4,118 research outputs found
Artistic Identities and Professional Strategies : Francophone Musicians in France and Britain
Funding This work was supported by Arts and Humanities Research Council [grant number AH/E508628/1] and European Commission [grant number HPSE-CT-2002-00133].Peer reviewedPostprin
Branching diffusion representation of semilinear PDEs and Monte Carlo approximation
We provide a representation result of parabolic semi-linear PD-Es, with
polynomial nonlinearity, by branching diffusion processes. We extend the
classical representation for KPP equations, introduced by Skorokhod (1964),
Watanabe (1965) and McKean (1975), by allowing for polynomial nonlinearity in
the pair , where is the solution of the PDE with space gradient
. Similar to the previous literature, our result requires a non-explosion
condition which restrict to "small maturity" or "small nonlinearity" of the
PDE. Our main ingredient is the automatic differentiation technique as in Henry
Labordere, Tan and Touzi (2015), based on the Malliavin integration by parts,
which allows to account for the nonlinearities in the gradient. As a
consequence, the particles of our branching diffusion are marked by the nature
of the nonlinearity. This new representation has very important numerical
implications as it is suitable for Monte Carlo simulation. Indeed, this
provides the first numerical method for high dimensional nonlinear PDEs with
error estimate induced by the dimension-free Central limit theorem. The
complexity is also easily seen to be of the order of the squared dimension. The
final section of this paper illustrates the efficiency of the algorithm by some
high dimensional numerical experiments
Triplet-singlet conversion by broadband optical pumping
We demonstrate the conversion of cold Cs_{2} molecules initially distributed
over several vibrational levels of the lowest triplet state a^{3}\Sigma_{u}^{+}
into the singlet ground state X^{1}\Sigma_{g}^{+}. This conversion is realized
by a broadband laser exciting the molecules to a well-chosen state from which
they may decay to the singlet state throug\textcolor{black}{h two sequential
single-photon emission steps: Th}e first photon populates levels with mixed
triplet-singlet character, making possible a second spontaneous emission down
to several vibrational levels of the X^{1}\Sigma_{g}^{+} states. By adding an
optical scheme for vibrational cooling, a substantial fraction of molecules are
transferred to the ground vibrational level of the singlet state. The
efficiency of the conversion process, with and without vibrational cooling, is
discussed at the end of the article. The presented conversion is general in
scope and could be extended to other molecules.Comment: 5 pages, 4 figure
Efficient formation of deeply bound ultracold molecules probed by broadband detection
Using a non-selective broadband detection scheme we discovered an efficient
mechanism of formation of ultracold Cs molecules in deeply bound levels
() of their electronic ground state X. They are formed by
a one-photon photoassociation of ultracold cesium atoms in a manifold of
excited electronic states, followed by a two-step spontaneous emission cascade.
We were able to form about molecules per second in these low
vibrational levels of the ground state. This detection scheme could be
generalized to other molecular species for the systematic investigation of cold
molecule formation mechanisms.Comment: 4 page
- …