4,798 research outputs found
Polynomial Relations in the Centre of U_q(sl(N))
When the parameter of deformation q is a m-th root of unity, the centre of
U_q(sl(N))$ contains, besides the usual q-deformed Casimirs, a set of new
generators, which are basically the m-th powers of all the Cartan generators of
U_q(sl(N)). All these central elements are however not independent. In this
letter, generalising the well-known case of U_q(sl(2)), we explicitly write
polynomial relations satisfied by the generators of the centre. Application to
the parametrization of irreducible representations and to fusion rules are
sketched.Comment: 8 pages, minor TeXnical revision to allow automatic TeXin
Deformed one-loop amplitudes in N = 4 super-Yang-Mills theory
We investigate Yangian-invariant deformations of one-loop amplitudes in N = 4
super-Yang-Mills theory employing an algebraic representation of amplitudes. In
this language, we reproduce the deformed massless box integral describing the
deformed four-point one-loop amplitude and compare different realizations of
said amplitude.Comment: 19 page
A dictionary between R-operators, on-shell graphs and Yangian algebras
We translate between different formulations of Yangian invariants relevant
for the computation of tree-level scattering amplitudes in N=4
super-Yang--Mills theory. While the R-operator formulation allows to relate
scattering amplitudes to structures well known from integrability, it can
equally well be connected to the permutations encoded by on-shell graphs.Comment: 44 pages; replaced with published versio
Eigenstate versus Zeeman-based approaches to the solid-effect
The solid effect is one of the simplest and most effective mechanisms for
Dynamic Nuclear Polarization. It involves the exchange of polarization between
one electron and one nuclear spin coupled via the hyperfine interaction. Even
for such a small spin system, the theoretical understanding is complicated by
the contact with the lattice and the microwave irradiation. Both being weak,
they can be treated within perturbation theory. In this work, we analyze the
two most popular perturbation schemes: the Zeeman and the eigenstate-based
approaches which differ in the way the hyperfine interaction is treated. For
both schemes, we derive from first principles an effective Liouville equation
which describes the density matrix of the spin system; we then study
numerically the behavior of the nuclear polarization for several values of the
hyperfine coupling. In general, we obtain that the Zeeman-based approach
underestimates the value of the nuclear polarization. By performing a
projection onto the diagonal part of the spin-system density matrix, we are
able to understand the origin of the discrepancy, which is due to the presence
of parasite leakage transitions appearing whenever the Zeeman basis is
employed.Comment: 9 pages, 4 figures, 7 pages of supplementary materia
Darcy law for yield stress fluid
Predicting the flow of non-Newtonian fluids in porous structure is still a
challenging issue due to the interplay betwen the microscopic disorder and the
non-linear rheology. In this letter, we study the case of an yield stress fluid
in a two-dimensional structure. Thanks to a performant optimization algorithm,
we show that the system undergoes a continuous phase transition in the behavior
of the flow controlled by the applied pressure drop. In analogy with the
studies of the plastic depinning of vortex lattices in high-
superconductors we characterize the nonlinearity of the flow curve and relate
it to the change in the geometry of the open channels. In particular, close to
the transition, an universal scale free distribution of the channel length is
observed and explained theoretically via a mapping to the KPZ equation.Comment: 5 pages, 4 figures + 1 Supplementary materia
The critical catastrophe revisited
The neutron population in a prototype model of nuclear reactor can be
described in terms of a collection of particles confined in a box and
undergoing three key random mechanisms: diffusion, reproduction due to
fissions, and death due to absorption events. When the reactor is operated at
the critical point, and fissions are exactly compensated by absorptions, the
whole neutron population might in principle go to extinction because of the
wild fluctuations induced by births and deaths. This phenomenon, which has been
named critical catastrophe, is nonetheless never observed in practice: feedback
mechanisms acting on the total population, such as human intervention, have a
stabilizing effect. In this work, we revisit the critical catastrophe by
investigating the spatial behaviour of the fluctuations in a confined geometry.
When the system is free to evolve, the neutrons may display a wild patchiness
(clustering). On the contrary, imposing a population control on the total
population acts also against the local fluctuations, and may thus inhibit the
spatial clustering. The effectiveness of population control in quenching
spatial fluctuations will be shown to depend on the competition between the
mixing time of the neutrons (i.e., the average time taken for a particle to
explore the finite viable space) and the extinction time.Comment: 16 pages, 6 figure
A multi-level approach to flood frequency regionalisation
A multi-level approach to flood frequency regionalisation is given. Based on observed flood data, it combines physical and statistical criteria to cluster homogeneous groups in a geographical area. Seasonality analysis helps identify catchments with a common flood generation mechanism. Scale invariance of annual maximum flood, as parameterised by basin area, is used to check the regional homogeneity of flood peaks. Homogeneity tests are used to assess the statistical robustness of the regions. The approach is based on the appropriate use of the index flood method (Dalrymple, 1960) in regions with complex climate and topography controls. An application to north-western Italy is presented.</p> <p style='line-height: 20px;'><b>Keywords:</b> homogeneity, multi-level approach, regionalisation, seasonality, scale invariance, similarity, test
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