Bifurcations accompanying monotonic instability of an equilibrium of a cosymmetric dynamical system

It is well known that equilibrium in a cosymmetric system in the general position is a member of a one-parameter family. In the present paper the Lyapunov-Schmidt method and the method of the central manifold are used to analyze bifurcations of such a family of equilibria as well as internal bifurcations: transitions of the type focus-node, node-saddle, and so on during motion along the family. A series of scenarios of branching of families of equilibria and the change in the structure of their arcs, consisting of equilibria of the same type, is described. Bifurcations of stable and unstable arcs, coalescence and decomposition of families of equilibria, bifurcation of the loss of smoothness by the family of equilibria, and branching of a small equilibrium cycle from a corner point of the family of equilibria are investigated in detail. The variability of the spectrum along a family gives rise to a variety of new phenomena that are not encountered in the classical case of an isolated equilibrium or in bifurcations of families of equilibria of a system with symmetry. They include protraction with respect to the branching parameter of the family of equilibria, Lyapunov instability of a family of equilibria with the attraction properties being preserved, and the appearance and disappearance of new stable and unstable arcs on the family of equilibria. (c) 2000 American Institute of Physics.     

Complex degree of mutual anisotropy of linear birefringence and optical activity of biological tissues in diagnostics of prostate cancer

We present theoretical fundamentals of polarization and correlation analysis of the optical anisotropy of biological tissues. Results of measurements of coordinate distributions of the complex degree of mutual anisotropy (CDMA) that are formed by birefringent structures of the prostate tissue with benign and malignant changes are compared. Magnitudes and ranges of variation of statistical (the firstto fourth-order distribution moments) and correlation (excess of autocorrelation functions) parameters of the coordinate CDMA distributions of histological sections of the prostate postoperative bioptic material are studied. Objective criteria of the diagnostics of the appearance of pathology and of the differentiation of the degree of its severity are determined.     

Theory of measurement of entangled states

Problem on reconstruction of state of finite-dimension quantum information transfer channel, pure or mixed, by results of measurements of needed number of observables, is considered. It is shown that in general case it is needed to measure incompatible observables in number exceeding by one dimension of space of vectors of state. Each of incompatible observables is measured in its statistically valuable series of measurements. In special case, when one of observables is a non-demolition observable, measurement of the other observables is needed for realization of control of property of non-demolition. In case of paired channel it is shown that results of measurements of observables that do not demolish states of sub-channels are characterized by mutual distribution of probabilities while results of measurement of over-classical observables are characterized by mutual correlation only. This correlation vanishes completely in case of pure unentangled states.     

Fluctuations in the number of photons above the bifurcation point in the process of third harmonic generation

The quantum fluctuation of the number of photons of the fundamental mode and of the third harmonic in the process of intracavity generation of the third harmonic in the region of unstable behavior of the system is studied. The distribution functions of the number of photons of interacting modes, as well as the function of the joint distribution of the number of photons of the fundamental mode and of the third harmonic, are calculated in the positive P-representation.     

Generalization of the variational principle and the Hohenberg and Kohn theorems for excited states of Fermion systems

Through the entanglement of a collection of K non-interacting replicas of a system of N interacting Fermions, and making use of the properties of reduced density matrices the variational principle and the theorems of Hohenberg and Kohn are generalized to excited states. The generalization of the variational principle makes use of the natural orbitals of an N-particle density matrix describing the state of lowest energy of the entangled state. The extension of the theorems of Hohenberg and Kohn is based on the ground-state formulation of density functional theory but with a new interpretation of the concept of a ground state: It is the state of lowest energy of a system of KN Fermions that is described in terms of the excited states of the N-particle interacting system. This straightforward implementation of the line of reasoning of ground-state density functional theory to a new domain leads to a unique and logically valid extension of the theory to excited states that allows the systematic treatment of all states in the spectrum of the Hamiltonian of an interacting system.     

Scattering of centimeter radiowaves in a gas ionized by radioactive radiation: Cluster plasma formation

A theoretical explanation is proposed for an anomalously high reflectivity of air masses exposed to radioactive radiation relative to electromagnetic waves from the rf range. The mechanism of formation of the reflected signal is connected with a change in the electric parameters of the ionized gas. The concentration of free charges under the typical conditions of radioactive contamination is ten orders of magnitude lower than that required for the formation of an experimentally detectable reflected signal. The discrepancy between the values of reflectivity observed under the real conditions of radar probing and predicted theoretically on the basis of the elementary theory of a weakly ionized gas amounts to 20 orders of magnitude. It is shown that the inclusion of the variation of the mass and the critical capture radius of ions due to their hydration changes the difference between the theoretical predictions and the experimental observations insignificantly. The discrepancy becomes smaller (but only by 1.5 orders of magnitude) when the scattering of radiowaves from turbulent vortices is taken into account. The mechanism of the formation of the high reflectivity is associated with slowing down the recombination and with the accumulation of a profuse population of unrecombined ionic pairs stabilized in the clusters of water molecules. The steady-state concentration of such electrically neutral clusters is several orders of magnitude higher than the concentration of free hydrated ions. A variation of the intensity of ionizing radiation is accompanied by proportional variations of both components. The recombination barrier is formed as a result of drawing dipole molecules into the gap between ions at the final stage of motion of counterions towards one another before their recombination. The accumulation of ionic pairs ensures the multiple enhancement of the sensitivity of the electric properties of cold plasma to the effect of ionizing radiation. A quantitative kinetic theory of the effect is constructed. The numerical calculations of the parameters of the pre-recombination states of ions against the background of the molecular component are made using computer simulation at the microscopic level. The steady-state recombination rate is an exponential function of the pre-recombination barrier height and decreases rapidly even upon an insignificant change in the number of molecules involved in an ion recombination act. The obtained theoretical conclusions are confirmed by the independent results of observations of the strong absorption band in the atmosphere in the middle part of the IR spectrum, which is attributed to the anomalously high concentration of electrically neutral water clusters.     

Advantages of fluorescence over diffuse reflectance measurements tested in phantom experiments with dynamic inflow of ICG

Time-resolved measurements of diffuse reflectance and fluorescence were carried out using phantom with dynamic inflow of indocyanine green (ICG) in tubes located at different depths. Better sensitivity of fluorescence signals related to the inflow of the dye was observed in comparison to simultaneously acquired diffuse reflectance. Obtained results can be referred to results of in-vivo measurements. We have observed much larger amplitude of changes in relative number of detected photons, mean time of flight and variance of the distributions of times of arrival of fluorescence photons than amplitudes of respective parameters measured from diffuse reflectance distributions of times of flight of photons. The constructed phantom allows us to study influence of concentration of the dye in the tube and the surrounding medium as well as temporal relation between appearance of the boli in deeper and superficial tube. Results of the study were used in optimization of the time-resolved multichannel system for simultaneous monitoring of fluorescence and reflectance.     

Role of interactions of triplets of atoms in the formation of elastic properties of cubic crystals

It is widely known that the interaction of triplets of particles (which are not reducible to the sum of pair interactions) play an important role in formation the nonlinear and anisotropic properties of crystals. The aim of this work is to establish a general form of the dependence of these properties on interactions of triplets of atoms that is dependent only on the structure of the crystals. To separate the interactions of triplets of atoms from those of quadruples, we assume that the energy of triplets of interacting atoms depends only on the characteristics of a triangle whose vertices are the centers of gravity of interacting atoms. In this model, the internal energy must therefore be invariant upon rearrangement of the numbers of interacting atoms and any rotation of the triangle in isotropic space, P(3) × O(3). To specify the form of energy dependence on characteristics of selected triangles, we constructed an integral rational basis of invariants in dependence on the components of the vectors connecting the vertices of each triangle. Using the example of a simple dependence of the energy on basic invariants, we show how to move from the assumed energy dependence on invariants to the dependence of energy on lattice sums.     

Rapidly progressing photophysical and photochemical relaxation processes in complex organic molecules

Using methods of high-speed kinetic laser spectroscopy, we investigated the dynamics and mechanisms of rapidly progressing relaxation processes in multiatomic molecules. We separated intra- and intermolecular channels of relaxation of the vibrational energy of excitation by the rate of transformation of nonstationary absorption spectra in a picosecond range of times. The role of highly excited electronic states in the process of electronic-vibrational relaxation in molecules of the class of phenazines was ascertained. Applying femtosecond light pulses in a real time scale, we recorded the dynamics of the decay of optically induced anisotropy in rarefied vapors of organic compounds. Several mechanisms of transfer of a hydrogen atom in the process of formation of free radicals in photoreduction of ketones were established. The dynamics of formation of inter- and intramolecular exciplexes in binary gas-phase systems was investigated. We determined the mechanisms of intramolecular dissociation of a C–O chemical bond in spiropyrans and xanthene dyes. Photodissociation of S–S bonds in molecules of disulfides was studied. The possibility of the existence of states with intramolecular charge transport with a twisted configuration for organic free radicals is shown. To whom correspondence should be addressed. Institute of Molecular and Atomic Physics of the National Academy of Sciences of Belarus, 70, F. Skorina Ave., Minsk, 220072, Belarus. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 65, No. 5, pp. 635–661, September–October, 1998.     

Intraband radioluminescence of LiF crystals

Spectra of high-energy electrons are calculated in the electron-hole ionization-passive region of lithium fluoride crystals for the conditions of intense irradiation by short pulses of accelerated electrons. The yield of intraband radioluminescence of these crystals is estimated in comparison with the yield of this kind of luminescence of more extensively studied NaCl crystals. The calculations demonstrate that the yield of radioluminescence determined by electron transitions in the conduction band of LiF crystals is two orders of magnitude weaker than the yield of analogous luminescence of NaCl crystals. This is explained, first, by special features of the energy band structure and, second, by the form of the energy dependence of the density of states in the conduction band of LiF crystals. The yield of hole-type intraband radioluminescence is estimated for various assumed relations between the widths of the valence and the forbidden bands.     

Self-consistent Monte Carlo simulations of the electron and ion distributions of inhomogeneous liquid alkali metals. II. Longitudinal and transverse density distributions in the liquid-vapor interface of binary metallic alloys

We present the results of Monte Carlo simulations of the liquid-vapor interface of sodium-cesium alloys. The longitudinal density profile of each alloy shows that the liquid-vapor interface consists of a well-defined monolayer of cesium sitting on top of a slab of the bulk alloy. Underneath the monolayer there is a slight excess of sodium. A comparison with a van der Waals analog of one of the alloys shows that the presence of the well-defined monolayer of cesium on the outside of the liquid-vapor interface is a feature peculiar to metallic mixtures. The transverse pair correlation functions of the cesium monolayer are insensitive to the composition of the bulk of the slab.     

Effect of hydrogen on the formation of the atomic structure of linear carbon chains: An ab initio approach

An ab initio study of the features of the formation of the atomic structure of carbon chains, which are structural parts of films of linear carbon chains, has been performed using the electron density functional theory. It has been shown that the formation and stabilization of experimentally observed kinks of carbon chains require the presence of hydrogen impurities in the chamber during the synthesis of linear carbon chains. The kinks of a carbon chain are formed in the process of the adsorption of hydrogen atoms on a chain. The optimal kink angle of carbon chains has been determined. The stability of kinks of carbon chains has been estimated as a function of the length of linear fragments. An additional mechanism has been proposed for the formation of kinks in carbon chains owing to the joining of short carbon chains with hydrogen ends.     

The possibility of the classification of infrasonic signals using methods for checking statistical hypotheses

This work is devoted to the possibility of the classification of signals using methods for checking statistical hypotheses. On the basis of analysis of the typical peculiarities of signals that belong to the same class we performed an empirical derivation of the shape of the class. The mechanism of the definition of the separability of signals of each class, as well as the level of criterion for defining critical domain were suggested. A classification algorithm was obtained on the basis of the research. The efficiency of the suggested methodology was tested on the problem of separability of infrasonic signals recorded in the atmosphere.     

Diagnostics of drift velocities of electrons in a laser plasma by spectropolarimetry of the plasma emission

Expressions are obtained for the rate constants of the induction of ordering of angular momenta in an ensemble of ions formed as a result of trapping of electrons in a laser plasma. Dependences of the degree of polarization of plasma radiation on the drift energy of free electrons of the plasma are obtained. Drift energies of electrons at different distances from the target are determined on the basis of experimental data.     

Formation of radio signal spectral lines in propagation through circumsolar plasma

Conclusions The available experimental data on spectral line broadening for monochromatic radio waves propagating in the circumsolar plasma indicate the presence within the spatial spectrum of plasma inhomogeneities of an internal turbulence scale, the effect of which manifests itself in the finite values of the moments of the energy density distribution over frequency and in normatization of the spectral line form in the strong signal scattering regime. Theoretical analysis of line broadening produced by moving inhomogeneities in the solar corona has established a relationship between the second and fourth moments of the spectrum and the turbulence characteristics, permitting determination of the radial profile of the internal inhomogeneity scale for a known velocity of motion. According to Venera 10 data, the internal turbulence scale of the circumsolar plasma is of the order of magnitude of several km at distances of 5–10 solar radii and increases sharply with radial distanee. The change in the value of the internal turbulence scale with distance is of the same type as the dependence of ionic gyroradius on distance to the sun.Analysis of spectral broadening of radio signals is an effective means of studying such characteristics of inhomogeneities in the circumsolar plasma as the form of the spatial spectrum, the intensity of inhomogeneities, their rate of motion, the internal turbulence scale, and the radial profiles of these quantities. Simultaneously, the peculiarities discovered in the behavior of the spatial spectrum of the inhomogeneities require the completion of a stricter analysis of line broadening with consideration of radial variation of both the internal and external turbulence scales, a process which may explain other peculiarities of the spectral broadening of radio signals in the moderate and intense scattering regimes.Institute of Radio Technology and Electronics, Academy of Sciences of the USSR. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 22, No. 9, pp. 1051–1060, September, 1979.     

Photoprocesses with the sub-Doppler spectral selectivity excited by the monochromatic optical pulse in a thin gas cell

The method of sub-Doppler spectroscopy is theoretically elaborated, which is based on the specific dynamics of a number of optically excited atomic particles (atoms or molecules) of a rarefied gas medium in a thin cell after the action of the resonance pulse of the monochromatic radiation. Corresponding calculations are carried out on the basis of density matrix equations for the resonance optical transition between Zeeman degenerate ground and excited quantum levels of particles in case of the linear polarization of the laser pulse at its normal incidence on the cell. The situation is considered when the radiative lifetime of the excited level is much more than the characteristic transit time of particles between nearest plane-parallel walls of the cell. Then the distribution of a number of excited particles versus the pulse frequency detuning narrows in the process of particles collisions with walls of the cell after action of the laser pulse. The factor of such a narrowing (in comparison with the Doppler broadening of the spectral line of the resonance transition) may be more than the ratio of the characteristic transverse size of the thin gas cell to its inner thickness. We discuss possible use of given sub-Doppler resonances (of the number of excited particles) in the high-resolution spectroscopy and also in high-selective processes of photo-ionization and photo-dissociation, especially, for isotope (or isomer) separation and detection of rare (in particular single) atoms or molecules of a gas medium.     

Measuring the polarization of coherent light beams

We consider the conditions of interference of totally polarized light beams of arbitrary polarization that allow one to measure their vector characteristics by means of optical heterodyning. It is shown that the intensity of a light beam resulted from the superposition of two plane totally polarized waves with arbitrary polarizations represents a sum of two interference patterns, each of them being the result of superposition of conamed components of an orthogonal expansion of the electric field of the total light wave. The possibility of electronic registration of information in real time is demonstrated.