The Feynman diagrams in theories with matrix fields $\Phi\in\mathop{\bf Mat}\nolimits(N,N)$ are ribbon graphs. There is a one-to-one correspondence between the ribbon graphs and surfaces with boundary having cell structures. The exponents of $N$ in the Feynman integrals depend only on the topology of the corresponding surfaces. It is shown that this is also true of generalized ribbon graphs. Such graphs correspond to surfaces with decomposition into spheres with holes.
Show AbstractThe filled waveguide spectral problem eigenvalues embedded in the continuous spectrum are considered. An example of waveguide filling perturbation under which the embedded eigenvalues of the filled waveguide spectral problem disappear is given.
Show AbstractExpressions £or thermodynamic functions in terms of simple statistical operators are obtained. The problem of thermodynamic compatibility of the thermal and caloric equations of state for quantum systems is solved.
Show AbstractIn the rigid rotator model, the rotational dynamics of a two-dimensional molecular hydrogen ion was studied. The effect of dynamic orientation of a nuclear wave packet along and across the laser field polarization direction at the laser parameters for which the dissociation probability is low was revealed.
Show AbstractIn an isothermal mode for HoBa$_2$Cu$_3$O$_6$ in a tetragonal phase including anisotropic bilinear interaction, the Zeeman effect, magnetization and differential magnetic susceptibility are calculated. Magnetic ordering in a basal plane in an external magnetic field $\bH\paral[001]$ near the energy levels crossover that is accompanied with the magnetic moment deflection from the field direction is shown to exist. The phase diagram dependence on the anisotropic bilinear interaction parameters, temperature and other factors is studied.
Show AbstractUsing the Japan region as an example, the relationship between seismicity and parameters of the seismotectonic strain rate tensor is studied. It is shown that the ranges of minimum values of the seismotectonic strain rate tensor determine localization of zones of relative seismic quiescence preceding strong earthquakes. To identify the seismic quiescence zones, the seismotectonic strain rate tensors and their invariants are calculated using the data on seismic focus mechanisms in Japan.
Show AbstractPrediction of mean monthly temperature by the probabilistic method of reduction of measurement of the dynamic pattern of space-time temperature variations over the former USSR territory is studied. Based on the dynamics of the temperature distribution fronts isolines, the vector field of prevalent heat flows is determined and a model of the temperature field dynamics for each region is constructed.
Show Abstract
