370 research outputs found
Thermodynamic Properties of a Quantum Group Boson Gas
An approach is proposed enabling to effectively describe the behaviour of a
bosonic system. The approach uses the quantum group formalism. In
effect, considering a bosonic Hamiltonian in terms of the
generators, it is shown that its thermodynamic properties are connected to
deformation parameters and . For instance, the average number of
particles and the pressure have been computed. If is fixed to be the same
value for , our approach coincides perfectly with some results developed
recently in this subject. The ordinary results, of the present system, can be
found when we take the limit .Comment: 13 pages, Late
On a nonstandard two-parametric quantum algebra and its connections with and
A quantum algebra associated with a nonstandard
-matrix with two deformation parameters is studied and, in
particular, its universal -matrix is derived using Reshetikhin's
method. Explicit construction of the -dependent nonstandard -matrix
is obtained through a coloured generalized boson realization of the universal
-matrix of the standard corresponding to a
nongeneric case. General finite dimensional coloured representation of the
universal -matrix of is also derived. This
representation, in nongeneric cases, becomes a source for various
-dependent nonstandard -matrices. Superization of leads to the super-Hopf algebra . A contraction
procedure then yields a -deformed super-Heisenberg algebra
and its universal -matrix.Comment: 17pages, LaTeX, Preprint No. imsc-94/43 Revised version: A note added
at the end of the paper correcting and clarifying the bibliograph
Multi-decadal atmospheric and marine climate variability in southern Iberia during the mid- to late-Holocene
To assess the regional multi-decadal to multicentennial climate variability along the southern Iberian Peninsula during the mid- to late-Holocene record of paleoenvironmental indicators from marine sediments were established for two sites in the Alboran Sea (ODP-161-976A) and the Gulf of Cadiz (GeoB5901-2). High-resolution records of organic geochemical properties and planktic foraminiferal assemblages are used to decipher precipitation and vegetation changes as well as hydrological conditions with respect to sea surface temperature (SST) and marine primary productivity (MPP). As a proxy for precipitation change, records of plant-derived n-alkane composition suggest a series of five distinct dry episodes in southern Iberia at 5.4 +/- 0.3 ka cal BP, from 5.1 to 4.9 +/- 0.1 ka cal BP, from 4.8 to 4.7 +/- 0.1 ka cal BP, from 4.4 to 4.3 +/- 0.1 ka cal BP, and at 3.7 +/- 0.1 ka cal BP. During each dry episode the vegetation suffered from reduced water availability. Interestingly, the dry phase from 4.4 to 4.3 +/- 0.1 ka cal BP is followed by a rapid shift towards wetter conditions revealing a more complex pattern in terms of its timing and duration than was described for the 4.2 ka event in other regions. The series of dry episodes as well as closely connected hydrological variability in the Alboran Sea were probably driven by NAO-like (North Atlantic Oscillation) variability. In contrast, surface waters in the Gulf of Cadiz appear to have responded more directly to North Atlantic cooling associated with Bond events. In particular, during Bond events 3 and 4, a pronounced increase in seasonality with summer warming and winter cooling is found.DFG (German Research Foundation)
CRC 1266
2901391021
Fundacao para a Ciencia e Tecnologia
SFRH/BPD/111433/2015info:eu-repo/semantics/publishedVersio
Minimal deformations of the commutative algebra and the linear group GL(n)
We consider the relations of generalized commutativity in the algebra of
formal series , which conserve a tensor -grading and
depend on parameters . We choose the -preserving version of
differential calculus on . A new construction of the symmetrized tensor
product for -type algebras and the corresponding definition of minimally
deformed linear group and Lie algebra are proposed. We
study the connection of and with the special matrix
algebra \mbox{Mat} (n,Q) containing matrices with noncommutative elements.
A definition of the deformed determinant in the algebra \mbox{Mat} (n,Q) is
given. The exponential parametrization in the algebra \mbox{Mat} (n,Q) is
considered on the basis of Campbell-Hausdorf formula.Comment: 14 page
Representations of the quantum matrix algebra
It is shown that the finite dimensional irreducible representaions of the
quantum matrix algebra ( the coordinate ring of ) exist only when both q and p are roots of unity. In this case th e space of
states has either the topology of a torus or a cylinder which may be thought of
as generalizations of cyclic representations.Comment: 20 page
Lagrangian and Hamiltonian Formalism on a Quantum Plane
We examine the problem of defining Lagrangian and Hamiltonian mechanics for a
particle moving on a quantum plane . For Lagrangian mechanics, we
first define a tangent quantum plane spanned by noncommuting
particle coordinates and velocities. Using techniques similar to those of Wess
and Zumino, we construct two different differential calculi on .
These two differential calculi can in principle give rise to two different
particle dynamics, starting from a single Lagrangian. For Hamiltonian
mechanics, we define a phase space spanned by noncommuting
particle coordinates and momenta. The commutation relations for the momenta can
be determined only after knowing their functional dependence on coordinates and
velocities.
Thus these commutation relations, as well as the differential calculus on
, depend on the initial choice of Lagrangian. We obtain the
deformed Hamilton's equations of motion and the deformed Poisson brackets, and
their definitions also depend on our initial choice of Lagrangian. We
illustrate these ideas for two sample Lagrangians. The first system we examine
corresponds to that of a nonrelativistic particle in a scalar potential. The
other Lagrangian we consider is first order in time derivative
The exponential map for representations of
For the quantum group and the corresponding quantum algebra
Fronsdal and Galindo explicitly constructed the so-called
universal -matrix. In a previous paper we showed how this universal
-matrix can be used to exponentiate representations from the quantum algebra
to get representations (left comodules) for the quantum group. Here, further
properties of the universal -matrix are illustrated. In particular, it is
shown how to obtain comodules of the quantum algebra by exponentiating modules
of the quantum group. Also the relation with the universal -matrix is
discussed.Comment: LaTeX-file, 7 pages. Submitted for the Proceedings of the 4th
International Colloquium ``Quantum Groups and Integrable Systems,'' Prague,
22-24 June 199
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