概率分布对系统性能有显著的影响,原有公式在某些情况下的计算结果有较大偏差,而改进公式的计算结果具有更好的适应性和准确性。该改进公式可有效评估湍流条件下FSO系统性能,并为相关理论研究提供参考。     

Trend to Equilibrium of a Degenerate Relativistic Gas

We examine the problem of the trend to equilibrium for a relativistic gas which may follow Fermi–Dirac, Bose–Einsten, classical Boltzmann statistics. We use the relativistic version of the quasiclassical Boltzmann equation for fermions and bosons, the Uehling–Uhlenbeck equation.     

Photoproduction of Triplets on Free Electrons and the Search for the Dark Photon

We have investigated the photoproduction of triplets on free electrons, γe^– → e⁺e^–e^–, in which dark photon A′ can be formed as an intermediate state with subsequent decay into an e⁺e^– pair. This effect appears as a result of the so-called kinetic mixing and is characterized by the small parameter describing the intensity of the interaction of the dark photon with charged Standard Model (SM) particles in terms of electric charge e. The search for a manifestation of A′ in this process is advantageous since the background to the A′ signal is purely electrodynamic and, hence, can be calculated with the required accuracy. We calculate this background taking into account the identity of final electrons. As regards A′, its contribution is taken into account only in Compton-type diagrams (of virtual Compton scattering) in which a virtual dark photon is a time-like particle and its propagator has the form of a Breit–Wigner resonance. It is only in the vicinity of resonance that A′ can be manifested. We calculate the invariant mass distribution of both e⁺e^– pairs formed in the process and analyze the kinematic region in which relatively small squares of momenta transferred from the target electron to the formed electrons are excluded. In these conditions, the contribution to the differential cross section from Compton-type diagrams is not suppressed relative to the contribution of the remaining (Borsellino) diagrams. A number of limitations on parameter depending on the dark photon mass and the statistics (number) of events are obtained for a special method of gathering events in which the invariant mass of one e⁺e^– pair remains fixed and of the other pair is scanned.     

On Equilibrium Distribution of a Reversible Growth Model

We study a probabilistic model of interacting spins indexed by elements of a finite subset of the d-dimensional integer lattice, d≥1. Conditions of time reversibility are examined. It is shown that the model equilibrium distribution converges to a limit distribution as the indexing set expands to the whole lattice. The occupied site percolation problem is solved for the limit distribution. Two models with similar dynamics are also discussed.     

Distribution of Electrons and Ions Near an Absorbing Spherical Body in a Nonequilibrium Plasma

Journal of Experimental and Theoretical Physics - The applicability of the collision kinetic model of point sinks, viz., the linearized theory of screening of the electric field produced by a...     

The Role of High-Velocity Electrons in a Hollow-Cathode Discharge

In this paper, the features of a low-pressure discharge in a hollow cathode are considered. It has been shown that a free mode can be realized with a double electric layer at the cathode and high density of the current of high-velocity electrons in the discharge bulk, considerably exceeding the current density at the cathode. In this case, the rate of ionization by high-velocity electrons considerably exceeds the rate of ionization by plasma electrons.     

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.     

Electrons in a curvilinear quantum wire

The adiabatic motion of electrons in curvilinear quantum wires was studied. It was assumed that the cross section of a wire was constant along its length. The potential that limited electron motion across a wire and the shape of the cross section of the wire were considered arbitrary, while the curvature and the torsion (defined as the derivative of the cross section rotation angle with respect to the length) were assumed to be small. An effective nonrelativistic Hamiltonian for the motion of electrons along a wire with the conservation of transverse quantum numbers was obtained. The spin-orbit coupling Hamiltonian related to the curvature and torsion of a wire was found. Particular cases of a rectilinear twisted quantum wire with a noncircular cross section and a curvilinear quantum wire on a plane were studied. Various transverse potential models limiting the motion of electrons were considered. In particular, the coefficients of the effective Hamiltonian for quantum wires with rectangular and circular cross sections and hard walls and for wires with a parabolic potential were found.     

Real Time Gas Flow Control and Analysis for High Power Infrared Gas Lasers

The composition of various gas effluents and their flow parameters viz. flow rate, pressure and Mach number are very crucial in determining the output of high power infrared gas lasers. PC based real time gas Flow Control and Analysis (FCA) System which is the heart of the high power infrared gas lasers such as CO₂ Gas Dynamic Laser (10.6m), Hydrogen Fluoride-Deuterium Fluoride (2.7–3.4m) and Chemical Oxygen Iodine Laser (1.315m) has been developed and successfully tested for its applications in Chemical Oxygen Iodine Laser (COIL). The system has been realized using the state of the art PCI bus based high-speed data processing electronics, a personal computer and electro-pneumatic components. The system has demonstrated its capability of controlling the flow rates in the range of 1-6500 lpm (in case of nitrogen) with a response time of 50 msec which is mainly limited by the response of the electro-pneumatic valves and pressure reducers used in the present system. The developed system also has the potential to monitor, estimate and display various flow parameters at critical locations of the laser system. More than 600 successful power runs of the COIL have been given using the developed FCA system.     

实际大气中激光闪烁的概率分布

根据湍流大气激光对数强度的最低几阶中心矩建立了一种最大似然概率分布模型,该模型可以方便和准确地描述实际概率分布,根据实验结果分析了激光地数强度的概率分布的偏斜度和陆峭度的特征。发现在弱起伏条件下,对数强度的概率分布一般接近于正态分布,当偏离正态分布时,概率密度分布的偏斜度总为负,陆峭度总是为正。