Invariant-algebraic approach to problems of quantum optics

A general approach is formulated for analyzing algebraic models of quantum composite systems with an internal symmetry described by group G. The case G = SU(2) is examined in detail as applied to the analysis of polarization invariance in quantum optics. A new class of fully depolarizable quantum states of light (scalar biphotons) is defined and investigated. Certain interactions of scalar biphoton light with material media are considered in the context of Dicke and Jaynes-Cummings models.Landsberg Optics Division, Lebedev Physics Institute. Translated from Preprint No. 137 of the Lebedev Physics Institute, Academy of Sciences of the USSR, Moscow, 1990.     

On the possibility of phase transitions in dusty plasma structures in a glow discharge under the action of a magnetic field

The melting of a dusty plasma structure formed in a stratum of a glow discharge caused by application of a magnetic field and its subsequent increase is studied. The images of two-dimensional cross sections of dusty plasma structures previously obtained by the authors are considered. To identify the phase, the correlation functions are calculated and visual comparison with the space lattices of ideal crystals is performed. It is found that, under the conditions of the previous study of the authors, as the magnetic field increases, the phase state of the dusty structure changes from an anisotropic liquidlike (liquid-ice) state to a disordered one. There is a tendency to a change in the type of the space lattice of the structure.     

Plane poisson manifolds and finite-dimensional pseudogroups

Translated from Matematicheskie Zametki, Vol. 45, No. 3, pp. 53–65, March, 1989.