Variational approach to the excitonic phase transition in graphene

We analyze the Coulomb interacting problem in undoped graphene layers by using an excitonic variational ansatz. By minimizing the energy, we derive a gap equation which reproduces and extends known results. We show that a full treatment of the exchange term, which includes the renormalization of the Fermi velocity, tends to suppress the phase transition by increasing the critical coupling at which the excitonic instability takes place.Comment: 4 page

Integration of Oscillatory and Subanalytic Functions

We prove the stability under integration and under Fourier transform of a concrete class of functions containing all globally subanalytic functions and their complex exponentials. This paper extends the investigation started in [J.-M. Lion, J.-P. Rolin: "Volumes, feuilles de Rolle de feuilletages analytiques et th\'eor\`eme de Wilkie" Ann. Fac. Sci. Toulouse Math. (6) 7 (1998), no. 1, 93-112] and [R. Cluckers, D. J. Miller: "Stability under integration of sums of products of real globally subanalytic functions and their logarithms" Duke Math. J. 156 (2011), no. 2, 311-348] to an enriched framework including oscillatory functions. It provides a new example of fruitful interaction between analysis and singularity theory.Comment: Final version. Accepted for publication in Duke Math. Journal. Changes in proofs: from Section 6 to the end, we now use the theory of continuously uniformly distributed modulo 1 functions that provides a uniform technical point of view in the proofs of limit statement

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

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

La producción de cal en los hornos verticales modernos

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The Physical Conditions and Dynamics of the Interstellar Medium in the Nucleus of M83: Observations of CO and CI

This paper presents CI, CO J=4-3, and CO J=3-2 maps of the barred spiral galaxy M83 taken at the James Clerk Maxwell Telescope. Observations indicate a double peaked structure which is consistent with gas inflow along the bar collecting at the inner Lindblad resonance. This structure suggests that nuclear starbursts can occur even in galaxies where this inflow/collection occurs, in contrast to previous studies of barred spiral galaxies. However, the observations also suggest that the double peaked emission may be the result of a rotating molecular ring oriented nearly perpendicular to the main disk of the galaxy. The CO J=4-3 data indicate the presence of warm gas in the nucleus that is not apparent in the lower-J CO observations, which suggests that CO J=1-0 emission may not be a reliable tracer of molecular gas in starburst galaxies. The twelve CI/CO J=4-3 line ratios in the inner 24'' x 24'' are uniform at the 2 sigma level, which indicates that the CO J=4-3 emission is originating in the same hot photon-dominated regions as the CI emission. The CO J=4-3/J=3-2 line ratios vary significantly within the nucleus with the higher line ratios occurring away from peaks of emission along an arc of active star forming regions. These high line ratios (>1) likely indicate optically thin gas created by the high temperatures caused by star forming regions in the nucleus of this starburst galaxy.Comment: 15 pages with 10 figures. To appear in the August 10 1998 issue of The Astrophysical Journa

Estimation of the Jump Size Density in a Mixed Compound Poisson Process

International audienceIn this paper, we consider a mixed compound Poisson process, i.e. a random sum of i.i.d. random variables where the number of terms is a Poisson process with random intensity. We study nonparametric estimators of the jump density by specific deconvolution methods. First, assuming that the random intensity has exponential distribution with unknown expectation , we propose two types of estimators based on the observation of an i.i.d. sample. Risks bounds and adaptive procedures are provided. Then, with no assumption on the distribution of the random intensity, we propose two nonparametric estimators of the jump density based on the joint observation of the number of jumps and the random sum of jumps. Risks bounds are provided, leading to unusual rates for one of the two estimators. The methods are implemented and compared via simulations. February 25, 201

Adaptive estimation in circular functional linear models

We consider the problem of estimating the slope parameter in circular functional linear regression, where scalar responses Y1,...,Yn are modeled in dependence of 1-periodic, second order stationary random functions X1,...,Xn. We consider an orthogonal series estimator of the slope function, by replacing the first m theoretical coefficients of its development in the trigonometric basis by adequate estimators. Wepropose a model selection procedure for m in a set of admissible values, by defining a contrast function minimized by our estimator and a theoretical penalty function; this first step assumes the degree of ill posedness to be known. Then we generalize the procedure to a random set of admissible m's and a random penalty function. The resulting estimator is completely data driven and reaches automatically what is known to be the optimal minimax rate of convergence, in term of a general weighted L2-risk. This means that we provide adaptive estimators of both the slope function and its derivatives

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