Evolution of probability measures associated with quantum systems

We derive the evolution equation for probability distributions and characteristic functions of the quantum tomograms associated with the linear and nonlinear evolutions of quantum states.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 142, No. 2, pp. 365–370, February, 2005.     

Dynamics of living polymers

We study theoretically the dynamics of living polymers which can add and subtract monomer units at their live chain ends. The classic example is ionic living polymerization. In equilibrium, a delicate balance is maintained in which each initiated chain has a very small negative average growth rate (velocity) just sufficient to negate the effect of growth rate fluctuations. This leads to an exponential molecular weight distribution (MWD) with mean . After a small perturbation of relative amplitude , e.g. a small temperature jump, this balance is destroyed: the velocity acquires a boost greatly exceeding its tiny equilibrium value. For the response has 3 stages: (1) Coherent chain growth or shrinkage, leaving a highly non-linear hole or peak in the MWD at small chain lengths. During this episode, lasting time , the MWDs first moment and monomer concentration m relax very close to equilibrium. (2) Hole-filling (or peak decay) after . The absence or surfeit of small chains is erased. (3) Global MWD shape relaxation after . By this time second and higher MWD moments have relaxed. During episodes (2) and (3) the fast variables ( ) are enslaved to the slowly varying number of free initiators (chains of zero length). Thus fast variables are quasi-statically fine-tuned to equilibrium. The outstanding feature of these dynamics is their ultrasensitivity: despite the perturbations linearity, the response is non-linear until the late episode (3). For very small perturbations, , response remains non-linear but with a less dramatic peak or hole during episode (1). Our predictions are in agreement with viscosity measurements on the most widely studied system, -methylstyrene.Received: 23 September 2003PACS: 82.35.-x Polymers: properties; reactions; polymerization - 05.40.-a Fluctuation phenomena, random processes, noise, and Brownian Motion - 87.15.Rn Biomolecules: structure and physical properties; Reactions and kinetics; polymerization     

Electric-discharge UV radiation source based on a Xe-CsCl vapor-gas mixture

A source of spontaneous UV radiation (excilamp) with a maximum radiation intensity at a wavelength of 308 nm is created. The active medium of the excilamp consists of a mixture of Xe with a CsCl vapor, and this mixture is excited in a longitudinal pulsed-periodic discharge. The B → X transition in the XeCl* exciplex molecule most strongly contributes to the total UV radiation power of the excilamp. The spectral composition of the UV radiation, the time characteristics of the source, and the formation of exciplex molecules as a function of the main discharge excitation parameters are studied.     

Thed(7Li,p)8Li cross section nearE cm=0.61 MeV

The absolute cross sectionσ of thed(⁷Li,p)⁸Li reaction near theE _cm=0.61 MeV resonance has been measured using a⁷Li ion beam and a windowless gas target system filled with D₂ gas. The proton yield of the reaction and theβ-delayedα-activity of the residual nuclides⁸Li were observed both concurrently with the elastic scattering yield, relatingσ to the Rutherford scattering cross sectionσ _R. The resulting values,σ (fromp)=143.6±8.9 mb andσ (from⁸Li)=151±20 mb, lead to a weighted mean value ofσ=153±6 mb (x ²=2.26) including all available values andσ=146±5 mb (x ²=0.05) removing some values from the data set. The consequences for the expected flux of high-energy solar neutrinos are discussed.     

Direct measurements of energy relaxation times on an AlGaAs/GaAs heterointerface in the range 4.2–50 K

The temperature dependence of the energy relaxation time τ_e (T) of a two-dimensional electron gas at an AlGaAs/GaAs heterointerface is measured under quasiequilibrium conditions in the region of the transition from scattering by acoustic phonons to scattering with the participation of optical phonons. The temperature interval of constant τ_e, where scattering by the deformation potential predominates, is determined. In the preceding, low-temperature region, where piezoacoustic and deformation-potential-induced scattering processes coexist, τ _e decreases slowly with increasing temperature. Optical phonons start to participate in the scattering processes at T∼25 K (the characteristic phonon lifetime was equal to τ_LOτ4.5 ps). The energy losses calculated from the τ_e data in a model with an effective nonequilibrium electron temperature agree with the published data obtained under strong heating conditions. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 5, 371–375 (10 September 1996)     

Criteria for Separability of Multipartite Quantum System

We first present the Hamel base of the density operator space for multipartite quantum system, and thus establish a representation of density matrix. Moreover, according to the structure of the density matrix for multipartite quantum system, we present two necessary criteria for separability of multipartite quantum system of arbitrary dimensions.     

Electrical conductivity and band structure of thin polycrystalline EuS films

A study of the electrical resistance of thin polycrystalline EuS films (0.4–0.8 μm thick) in the temperature range 120–480 K has provided the basis for a model of the band structure of this substance. It has been shown that the main impurity levels in thin polycrystalline EuS films are those related with localized states near the conduction band bottom, as well as the E _i donor levels of Eu ions outside regular lattice sites. The “tail” of the localized states extends in energy up to at least ?0.45 eV.     

Numerical comparison of classical and permutation statistical hypothesis testing methods

The article is devoted to the classical problem of statistical hypothesis testing for the equality of two distributions. For normal distributions, Student’s test is optimal in many senses. However, in practice, distributions to be compared are often not normal and, generally speaking, unknown. When nothing is known about the distributions to be compared, one usually applies the nonparametric Kolmogorov–Smirnov test to solve this problem. In the present paper, methods are considered that are based on permutations and, in recent years, have attracted interest for their simplicity, universality, and relatively high efficiency. Methods of stochastic simulation are applied to the comparative analysis of the power of a few permutation tests and classical methods (such as the Kolmogorov–Smirnov test, Student’s test, and the Mann–Whitney test) for a wide class of distribution functions. Normal distributions, Cauchy distributions, and their mixtures, as well as exponential, Weibull, Fisher’s, and Student’s distributions are considered. It is established that, for many typical distributions, the permutation method based on the sum of the absolute values of differences is the most powerful one. The advantage of this method over other ones is especially large when one compares symmetric distributions with the same centers. Thus, this permutation method can be recommended for application in cases when the distributions to be compared are different from normal ones.     

Relaxation and thermodynamic parameters of the theory of spin-wave damping in low-dimensional magnetic materials

Several basic parameters of the surface spectrum of a system are estimated with respect to the spin-spin interaction. An expression for the surface relaxation time and its numerical estimation are given. The dependence of the relaxation time on the geometric factor determined by the surface geometry only is presented. The conditions for the resonance absorption of spin-wave energy by the surface are considered. Certain expressions for the thermodynamic potentials taking the effect of surface resonance on the equilibrium properties of the system into account are given.     

Probability model for the scattering of centimeter waves by an object located near a disturbed ocean surface

A two-dimensional (joint) probability density function is obtained for the amplitude and phase of the backscattered field from a point isotropic reflector located near a statistically rough interface between two media. It is shown that the power of the scattered signal may be enhanced by a factor of more than 16 compared to free space. The probability that fluctuations in the effective scattering area may overshoot a fixed level is estimated. Zh. Tekh. Fiz. 67, 83–88 (September 1997)