The von Neumann Hierarchy for Correlation Operators of Quantum Many-Particle Systems

The Cauchy problem for the von Neumann hierarchy of nonlinear equations is investigated. One describes the evolution of all possible states of quantum many-particle systems by the correlation operators. A solution of such nonlinear equations is constructed in the form of an expansion over particle clusters whose evolution is described by the corresponding order cumulant (semi-invariant) of evolution operators for the von Neumann equations. For the initial data from the space of sequences of trace class operators the existence of a strong and a weak solution of the Cauchy problem is proved. We discuss the relationships of this solution both with the $s$-particle statistical operators, which are solutions of the BBGKY hierarchy, and with the $s$-particle correlation operators of quantum systems.Comment: 26 page

Dynamic susceptibility of a spin ice near the critical point

We consider spin ice magnets (primarily, $\mathrm{Dy_2Ti_2O_7}$) in the vicinity of their critical point on the $(H,T)$ plane. We find that the longitudinal susceptibility diverges at the critical point, leading to the behaviour qualitatively similar to the one which would result from non-zero conductance of magnetic charges. We show that dynamics of critical fluctuations belongs to the universality class of easy-axis ferroelectric and calculate logarithmic corrections (within two-loop approximation) to the mean-field critical behavior.Comment: 5 pages, 3 figures. Some misprints are corrected, among them are the formula (20) and the estimation for $\Gamma_c

RYE CHROMATIN INTROGRESSION IN THE BREAD WHEAT GENOME: CYTOGENETIC ASPECTS

Alien chromatin introgression into the genome of common wheat Triticum aestivum L. is the most efficient way to enrich the gene pool of this crop. To improve the breeding value of wheat accessions, rye Secale cereale L is used as a donor of characters. Transfer of rye genetic material has certain specific features. The combination of the two cereal genomes in a single nucleus results in imbalance in all genetic systems. Fertility restoration in amphihaploids is the first step in the formation of introgression accessions. It is followed by the hybrid genome reorganization, which leads to cytological and genetic stability in the diploid progeny. In this paper, we present and analyze results that were obtained in the study of the two steps of wheat-rye hybrid genome reorganization: (1) breaching of F1 hybrid sterility (cytogenetic mechanisms of unreduced gamete formation) and (2) reorganization of wheat subgenomes during the introgression of single rye chromosomes