5,042 research outputs found
Compatible Lie brackets related to elliptic curve
For the direct sum of several copies of sl_n, a family of Lie brackets
compatible with the initial one is constructed. The structure constants of
these brackets are expressed in terms of theta-functions associated with an
elliptic curve. The structure of Casimir elements for these brackets is
investigated. A generalization of this construction to the case of
vector-valued theta-functions is presented. The brackets define a
multi-hamiltonian structure for the elliptic sl_n-Gaudin model. A different
procedure for constructing compatible Lie brackets based on the argument shift
method for quadratic Poisson brackets is discussed.Comment: 18 pages, Late
Some symmetry classifications of hyperbolic vector evolution equations
Motivated by recent work on integrable flows of curves and 1+1 dimensional
sigma models, several O(N)-invariant classes of hyperbolic equations for an -component vector are considered. In each
class we find all scaling-homogeneous equations admitting a higher symmetry of
least possible scaling weight. Sigma model interpretations of these equations
are presented.Comment: Revision of published version, incorporating errata on geometric
aspects of the sigma model interpretations in the case of homogeneous space
Electronic states in heterostructures formed by ultranarrow layers
Low-energy electronic states in heterosrtuctures formed by ultranarrow layer
(single or several monolayers thickness) are studied theoretically. The host
material is described within the effective mass approximation and effect of
ultranarrow layers is taken into account within the framework of the transfer
matrix approach. Using the current conservation requirement and the inversion
symmetry of ultranarrow layer, the transfer matrix is written through two
phenomenological parameters. The binding energy of localized state, the
reflection (transmission) coefficient for the single ultranarrow layer case,
and the energy spectrum of superlattice are determined by these parameters.
Spectral dependency of absorption in superlattice due to photoexcitation of
electrons from localized states into minibands is strongly dependent on the
ultranarrow layers characteristics. Such a dependency can be used for
verification of the transfer matrix parameters.Comment: 7 pages, 7 figure
Integrable quadratic Hamiltonians on so(4) and so(3,1)
We investigate a special class of quadratic Hamiltonians on so(4) and so(3,1)
and describe Hamiltonians that have additional polynomial integrals. One of the
main results is a new integrable case with an integral of sixth degree.Comment: 16 page
Phase Transitions in liquid Helium 3
The phase transitions of liquid Helium 3 are described by truncations of an
exact nonperturbative renormalization group equation. The location of the first
order transition lines and the jump in the order parameter are computed
quantitatively. At the triple point we find indications for partially universal
behaviour. We suggest experiments that could help to determine the effective
interactions between fermion pairs.Comment: 4 pages, 6 figures, LaTe
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