3,366 research outputs found
Decomposition of symmetric tensor fields in the presence of a flat contact projective structure
Let be an odd-dimensional Euclidean space endowed with a contact 1-form
. We investigate the space of symmetric contravariant tensor fields on
as a module over the Lie algebra of contact vector fields, i.e. over the
Lie subalgebra made up by those vector fields that preserve the contact
structure. If we consider symmetric tensor fields with coefficients in tensor
densities, the vertical cotangent lift of contact form is a contact
invariant operator. We also extend the classical contact Hamiltonian to the
space of symmetric density valued tensor fields. This generalized Hamiltonian
operator on the symbol space is invariant with respect to the action of the
projective contact algebra . The preceding invariant operators lead
to a decomposition of the symbol space (expect for some critical density
weights), which generalizes a splitting proposed by V. Ovsienko
The conservation of Belgian Marine Natura 2000 sites: the first steps into a brave new world?
On sl(2)-equivariant quantizations
By computing certain cohomology of Vect(M) of smooth vector fields we prove
that on 1-dimensional manifolds M there is no quantization map intertwining the
action of non-projective embeddings of the Lie algebra sl(2) into the Lie
algebra Vect(M). Contrariwise, for projective embeddings sl(2)-equivariant
quantization exists.Comment: 09 pages, LaTeX2e, no figures; to appear in Journal of Nonlinear
Mathematical Physic
A numerical approach to large deviations in continuous-time
We present an algorithm to evaluate the large deviation functions associated
to history-dependent observables. Instead of relying on a time discretisation
procedure to approximate the dynamics, we provide a direct continuous-time
algorithm, valuable for systems with multiple time scales, thus extending the
work of Giardin\`a, Kurchan and Peliti (PRL 96, 120603 (2006)).
The procedure is supplemented with a thermodynamic-integration scheme, which
improves its efficiency. We also show how the method can be used to probe large
deviation functions in systems with a dynamical phase transition -- revealed in
our context through the appearance of a non-analyticity in the large deviation
functions.Comment: Submitted to J. Stat. Mec
Natural and projectively equivariant quantizations by means of Cartan Connections
The existence of a natural and projectively equivariant quantization in the
sense of Lecomte [20] was proved recently by M. Bordemann [4], using the
framework of Thomas-Whitehead connections. We give a new proof of existence
using the notion of Cartan projective connections and we obtain an explicit
formula in terms of these connections. Our method yields the existence of a
projectively equivariant quantization if and only if an \sl(m+1,\R)-equivariant
quantization exists in the flat situation in the sense of [18], thus solving
one of the problems left open by M. Bordemann.Comment: 13 page
Optimization of Generalized Multichannel Quantum Defect reference functions for Feshbach resonance characterization
This work stresses the importance of the choice of the set of reference
functions in the Generalized Multichannel Quantum Defect Theory to analyze the
location and the width of Feshbach resonance occurring in collisional
cross-sections. This is illustrated on the photoassociation of cold rubidium
atom pairs, which is also modeled using the Mapped Fourier Grid Hamiltonian
method combined with an optical potential. The specificity of the present
example lies in a high density of quasi-bound states (closed channel)
interacting with a dissociation continuum (open channel). We demonstrate that
the optimization of the reference functions leads to quantum defects with a
weak energy dependence across the relevant energy threshold. The main result of
our paper is that the agreement between the both theoretical approaches is
achieved only if optimized reference functions are used.Comment: submitte to Journal of Physics
First-order dynamical phase transition in models of glasses: an approach based on ensembles of histories
We investigate the dynamics of kinetically constrained models of glass
formers by analysing the statistics of trajectories of the dynamics, or
histories, using large deviation function methods. We show that, in general,
these models exhibit a first-order dynamical transition between active and
inactive dynamical phases. We argue that the dynamical heterogeneities
displayed by these systems are a manifestation of dynamical first-order phase
coexistence. In particular, we calculate dynamical large deviation functions,
both analytically and numerically, for the Fredrickson-Andersen model, the East
model, and constrained lattice gas models. We also show how large deviation
functions can be obtained from a Landau-like theory for dynamical fluctuations.
We discuss possibilities for similar dynamical phase-coexistence behaviour in
other systems with heterogeneous dynamics.Comment: 29 pages, 7 figs, final versio
Projectively equivariant quantizations over the superspace
We investigate the concept of projectively equivariant quantization in the
framework of super projective geometry. When the projective superalgebra
pgl(p+1|q) is simple, our result is similar to the classical one in the purely
even case: we prove the existence and uniqueness of the quantization except in
some critical situations. When the projective superalgebra is not simple (i.e.
in the case of pgl(n|n)\not\cong sl(n|n)), we show the existence of a
one-parameter family of equivariant quantizations. We also provide explicit
formulas in terms of a generalized divergence operator acting on supersymmetric
tensor fields.Comment: 19 page
Resonance trapping and saturation of decay widths
Resonance trapping appears in open many-particle quantum systems at high
level density when the coupling to the continuum of decay channels reaches a
critical strength. Here a reorganization of the system takes place and a
separation of different time scales appears. We investigate it under the
influence of additional weakly coupled channels as well as by taking into
account the real part of the coupling term between system and continuum. We
observe a saturation of the mean width of the trapped states. Also the decay
rates saturate as a function of the coupling strength. The mechanism of the
saturation is studied in detail. In any case, the critical region of
reorganization is enlarged. When the transmission coefficients for the
different channels are different, the width distribution is broadened as
compared to a chi_K^2 distribution where K is the number of channels. Resonance
trapping takes place before the broad state overlaps regions beyond the
extension of the spectrum of the closed system.Comment: 18 pages, 8 figures, accepted by Phys. Rev.
- …