The conflict interaction between two complex systems. Cyclic migration

We construct and study a discrete time model describing the conflict interaction between two complex systems with non-trivial internal structures. The external conflict interaction is based on the model of alternative interaction between a pair of non-annihilating opponents. The internal conflict dynamics is similar to the one of a predator-prey model. We show that the typical trajectory of the complex system converges to an asymptotic attractive cycle. We propose an interpretation of our model in terms of migration processes

Linear, diatomic crystal: single-electron states and large-radius excitons

The large-radius exciton spectrum in a linear crystal with two atoms in the unit cell was obtained using the single-electron eigenfunctions and the band structure, which were found by the zero-range potential (ZRP) method. The ground-state exciton binding energies for the crystal in vacuum appeared to be larger than the corresponding energy gaps for any set of the crystal parameters.Comment: 9 pages, 1 figure, 1 tabl

Non-Degenerate Ultrametric Diffusion

General non-degenerate p-adic operators of ultrametric diffusion are introduced. Bases of eigenvectors for the introduced operators are constructed and the corresponding eigenvalues are computed. Properties of the corresponding dynamics (i.e. of the ultrametric diffusion) are investigated.Comment: 19 pages, 3 figure