A matrix model for strings beyond the c=1 barrier: the spin-s Heisenberg model on random surfaces

We consider a spin-s Heisenberg model coupled to two-dimensional quantum gravity. We quantize the model using the Feynman path integral, summing over all possible two-dimensional geometries and spin configurations. We regularize this path integral by starting with the R-matrices defining the spin-s Heisenberg model on a regular 2d Manhattan lattice. 2d quantum gravity is included by defining the R-matrices on random Manhattan lattices and summing over these, in the same way as one sums over 2d geometries using random triangulations in non-critical string theory. We formulate a random matrix model where the partition function reproduces the annealed average of the spin-s Heisenberg model over all random Manhattan lattices. A technique is presented which reduces the random matrix integration in partition function to an integration over their eigenvalues.Comment: 18 pages, 6 figures. arXiv admin note: substantial text overlap with arXiv:1304.690

Series of the solutions to Yang-Baxter equations: Hecke type matrices and descendant R-, L-operators

We have constructed series of the spectral parameter dependent solutions to the Yang-Baxter equations defined on the tensor product of reducible representations with symmetry of quantum algebra. These series are produced as descendant solutions from the $sl_{q}(2)$-invariant Hecke type $R^{r\;r}(u)$-matrices. The analogues of the matrices of Hecke type with the symmetry of the quantum super-algebra $osp_q(1|2)$ are obtained precisely. For the homogeneous solutions $R^{r^2-1\;r^2-1}$ there are constructed Hamiltonian operators of the corresponding one-dimensional quantum integrable models, which describe rather intricate interactions between different kind of spin states. Centralizer operators defined on the products of the composite states are discussed. The inhomogeneous series of the operators $R^{r\mathcal{R}}(u)$, extended Lax operators of Hecke type, also are suggested.Comment: 36 pages; corrected typos, made some clarifications; the printed versio

Self-amplified Emission of Cherenkov Radiation from a Relativistic Particle Inside Layered Dielectric-filled Waveguide

It is shown that in some special cases the Cherenkov radiation from a charged particle moving along the axis of cylindrical waveguide filled with a semi-infinite material consisting of dielectric plates alternated with vacuum gaps is many times stronger than that in the waveguide filled with semi-infinite solid dielectric without vacuum gaps.Comment: 1 page, abstract submitted to 4th International Conference "Channeling 2010", Ferrara, Italy, October 3-8, 201

On the theory of coherent pair production in crystals in presence of acoustic waves

The influence of hypersonic waves excited in a single crystal is investigated on the process of electron-positron pair creation by high-energy photons. The coherent part of the corresponding differential cross-section is derived as a function of the amplitude and wave number of the hypersound. The values of the parameters are specified for which the latter affects remarkably on the pair creation cross-section. It is shown that under certain conditions the presence of hypersonic waves can result in enhancement of the process cross-section.Comment: 10 pages, 3 EPS figure

Radiation from a charged particle-in-flight from a laminated medium to vacuum

The radiation from a charged particle-in-flight from a semi-infinite laminated medium to vacuum and back,- from vacuum to the laminated medium, has been investigated. Expressions for the spectral-angular distribution of radiation energy in vacuum (at large distances from the boundary of laminated medium) were obtained for both the cases with no limitations on the amplitude and variation profile of the laminated medium permittivity. The results of appropriate numerical calculations are presented and possible applications of the obtained results are discussed.Comment: 8 pages, 6 figures, contribution to Proceedings of International Symposium RREPS-2009, 07-11 September, 2009, Zvenigorod, Russi