On the total curvatures of a tame function

Given a definable function f, enough differentiable, we study the continuity of the total curvature function t --> K(t), total curvature of the level {f=t}, and the total absolute curvature function t-->|K| (t), total absolute curvature of the level {f=t}. We show they admits at most finitely many discontinuities

Adaptive density estimation for stationary processes

We propose an algorithm to estimate the common density $s$ of a stationary process $X_1,...,X_n$. We suppose that the process is either $\beta$ or $\tau$-mixing. We provide a model selection procedure based on a generalization of Mallows' $C_p$ and we prove oracle inequalities for the selected estimator under a few prior assumptions on the collection of models and on the mixing coefficients. We prove that our estimator is adaptive over a class of Besov spaces, namely, we prove that it achieves the same rates of convergence as in the i.i.d framework

Spin degree of freedom in two dimensional exciton condensates

We present a theoretical analysis of a spin-dependent multicomponent condensate in two dimensions. The case of a condensate of resonantly photoexcited excitons having two different spin orientations is studied in detail. The energy and the chemical potentials of this system depend strongly on the spin polarization . When electrons and holes are located in two different planes, the condensate can be either totally spin polarized or spin unpolarized, a property that is measurable. The phase diagram in terms of the total density and electron-hole separation is discussed.Comment: 4 pages, 3 figures, Accepted for publication in Physical Review Letter

On small time asymptotics for rough differential equations driven by fractional Brownian motions

We survey existing results concerning the study in small times of the density of the solution of a rough differential equation driven by fractional Brownian motions. We also slightly improve existing results and discuss some possible applications to mathematical finance.Comment: This is a survey paper, submitted to proceedings in the memory of Peter Laurenc

Spin noise spectroscopy to probe quantum states of ultracold fermionic atomic gases

Ultracold alkali atoms provide experimentally accessible model systems for probing quantum states that manifest themselves at the macroscopic scale. Recent experimental realizations of superfluidity in dilute gases of ultracold fermionic (half-integer spin) atoms offer exciting opportunities to directly test theoretical models of related many-body fermion systems that are inaccessible to experimental manipulation, such as neutron stars and quark-gluon plasmas. However, the microscopic interactions between fermions are potentially quite complex, and experiments in ultracold gases to date cannot clearly distinguish between the qualitatively different microscopic models that have been proposed. Here, we theoretically demonstrate that optical measurements of electron spin noise -- the intrinsic, random fluctuations of spin -- can probe the entangled quantum states of ultracold fermionic atomic gases and unambiguously reveal the detailed nature of the interatomic interactions. We show that different models predict different sets of resonances in the noise spectrum, and once the correct effective interatomic interaction model is identified, the line-shapes of the spin noise can be used to constrain this model. Further, experimental measurements of spin noise in classical (Boltzmann) alkali vapors are used to estimate the expected signal magnitudes for spin noise measurements in ultracold atom systems and to show that these measurements are feasible

Study of ortho-to-paraexciton conversion in Cu2_2O by excitonic Lyman spectroscopy

Using time-resolved $1s$-$2p$ excitonic Lyman spectroscopy, we study the orthoexciton-to-paraexcitons transfer, following the creation of a high density population of ultracold $1s$ orthoexcitons by resonant two-photon excitation with femtosecond pulses. An observed fast exciton-density dependent conversion rate is attributed to spin exchange between pairs of orthoexcitons. Implication of these results on the feasibility of BEC of paraexcitons in Cu$_2$O is discussed

Fluctuations in the Irreversible Decay of Turbulent Energy

A fluctuation law of the energy in freely-decaying, homogeneous and isotropic turbulence is derived within standard closure hypotheses for 3D incompressible flow. In particular, a fluctuation-dissipation relation is derived which relates the strength of a stochastic backscatter term in the energy decay equation to the mean of the energy dissipation rate. The theory is based on the so-called ``effective action'' of the energy history and illustrates a Rayleigh-Ritz method recently developed to evaluate the effective action approximately within probability density-function (PDF) closures. These effective actions generalize the Onsager-Machlup action of nonequilibrium statistical mechanics to turbulent flow. They yield detailed, concrete predictions for fluctuations, such as multi-time correlation functions of arbitrary order, which cannot be obtained by direct PDF methods. They also characterize the mean histories by a variational principle.Comment: 26 pages, Latex Version 2.09, plus seceq.sty, a stylefile for sequential numbering of equations by section. This version includes new discussion of the physical interpretation of the formal Rayleigh-Ritz approximation. The title is also change

The VIPERS Multi-Lambda Survey. II. Diving with massive galaxies in 22 square degrees since z = 1.5

We investigate the evolution of the galaxy stellar mass function (SMF) and stellar mass density from redshift z=0.2 to z=1.5 of a $K_{AB}$<22-selected sample with highly reliable photometric redshifts and over an unprecedentedly large area. Our study is based on NIR observations carried out with WIRCam at CFHT over the footprint of the VIPERS spectroscopic survey and benefits from the high quality optical photometry from the CFHTLS and UV observations with the GALEX satellite. The accuracy of our photometric redshifts is $\sigma_z$ < 0.03 and 0.05 for the bright ($i_{AB}$22.5) samples, respectively. The SMF is measured with ~760,000 galaxies down to $K_s$=22 and over an effective area of ~22.4 deg$^2$, the latter of which drastically reduces the statistical uncertainties (i.e. Poissonian error & cosmic variance). We point out the importance of a careful control of the photometric calibration, whose impact becomes quickly dominant when statistical uncertainties are reduced, which will be a major issue for future generation of cosmological surveys with, e.g. EUCLID or LSST. By exploring the rest-frame (NUV-r) vs (r-$K_s$) color-color diagram separating star-forming and quiescent galaxies, (1) we find that the density of very massive log($M_*/ M_{\odot}$) > 11.5 galaxies is largely dominated by quiescent galaxies and increases by a factor 2 from z~1 to z~0.2, which allows for additional mass assembly via dry mergers, (2) we confirm a scenario where star formation activity is impeded above a stellar mass log($M^*_{SF} / M_{\odot}$) = 10.64$\pm$0.01, a value that is found to be very stable at 0.2 < z < 1.5, (3) we discuss the existence of a main quenching channel that is followed by massive star-forming galaxies, and finally (4) we characterise another quenching mechanism required to explain the clear excess of low-mass quiescent galaxies observed at low redshift.Comment: 22 pages, 20 figures. Accepted for publication in A&A. Version to be publishe

Effects of density imbalance on the BCS-BEC crossover in semiconductor electron-hole bilayers

We study the occurrence of excitonic superfluidity in electron-hole bilayers at zero temperature. We not only identify the crossover in the phase diagram from the BCS limit of overlapping pairs to the BEC limit of non-overlapping tightly-bound pairs but also, by varying the electron and hole densities independently, we can analyze a number of phases that occur mainly in the crossover region. With different electron and hole effective masses, the phase diagram is asymmetric with respect to excess electron or hole densities. We propose as the criterion for the onset of superfluidity, the jump of the electron and hole chemical potentials when their densities cross.Comment: 4 pages, 3 figure