29 research outputs found
Generalizations of Poisson Structures Related to Rational Gaudin Model
The Poisson structure arising in the Hamiltonian approach to the rational Gaudin model looks very similar to the so-called modified Reflection Equation Algebra. Motivated by this analogy, we realize a braiding of the mentioned Poisson structure, i.e. we introduce a ”braided Poisson” algebra associated with an involutive solution to the quantum Yang-Baxter equation. Also, we exhibit another generalization of the Gaudin type Poisson structure by replacing the first derivative in the current parameter, entering the so-called local form of this structure, by a higher order derivative. Finally, we introduce a structure, which combines both generalizations. Some commutative families in the corresponding braided Poisson algebra are found
Pre-torsors and Galois comodules over mixed distributive laws
We study comodule functors for comonads arising from mixed distributive laws.
Their Galois property is reformulated in terms of a (so-called) regular arrow
in Street's bicategory of comonads. Between categories possessing equalizers,
we introduce the notion of a regular adjunction. An equivalence is proven
between the category of pre-torsors over two regular adjunctions
and on one hand, and the category of regular comonad arrows
from some equalizer preserving comonad to on
the other. This generalizes a known relationship between pre-torsors over equal
commutative rings and Galois objects of coalgebras.Developing a bi-Galois
theory of comonads, we show that a pre-torsor over regular adjunctions
determines also a second (equalizer preserving) comonad and a
co-regular comonad arrow from to , such that the
comodule categories of and are equivalent.Comment: 34 pages LaTeX file. v2: a few typos correcte
Kappa-Minkowski spacetime, Kappa-Poincar\'{e} Hopf algebra and realizations
We unify kappa-Minkowki spacetime and Lorentz algebra in unique Lie algebra.
Introducing commutative momenta, a family of kappa-deformed Heisenberg algebras
and kappa-deformed Poincare algebras are defined. They are specified by the
matrix depending on momenta. We construct all such matrices. Realizations and
star product are defined and analyzed in general and specially, their relation
to coproduct of momenta is pointed out. Hopf algebra of the Poincare algebra,
related to the covariant realization, is presented in unified covariant form.
Left-right dual realizations and dual algebra are introduced and considered.
The generalized involution and the star inner product are analyzed and their
properties are discussed. Partial integration and deformed trace property are
obtained in general. The translation invariance of the star product is pointed
out. Finally, perturbative approach up to the first order in is presented
in Appendix.Comment: references added, typos corrected, acceped in J. Phys.
Noncommutative Differential Forms on the kappa-deformed Space
We construct a differential algebra of forms on the kappa-deformed space. For
a given realization of the noncommutative coordinates as formal power series in
the Weyl algebra we find an infinite family of one-forms and nilpotent exterior
derivatives. We derive explicit expressions for the exterior derivative and
one-forms in covariant and noncovariant realizations. We also introduce
higher-order forms and show that the exterior derivative satisfies the graded
Leibniz rule. The differential forms are generally not graded-commutative, but
they satisfy the graded Jacobi identity. We also consider the star-product of
classical differential forms. The star-product is well-defined if the
commutator between the noncommutative coordinates and one-forms is closed in
the space of one-forms alone. In addition, we show that in certain realizations
the exterior derivative acting on the star-product satisfies the undeformed
Leibniz rule.Comment: to appear in J. Phys. A: Math. Theo
Challenges in QCD matter physics - The Compressed Baryonic Matter experiment at FAIR
Substantial experimental and theoretical efforts worldwide are devoted to
explore the phase diagram of strongly interacting matter. At LHC and top RHIC
energies, QCD matter is studied at very high temperatures and nearly vanishing
net-baryon densities. There is evidence that a Quark-Gluon-Plasma (QGP) was
created at experiments at RHIC and LHC. The transition from the QGP back to the
hadron gas is found to be a smooth cross over. For larger net-baryon densities
and lower temperatures, it is expected that the QCD phase diagram exhibits a
rich structure, such as a first-order phase transition between hadronic and
partonic matter which terminates in a critical point, or exotic phases like
quarkyonic matter. The discovery of these landmarks would be a breakthrough in
our understanding of the strong interaction and is therefore in the focus of
various high-energy heavy-ion research programs. The Compressed Baryonic Matter
(CBM) experiment at FAIR will play a unique role in the exploration of the QCD
phase diagram in the region of high net-baryon densities, because it is
designed to run at unprecedented interaction rates. High-rate operation is the
key prerequisite for high-precision measurements of multi-differential
observables and of rare diagnostic probes which are sensitive to the dense
phase of the nuclear fireball. The goal of the CBM experiment at SIS100
(sqrt(s_NN) = 2.7 - 4.9 GeV) is to discover fundamental properties of QCD
matter: the phase structure at large baryon-chemical potentials (mu_B > 500
MeV), effects of chiral symmetry, and the equation-of-state at high density as
it is expected to occur in the core of neutron stars. In this article, we
review the motivation for and the physics programme of CBM, including
activities before the start of data taking in 2022, in the context of the
worldwide efforts to explore high-density QCD matter.Comment: 15 pages, 11 figures. Published in European Physical Journal
Generalized kappa-deformed spaces, star-products, and their realizations
In this work we investigate generalized kappa-deformed spaces. We develop a
systematic method for constructing realizations of noncommutative (NC)
coordinates as formal power series in the Weyl algebra. All realizations are
related by a group of similarity transformations, and to each realization we
associate a unique ordering prescription. Generalized derivatives, the Leibniz
rule and coproduct, as well as the star-product are found in all realizations.
The star-product and Drinfel'd twist operator are given in terms of the
coproduct, and the twist operator is derived explicitly in special
realizations. The theory is applied to a Nappi-Witten type of NC space
Fixed neutron absorbers for improved nuclear safety and better economics in nuclear fuel storage, transport and disposal
Current designs of both large reactor units and small modular reactors utilize a nuclear fuel with increasing enrichment. This increasing demand for better nuclear fuel utilization is a challenge for nuclear fuel handling facilities. The operation with higher enriched fuels leads to reduced reserves to legislative and safety criticality limits of spent fuel transport, storage and final disposal facilities. Design changes in these facilities are restricted due to a boron content in steel and aluminum alloys that are limited by rolling, extrusion, welding and other manufacturing processes. One possible solution for spent fuel pools and casks is the burnup credit method that allows decreasing very high safety margins associated with the fresh fuel assumption in spent fuel facilities. This solution can be supplemented or replaced by an alternative solution based on placing the neutron absorber material directly into the fuel assembly, where its efficiency is higher than between fuel assemblies. A neutron absorber permanently fixed in guide tubes decreases system reactivity more efficiently than absorber sheets between the fuel assemblies. The paper summarizes possibilities of fixed neutron absorbers for various nuclear fuel and fuel handling facilities. Moreover, an absorber material was optimized to propose alternative options to boron. Multiple effective absorbers that do not require steel or aluminum alloy compatibility are discussed because fixed absorbers are placed inside zirconium or steel cladding