Composite particles in the Theory of Quantum Hall Effect

The formation of composite particles in the electron liquid under QHE conditions discussed by Jain in generalizing Laughlins many-particle state is considered by using a model for two-dimensional guiding center configurations. Describing the self-consistent field of electron repulsion by a negative parabolic potential on effective centers and an inter-center amount we show that with increasing magnetic field the ground state of so-called primary composite particles $\nu=\frac{1}{q}$, $q=1,3,5,...$, is given for higher negative quantum numbers of the total angular momentum. By clustering of primary composite particles due to absorption or emission of flux quanta we explain phenomenologically the quasi-particle structure behind the series of relevant filling factors $\nu=\frac{p}{q}$, $p=1,2,3,...$. Our considerations show that the complicate interplay of electron-magnetic field and electron-electron interactions in QHE systems may be understood in terms of adding flux quanta $\Phi_0$ to charges $e$ and binding of charges by flux quanta.Comment: RevTeX 3.0, LaTeX, 10 pages, one table at th en

On topological restrictions of the spacetime in cosmology

In this paper we discuss the restrictions of the spacetime for the standard model of cosmology by using results of the differential topology of 3- and 4-manifolds. The smoothness of the cosmic evolution is the strongest restriction. The Poincare model (dodecaeder model), the Picard horn and the 3-torus are ruled out by the restrictions but a sum of two Poincare spheres is allowed.Comment: 11 pages, 3 figures, accepted in Mod. Phys. Lett.