1,699 research outputs found
Quantum Lie algebras associated to and
Quantum Lie algebras \qlie{g} are non-associative algebras which are
embedded into the quantized enveloping algebras of Drinfeld and Jimbo
in the same way as ordinary Lie algebras are embedded into their enveloping
algebras. The quantum Lie product on \qlie{g} is induced by the quantum
adjoint action of . We construct the quantum Lie algebras associated to
and . We determine the structure constants and the
quantum root systems, which are now functions of the quantum parameter .
They exhibit an interesting duality symmetry under .Comment: Latex 9 page
On Quantum Lie Algebras and Quantum Root Systems
As a natural generalization of ordinary Lie algebras we introduce the concept
of quantum Lie algebras . We define these in terms of certain
adjoint submodules of quantized enveloping algebras endowed with a
quantum Lie bracket given by the quantum adjoint action. The structure
constants of these algebras depend on the quantum deformation parameter and
they go over into the usual Lie algebras when .
The notions of q-conjugation and q-linearity are introduced. q-linear
analogues of the classical antipode and Cartan involution are defined and a
generalised Killing form, q-linear in the first entry and linear in the second,
is obtained. These structures allow the derivation of symmetries between the
structure constants of quantum Lie algebras.
The explicitly worked out examples of and illustrate the
results.Comment: 22 pages, latex, version to appear in J. Phys. A. see
http://www.mth.kcl.ac.uk/~delius/q-lie.html for calculations and further
informatio
Pre-freezing of multifractal exponents in Random Energy Models with logarithmically correlated potential
Boltzmann-Gibbs measures generated by logarithmically correlated random
potentials are multifractal. We investigate the abrupt change ("pre-freezing")
of multifractality exponents extracted from the averaged moments of the measure
- the so-called inverse participation ratios. The pre-freezing can be
identified with termination of the disorder-averaged multifractality spectrum.
Naive replica limit employed to study a one-dimensional variant of the model is
shown to break down at the pre-freezing point. Further insights are possible
when employing zero-dimensional and infinite-dimensional versions of the
problem. In particular, the latter version allows one to identify the pattern
of the replica symmetry breaking responsible for the pre-freezing phenomenon.Comment: This is published version, 11 pages, 1 figur
The structure of quantum Lie algebras for the classical series B_l, C_l and D_l
The structure constants of quantum Lie algebras depend on a quantum
deformation parameter q and they reduce to the classical structure constants of
a Lie algebra at . We explain the relationship between the structure
constants of quantum Lie algebras and quantum Clebsch-Gordan coefficients for
adjoint x adjoint ---> adjoint. We present a practical method for the
determination of these quantum Clebsch-Gordan coefficients and are thus able to
give explicit expressions for the structure constants of the quantum Lie
algebras associated to the classical Lie algebras B_l, C_l and D_l.
In the quantum case also the structure constants of the Cartan subalgebra are
non-zero and we observe that they are determined in terms of the simple quantum
roots. We introduce an invariant Killing form on the quantum Lie algebras and
find that it takes values which are simple q-deformations of the classical
ones.Comment: 25 pages, amslatex, eepic. Final version for publication in J. Phys.
A. Minor misprints in eqs. 5.11 and 5.12 correcte
Fractional Laplacian in Bounded Domains
The fractional Laplacian operator, ,
appears in a wide class of physical systems, including L\'evy flights and
stochastic interfaces. In this paper, we provide a discretized version of this
operator which is well suited to deal with boundary conditions on a finite
interval. The implementation of boundary conditions is justified by appealing
to two physical models, namely hopping particles and elastic springs. The
eigenvalues and eigenfunctions in a bounded domain are then obtained
numerically for different boundary conditions. Some analytical results
concerning the structure of the eigenvalues spectrum are also obtained.Comment: 11 pages, 11 figure
Mitochondrial targeting adaptation of the hominoid-specific glutamate dehydrogenase driven by positive Darwinian selection
Many new gene copies emerged by gene duplication in hominoids, but little is known with respect to their functional evolution. Glutamate dehydrogenase (GLUD) is an enzyme central to the glutamate and energy metabolism of the cell. In addition to the single, GLUD-encoding gene present in all mammals (GLUD1), humans and apes acquired a second GLUD gene (GLUD2) through retroduplication of GLUD1, which codes for an enzyme with unique, potentially brain-adapted properties. Here we show that whereas the GLUD1 parental protein localizes to mitochondria and the cytoplasm, GLUD2 is specifically targeted to mitochondria. Using evolutionary analysis and resurrected ancestral protein variants, we demonstrate that the enhanced mitochondrial targeting specificity of GLUD2 is due to a single positively selected glutamic acid-to-lysine substitution, which was fixed in the N-terminal mitochondrial targeting sequence (MTS) of GLUD2 soon after the duplication event in the hominoid ancestor ~18â25 million years ago. This MTS substitution arose in parallel with two crucial adaptive amino acid changes in the enzyme and likely contributed to the functional adaptation of GLUD2 to the glutamate metabolism of the hominoid brain and other tissues. We suggest that rapid, selectively driven subcellular adaptation, as exemplified by GLUD2, represents a common route underlying the emergence of new gene functions
A (p,q) Deformation of the Universal Enveloping Superalgebra U(osp(2/2))
We investigate a two parameter quantum deformation of the universal
enveloping orthosymplectic superalgebra U(osp(2/2)) by extending the
Faddeev-Reshetikhin-Takhtajan formalism to the supersymetric case. It is shown
that possesses a non-commutative, non-cocommutative Hopf
algebra structure. All the results are expressed in the standard form using
quantum Chevalley basis.Comment: 8 pages; IC/93/41
Shock statistics in higher-dimensional Burgers turbulence
We conjecture the exact shock statistics in the inviscid decaying Burgers
equation in D>1 dimensions, with a special class of correlated initial
velocities, which reduce to Brownian for D=1. The prediction is based on a
field-theory argument, and receives support from our numerical calculations. We
find that, along any given direction, shocks sizes and locations are
uncorrelated.Comment: 4 pages, 8 figure
A mean-field kinetic lattice gas model of electrochemical cells
We develop Electrochemical Mean-Field Kinetic Equations (EMFKE) to simulate
electrochemical cells. We start from a microscopic lattice-gas model with
charged particles, and build mean-field kinetic equations following the lines
of earlier work for neutral particles. We include the Poisson equation to
account for the influence of the electric field on ion migration, and
oxido-reduction processes on the electrode surfaces to allow for growth and
dissolution. We confirm the viability of our approach by simulating (i) the
electrochemical equilibrium at flat electrodes, which displays the correct
charged double-layer, (ii) the growth kinetics of one-dimensional
electrochemical cells during growth and dissolution, and (iii) electrochemical
dendrites in two dimensions.Comment: 14 pages twocolumn, 17 figure
- âŠ