Exotic solutions in string theory

Solutions of classical string theory, correspondent to the world sheets, mapped in Minkowsky space with a fold, are considered. Typical processes for them are creation of strings from vacuum, their recombination and annihilation. These solutions violate positiveness of square of mass and Regge condition. In quantum string theory these solutions correspond to physical states |DDF>+|sp> with non-zero spurious component.Comment: accepted in Il Nuovo Cimento A for publication in 199

Relativistic Coulomb problem for particles with arbitrary half-integer spin

Using relativistic tensor-bispinorial equations proposed in hep-th/0412213 we solve the Kepler problem for a charged particle with arbitrary half-integer spin interacting with the Coulomb potential.Comment: Misprints are correcte

On the new approach to variable separation in the time-dependent Schr\"odinger equation with two space dimensions

We suggest an effective approach to separation of variables in the Schr\"odinger equation with two space variables. Using it we classify inequivalent potentials $V(x_1,x_2)$ such that the corresponding Schr\" odinger equations admit separation of variables. Besides that, we carry out separation of variables in the Schr\" odinger equation with the anisotropic harmonic oscillator potential $V=k_1x_1^2+k_2x_2^2$ and obtain a complete list of coordinate systems providing its separability. Most of these coordinate systems depend essentially on the form of the potential and do not provide separation of variables in the free Schr\" odinger equation ($V=0$).Comment: 21 pages, latex, to appear in the "Journal of Mathematical Physics" (1995

Resonantly suppressed transmission and anomalously enhanced light absorption in ultrathin metal films

We study light diffraction in the periodically modulated ultrathin metal films both analytically and numerically. Without modulation these films are almost transparent. The periodicity results in the anomalous effects, such as suppression of the transmittance accompanied by a strong enhancement of the absorptivity and specular reflectivity, due to excitation of the surface plasmon polaritons. These phenomena are opposite to the widely known enhanced transparency of periodically modulated optically thick metal films. Our theoretical analysis can be a starting point for the experimental investigation of these intriguing phenomena.Comment: 4 pages, 5 figure

Modification of the RLA model for presenting a cluster system of a composite material with a fractal filler structure

The paper proposes a modification of the diffusion-limited aggregation model to study the properties of a cluster system. A computational experiment to determine the mutual influence of the sticking probability and the volume concentration of particles on the formation of fractal clusters in a cluster system was carried out in accordance  with  the  second-order  orthogonal  central  compositional  plan  (OCCP).  As  a  result of a computational experiment in accordance with the OCCP, an equation was obtained for the dependence of the mass fractal dimension of clusters on the volume of particle concentration and the probability of adhesion of diffusing particles and cluster particles in the adhesion zone. This dependence was obtained in a range of volume concentration of particles from 2 to 5 % and the probability of adhesion of diffusing particles and particles of clusters in the adhesion zone from 0.2 to 1.The paper proposes a modification of the diffusion-limited aggregation model to study the properties of a cluster system. A computational experiment to determine the mutual influence of the sticking probability and the volume concentration of particles on the formation of fractal clusters in a cluster system was carried out in accordance  with  the  second-order  orthogonal  central  compositional  plan  (OCCP).  As  a  result of a computational experiment in accordance with the OCCP, an equation was obtained for the dependence of the mass fractal dimension of clusters on the volume of particle concentration and the probability of adhesion of diffusing particles and cluster particles in the adhesion zone. This dependence was obtained in a range of volume concentration of particles from 2 to 5 % and the probability of adhesion of diffusing particles and particles of clusters in the adhesion zone from 0.2 to 1