Chow motives of twisted flag varieties

Let G be an adjoint simple algebraic group of inner type. We express the Chow motive (with integral coefficients) of some anisotropic projective G-homogeneous varieties in terms of motives of simpler G-homogeneous varieties, namely, those that correspond to maximal parabolic subgroups of G. We decompose the motive of a generalized Severi-Brauer variety SB_2(A), where A is a division algebra of degree 5, into a direct sum of two indecomposable motives. As an application we provide another counter-example to the uniqueness of a direct sum decomposition in the category of motives with integral coefficients.Comment: 28 page

Scalar charged particle in Weyl--Wigner--Moyal phase space. Constant magnetic field

A relativistic phase-space representation for a class of observables with matrix-valued Weyl symbols proportional to the identity matrix (charge-invariant observables)is proposed. We take into account the nontrivial charge structure of the position and momentum operators. The evolution equation coincides with its analog in relativistic quantum mechanics with nonlocal Hamiltonian under conditions where particle-pair creation does not take place (free particle and constant magnetic field). The differences in the equations are connected with peculiarities of the constraints on the initial conditions. An effective increase in coherence between eigenstates of the Hamiltonian is found and possibilities of its experimental observation are discussed.Comment: 27 pages, 7 figures, minor correction

Possible peculiarities of synchrotron radiation in a strong magnetic field

Relativistic quantum effects on physical observables of scalar charged particles are studied. Possible peculiarities of their behavior that can be verified in an experiment can confirm several fundamental conceptions of quantum mechanics. For observables independent of charge variable, we propose relativistic Wigner function formalism that contains explicitly the measurement device frame. This approach can provide the description of charged particles gas (plasma). It differs from the traditional one but is consistent with the Copenhagen interpretation of quantum mechanics. The effects that are connected with this approach can be observed in astrophysical objects - neutron stars.Comment: 7 pages, no figures, Contribution to the 8-th Ukrainian Conference on Plasma Physics and Controlled Fusion, Alushta, Crimea, 11-17 September, 200

Relativistic Wigner Function, Charge Variable and Structure of Position Operator

The relativistic phase-space representation by means of the usual position and momentum operators for a class of observables with Weyl symbols independent of charge variable (i.e. with any combination of position and momentum) is proposed. The dynamical equation coincides with its analogue in the non-local theory (generalization of the Newton-Wigner position operator approach) under conditions when particles creation is impossible. Differences reveal themselves in specific constraints on possible initial conditions.Comment: 13 pages, no figures, Contribution to the Seventh International Conference on Squeezed States and Uncertainty Relations, Boston, Massachusetts,USA, 4-7 June 200

Quantum Phase Space in Relativistic Theory: the Case of Charge-Invariant Observables

Mathematical method of quantum phase space is very useful in physical applications like quantum optics and non-relativistic quantum mechanics. However, attempts to generalize it for the relativistic case lead to some difficulties. One of problems is band structure of energy spectrum for a relativistic particle. This corresponds to an internal degree of freedom, so-called charge variable. In physical problems we often deal with such of dynamical variables that do not depend on this degree of freedom. These are position, momentum, and any combination of them. Restricting our consideration to this kind of observables we propose the relativistic Weyl--Wigner--Moyal formalism that contains some surprising differences from its non-relativistic counterpart.Comment: Oral talk given at 5th International Conference "Symmetry in Nonlinear Mathematical Physics", Kiev, Ukraine (June 23-29, 2003

Photonic Drag Effect for One-Dimensional Electrons in a Longitudinal Magnetic Field with D(-)-Centers Participation

The impurity photonic drag effect (PDE), theory for semiconductive quantum wire (QW) in a longitudinal (along the quantum wire axis) magnetic field B, has been developed. The PDE is due to the photon longitudinal momentum transmission to localized electrons, under optical transitions from D(-)-states to QW hybrid-quantum states, if the QW is described by the parabolic confinement potential. The analytical expression for the drag current (DC) density has been obtained within the framework of zero-range potential model and in the effective mass approximation. The drag current spectral dependence has been investigated for various values of B and QW parameters, under electron scattering on the dotty-impurities system. The drag current spectral dependence is characterized by Zeeman doublet with a pronounced beak-type peak. This peak is related to electron optical transitions from D(-)-states to the states with the magnetic quantum number m=1. With an increase of the magnetic field B the beak-type peak is shifted to short-wave spectrum region, and the peak height considerably increases. We discuss the possibility of using of the one-dimensional drag current effect, in a longitudinal magnetic field, to develop a new type of laser radiation detectors.Comment: 26 pages, 3 figures, PDF file, 134 K

Dynamic percolation of electric conductivity and a trend towards fractal skeletal structuring in a random ensemble of magnetized nanodust

Numerical modeling of electrodynamic aggregation is carried out for a random ensemble of magnetized nanodust taken as a many body system of strongly magnetized thin rods (i.e., one-dimensional static magnetic dipoles), which possess electric conductivity and static electric charge, screened with its own static plasma sheath. The self-assembling of quasi-linear filaments from an ensemble of randomly situated basic blocks and the electric short-circuiting between biased electrodes are shown to be supported by the alignment of blocks in an external magnetic field. Statistical analysis of short-circuiting time allows tracing the dynamic percolation of electric conductivity and shows a decrease of percolation threshold for volume fraction, as compared with the observed percolation of carbon nanotubes in liquids and polymer composites. Modeling of short-circuiting stage of evolution is continued with tracing the dynamics of pinching of electric current filaments to show the interplay of all the magnetic and electric mechanisms of filaments networking. A trend towards a fractal skeletal structuring (namely, repeat of original basic block at a larger length scale) is illustrated with the evidence for generation of a bigger magnetic dipole.Comment: 21 pages, 16 figure

Single leptoquark production associated with hard photon emission in ep collisions at high energies

In this paper we consider single leptoquark resonance production associated with the emission of a hard photon. We have obtained analytical formulae for differential and total cross sections for the cases of scalar and vector leptoquarks. We have found that in reactions with scalar leptoquarks there is no photon radiation in some directions depending on the leptoquark electric charge (the radiative amplitude zero - the RAZ effect). For vector leptoquarks the exact RAZ is present only in the case of Yang-Mills coupling. We propose to use the RAZ effect to determine the types of leptoquarks. We conclude also that this effect opens a possibility to measure the leptoquark anomalous magnetic moment.Comment: 11 pages, one figure is prepared in 'eps' format and stored in the file 'raz_cms.uu' compressed and uuencoded by standard script 'uufiles

Noise-induced transitions in a double-well oscillator with nonlinear dissipation

We develop a model of bistable oscillator with nonlinear dissipation. Using a numerical simulation and an electronic circuit realization of this system we study its response to additive noise excitations. We show that depending on noise intensity the system undergoes multiple qualitative changes in the structure of its steady-state probability density function (PDF). In particular, the PDF exhibits two pitchfork bifurcations versus noise intensity, which we describe using an effective potential and corresponding normal form of the bifurcation. These stochastic effects are explained by the partition of the phase space by the nullclines of the deterministic oscillator.Comment: 7 pages (main paper with references), 7 figure

Relativistic coherent states and charge structure of the coordinate and momentum operators

We consider relativistic coherent states for a spin-0 charged particle that satisfy the next additional requirements: (i) the expected values of the standard coordinate and momentum operators are uniquely related to the real and imaginary parts of the coherent state parameter; (ii) these states contain only one charge component. Three cases are considered: free particle, relativistic rotator, and particle in a constant homogeneous magnetic field. For the rotational motion of the two latter cases, such a description leads to the appearance of the so-called nonlinear coherent states.Comment: 11 pages, 10 figure