Weak KAM for commuting Hamiltonians

For two commuting Tonelli Hamiltonians, we recover the commutation of the Lax-Oleinik semi-groups, a result of Barles and Tourin ([BT01]), using a direct geometrical method (Stoke's theorem). We also obtain a "generalization" of a theorem of Maderna ([Mad02]). More precisely, we prove that if the phase space is the cotangent of a compact manifold then the weak KAM solutions (or viscosity solutions of the critical stationary Hamilton-Jacobi equation) for G and for H are the same. As a corrolary we obtain the equality of the Aubry sets, of the Peierls barrier and of flat parts of Mather's $\alpha$ functions. This is also related to works of Sorrentino ([Sor09]) and Bernard ([Ber07b]).Comment: 23 pages, accepted for publication in NonLinearity (january 29th 2010). Minor corrections, fifth part added on Mather's $\alpha$ function (or effective Hamiltonian

Duality relations in the auxiliary field method

The eigenenergies $\epsilon^{(N)}(m;\{n_i,l_i\})$ of a system of $N$ identical particles with a mass $m$ are functions of the various radial quantum numbers $n_i$ and orbital quantum numbers $l_i$. Approximations $E^{(N)}(m;Q)$ of these eigenenergies, depending on a principal quantum number $Q(\{n_i,l_i\})$, can be obtained in the framework of the auxiliary field method. We demonstrate the existence of numerous exact duality relations linking quantities $E^{(N)}(m;Q)$ and $E^{(p)}(m';Q')$ for various forms of the potentials (independent of $m$ and $N$) and for both nonrelativistic and semirelativistic kinematics. As the approximations computed with the auxiliary field method can be very close to the exact results, we show with several examples that these duality relations still hold, with sometimes a good accuracy, for the exact eigenenergies $\epsilon^{(N)}(m;\{n_i,l_i\})$

On the number of Mather measures of Lagrangian systems

In 1996, Ricardo Ricardo Ma\~n\'e discovered that Mather measures are in fact the minimizers of a "universal" infinite dimensional linear programming problem. This fundamental result has many applications, one of the most important is to the estimates of the generic number of Mather measures. Ma\~n\'e obtained the first estimation of that sort by using finite dimensional approximations. Recently, we were able with Gonzalo Contreras to use this method of finite dimensional approximation in order to solve a conjecture of John Mather concerning the generic number of Mather measures for families of Lagrangian systems. In the present paper we obtain finer results in that direction by applying directly some classical tools of convex analysis to the infinite dimensional problem. We use a notion of countably rectifiable sets of finite codimension in Banach (and Frechet) spaces which may deserve independent interest

Finite-size analysis of the Fermi liquid properties of the homogeneous electron gas

We analyze the extrapolation to the thermodynamic limit of Fermi liquid properties of the homogeneous electron gas in two and three dimensions. Using field theory, we explicitly calculate finite-size effects of the total energy, the renormalization factor, and the effective mass at the Fermi surface within the random phase approximation (RPA) and discuss the validity for general metallic systems.Comment: 6 page

Heavy-Light Semileptonic Decays in Staggered Chiral Perturbation Theory

We calculate the form factors for the semileptonic decays of heavy-light pseudoscalar mesons in partially quenched staggered chiral perturbation theory (\schpt), working to leading order in $1/m_Q$, where $m_Q$ is the heavy quark mass. We take the light meson in the final state to be a pseudoscalar corresponding to the exact chiral symmetry of staggered quarks. The treatment assumes the validity of the standard prescription for representing the staggered ``fourth root trick'' within \schpt by insertions of factors of 1/4 for each sea quark loop. Our calculation is based on an existing partially quenched continuum chiral perturbation theory calculation with degenerate sea quarks by Becirevic, Prelovsek and Zupan, which we generalize to the staggered (and non-degenerate) case. As a by-product, we obtain the continuum partially quenched results with non-degenerate sea quarks. We analyze the effects of non-leading chiral terms, and find a relation among the coefficients governing the analytic valence mass dependence at this order. Our results are useful in analyzing lattice computations of form factors $B\to\pi$ and $D\to K$ when the light quarks are simulated with the staggered action.Comment: 53 pages, 8 figures, v2: Minor correction to the section on finite volume effects, and typos fixed. Version to be published in Phys. Rev.

A high-speed optical star network using TDMA and all-optical demultiplexing techniques

The authors demonstrate the use of time-division multiplexing (TDM) to realize a high capacity optical star network. The fundamental element of the demonstration network is a 10 ps, wavelength tunable, low jitter, pulse source. Electrical data is encoded onto three optical pulse trains, and the resultant low duty cycle optical data channels are multiplexed together using 25 ps fiber delay lines. This gives an overall network capacity of 40 Gb/s. A nonlinear optical loop mirror (NOLM) is used to carry out the demultiplexing at the station receiver. The channel to be switched out can be selected by adjusting the phase of the electrical signal used to generate the control pulses for the NOLM. By using external injection into a gain-switched distributed feedback (DFB) laser we are able to obtain very low jitter control pulses of 4-ps duration (RMS jitter <1 ps) after compression of the highly chirped gain switched pulses in a normal dispersive fiber. This enables us to achieve excellent eye openings for the three demultiplexed channels. The difficulty in obtaining complete switching of the signal pulses is presented. This is shown to be due to the deformation of the control pulse in the NOLM (caused by the soliton effect compression). The use of optical time-division multiplexing (OTDM) with all-optical switching devices is shown to be an excellent method to allow us to exploit as efficiently as possible the available fiber bandwidth, and to achieve very high bit-rate optical networks

Optimizing ISOCAM data processing using spatial redundancy

We present new data processing techniques that allow to correct the main instrumental effects that degrade the images obtained by ISOCAM, the camera on board the Infrared Space Observatory (ISO). Our techniques take advantage of the fact that a position on the sky has been observed by several pixels at different times. We use this information (1) to correct the long term variation of the detector response, (2) to correct memory effects after glitches and point sources, and (3) to refine the deglitching process. Our new method allows the detection of faint extended emission with contrast smaller than 1% of the zodiacal background. The data reduction corrects instrumental effects to the point where the noise in the final map is dominated by the readout and the photon noises. All raster ISOCAM observations can benefit from the data processing described here. These techniques could also be applied to other raster type observations (e.g. ISOPHOT or IRAC on SIRTF).Comment: 13 pages, 10 figures, to be published in Astronomy and Astrophysics Supplement Serie

Lattice results for the decay constant of heavy-light vector mesons

We compute the leptonic decay constants of heavy-light vector mesons in the quenched approximation. The reliability of lattice computations for heavy quarks is checked by comparing the ratio of vector to pseudoscalar decay constant with the prediction of Heavy Quark Effective Theory in the limit of infinitely heavy quark mass. Good agreement is found. We then calculate the decay constant ratio for B mesons: $f_{B^*}/f_B= 1.01(0.01)(^{+0.04}_{-0.01})$. We also quote quenched $f_{B^*}=177(6)(17)$ MeV.Comment: 11 pages, 3 postscript figs., revtex; two references adde