909 research outputs found
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 -invariant Hecke type
-matrices. The analogues of the matrices of Hecke type with the
symmetry of the quantum super-algebra are obtained precisely. For
the homogeneous solutions 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 ,
extended Lax operators of Hecke type, also are suggested.Comment: 36 pages; corrected typos, made some clarifications; the printed
versio
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
An Integrable Model with non-reducible three particle R-Matrix
We define an integrable lattice model which, in the notation of Yang, in
addition to the conventional 2-particle -matrices also contains
non-reducible 3-particle -matrices. The corresponding modified Yang-Baxter
equations are solved and an expression for the transfer matrix is found as a
normal ordered exponential of a (non-local) Hamiltonian.Comment: 13 pages, 4 figure
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