Geophysical aspects of anomalous phenomena and global ecology

We present the results of investigation of anomalous phenomena from geophysical perspectives. We consider technogenic contributions to the generation of luminous formations above the territories of cities located in complex geophysical conditions. We discuss hypotheses concerning the hybrid nature of the reasons for appearance of anomalous phenomena, involving both natural and technogenic processes. We clarify the conditions for generation of luminous formations in energetically active zones, in which vertical energy reflux processes occur. We give brief characteristics of the collective behavior of anomalous phenomena and their connection with geoheliophysical processes.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 30–38, March, 1992.     

Deterministic chaos and natural phenomena

The natural time seriesf ₀ F ₂, F10.7, and AE are analyzed and low-dimensional attractors are found, characterized by the correlation dimension and the lower bound of the Kolmogorov entropy. Sources of noise in natural time series are discussed and the concept of extended systems is introduced and used to explain why the number of data required to calculate the correlation dimension of natural time series is higher than that reported by other authors.     

Distribution of anomalous exponents of natural images

Recent studies of correlations of intensity in databases of natural images revealed a remarkable property. The two point correlations are described in terms of power law behavior, with an exponent which seems to be robust. In the present Letter we consider the statistical meaning of that result. We study many individual images of one of the databases considered. We find that the same law characterizing the correlations in the whole database governs also images randomly chosen from that database, with one essential difference. The exponent characterizing each image is specific and differs from the exponent characterizing the whole database. The distribution of single image exponents has been measured and found to exhibit a rather heavy tail. The database exponent cannot, thus, be considered as a statistical representative of a single image exponent. Possible reasons for the diversity in image exponents are discussed.     

Chiral perturbation theory for anomalous processes

A general expression containing all the divergences in Chiral Perturbation Theory at one loop for anomalous processes has been calculated. The nonrenormalization of some amplitudes (Adler-Bardeen theorem) is observed. The different types of corrections are identified. The contributions from vector meson exchange are determined for all anomalous processes. Explicit cancellation of divergences is shown for π⁰, η and η′ decays to γγ^*. The dependence on the γ^* mass squared is predicted to be essentially the same for all the three processes. It proceeds mainly through the VMD estimate of the finite parts of the next order Lagrangian and compares reasonably well with the available experimental data.     

Quantum theory of transverse galvano-magnetic phenomena

A quantum theory of electrical conduction in crosfsed electric and magnetic fields is given for the limit of very weak scattering. A density matrix formulation of the problem is used, and an arbitrary scattering mechanism is considered. The theory is found to be completely equivalent to theories given earlier by and by and .

Formulae are given for the resistivity in the quantum limit for both longitudinal and transverse orientations of electric field, for degenerate and non-degenerate statistics, and for several different scattering mechanisms. The oscillatory conductivity is calculated for acoustical and ionized-impurity scattering mechanisms. Formulae obtained for the quantum transport effects are in disagreement with the formulae of and of . The discrepancy is attributed to unwarranted approximations in those authors' treatments of scattering.     

A different theory of anomalous magnetic moment

The invariance of Dirac's equation under rotation has been used to obtain the wave equation for a particle interacting with an electromagnetic field. The origin of the anomalous magnetic moment of a particle has been attributed to the existence of mass due to spin. These masses for a few representative particles have been calculated. In particular these calculations give a mass of 592.074 eV for a neutrino. An operator for the spin angular velocity has been constructed and the values of spin angular velocities for the particles have also been calculated.     

Mean field theory of self-organized critical phenomena

A mean field theory is presented for the recently discovered self-organized critical phenomena. The critical exponents are calculated and found to be the same as the mean field values for percolation. The power spectrum has 1/f behavior with exponentg4=1.     

Quantum field theory of optical birefringence phenomena

The inverse Faraday effect, in which a magnetization is induced in a solution through which is passed a polarized light beam of arbitrary ellipticity, is discussed on the basis of the S-matrix formulation of optical birefringence. It is shown that the Faraday effect and the inverse Faraday effect are topologically identical problems of diagrammatic perturbation theory and so it follows automatically that the magnetization should be proportional to the Verdet constant. The optical Faraday effect is the circular birefringence induced by an intense circularly polarized beam of light propagated colinearly with the weak measuring beam: the electric vector of the circularly polarized beam interacts with the molecule in a way that resembles the interaction of a static magnetic field. The interrelations of these two effects and the normal Faraday effect the self-rotation of the polarization ellipse of an intense beam are discussed.     

On the perturbation theory of critical phenomena

It is shown how, using the ideas of Brezin, Le Guillou and Zinn-Justin, one may obtain the critical properties of the φ⁴ model from renormalised perturbation theory without the use of the Callan-Symanzik equation and an associated approximation     

An anomalous transformation in string field theory

Conformal field theory techniques are used to analyze a recently proposed transformation of Witten's interaction vertex from center-of-mass to mid-point variables. As presented in the literature the transformed vertex has the surprising property of being non-local in the mid-point coordinates unless an additional non-unitary transformation is performed. This renders the kinetic term non-local and poses additional problems. Here we show that, besides being non-local, the transformed vertex does not satisfy the overlap equations and fails to be BRST invariant. These bad properties are the result of an associativity anomaly of the type considered by Horowitz and Strominger. However, this anomaly is “almost trivial” in the sense that most of its bad effects can be avoided by choosing a proper regularization.     

On anomalous diffusion of fractal clusters under certain realistic physical conditions

Summary Diffusion of a fractal cluster of dimensiond _f in a three-dimensional space is investigated. The diffusion process is assumed to be modelled by a standard parabolic diffusion equation, although a more general case represented by the Fokker-Planck-Kolmogoroff equation is also introduced. The mean-square displacement of the cluster mass centre is analysed and its anomalous behaviour is presented and critically discussed. The results obtained can be applied to describe some effects which may occur during the diffusion-limited cluster-cluster aggregation process, especially when the viscosity of the solvent is changed in time and/or a directed transport of clusters is present in the system. Paper presented at the I International Conference on Scaling Concepts and Complex Fluids, Copanello, Italy, July 4–8, 1994.     

The statistical theory of anomalous fermion number non-conservation

We present a non-equilibrium method for studying anomalous B-non-conservation in the electroweak theory at finite temperature. We derive formally the equation of B-evolution advocated previously on physical grounds. The kinetic coefficient in it is quite generally expressed through a thermodynamic average. This expression allows for an estimate of higher order corrections and is applicable both below and above the phase transition temperature.