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 $(u, Du)$, where $u$ is the solution of the PDE with space gradient $Du$. 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$_2$ molecules in deeply bound levels ($v=1-9$) of their electronic ground state X$^1 \Sigma_g^+$. 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 $10^5-10^6$ 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