Generalized adiabatic invariance

In this paper we find the quantities that are adiabatic invariants of any desired order for a general slowly time-dependent Hamiltonian. In a preceding paper, we chose a quantity that was initially an adiabatic invariant to first order, and sought the conditions to be imposed upon the Hamiltonian so that the quantum mechanical adiabatic theorem would be valid to mth order. [We found that this occurs when the first (m - 1) time derivatives of the Hamiltonian at the initial and final time instants are equal to zero.] Here we look for a quantity that is an adiabatic invariant to mth order for any Hamiltonian that changes slowly in time, and that does not fulfill any special condition (its first time derivatives are not zero initially and finally).

Entropy change and magnetocaloric effect in Gd5(SixGe1-x)4

Isothermal magnetization curves up to 23 T have been measured in Gd5Si1.8Ge2.2. We show that the values of the entropy change at the first-order magnetostructural transition, obtained from the Clausius-Clapeyron equation and the Maxwell relation, are coincident, provided the Maxwell relation is evaluated only within the transition region and the maximum applied field is high enough to complete the transition. These values are also in agreement with the entropy change obtained from differential scanning calorimetry. We also show that a simple phenomenological model based on the temperature and field dependence of the magnetization accounts for these results.

Magnetic field induced entropy change and magnetoelasticity in Ni-Mn-Ga alloys

The magnetocaloric effect that originates from the martensitic transition in the ferromagnetic Ni-Mn-Gashape-memory alloy is studied. We show that this effect is controlled by the magnetostructural coupling at boththe martensitic variant and magnetic domain length scales. A large entropy change induced by moderatemagnetic fields is obtained for alloys in which the magnetic moment of the two structural phases is not verydifferent. We also show that this entropy change is not associated with the entropy difference between themartensitic and the parent phase arising from the change in the crystallographic structure which has beenfound to be independent of the magnetic field within this range of fields.

Quantum critical effects in mean-field glassy systems

We consider the effects of quantum fluctuations in mean-field quantum spin-glass models with pairwise interactions. We examine the nature of the quantum glass transition at zero temperature in a transverse field. In models (such as the random orthogonal model) where the classical phase transition is discontinuous an analysis using the static approximation reveals that the transition becomes continuous at zero temperature.

A Geometric Characterization of Interpolation in $\hat{\E}^\prime(\R)$

We give a geometric description of the interpolating varieties for the algebra of Fourier transforms of distributions (or Beurling ultradistributions) with compact support on the real line.

Option valuation as an expectation in the complex domain: The Black-Scholes case

It is very well known that the first succesful valuation of a stock option was done by solving a deterministic partial differential equation (PDE) of the parabolic type with some complementary conditions specific for the option. In this approach, the randomness in the option value process is eliminated through a no-arbitrage argument. An alternative approach is to construct a replicating portfolio for the option. From this viewpoint the payoff function for the option is a random process which, under a new probabilistic measure, turns out to be of a special type, a martingale. Accordingly, the value of the replicating portfolio (equivalently, of the option) is calculated as an expectation, with respect to this new measure, of the discounted value of the payoff function. Since the expectation is, by definition, an integral, its calculation can be made simpler by resorting to powerful methods already available in the theory of analytic functions. In this paper we use precisely two of those techniques to find the well-known value of a European call

Alexandre Sauvaige. L'Etiquette du temps.

Manuscrit orné de dessins à la plume et aux armes de François de Rochechouart, gouverneur du Gênes sous Louis XII. Anciennes collections Mc Carthy, Georges Hilbert, Robert Hoe et comte Paul Durrieu.

Estimating biophysical variable dependences with kernels

This paper introduces a nonlinear measure of dependence between random variables in the context of remote sensing data analysis. The Hilbert-Schmidt Independence Criterion (HSIC) is a kernel method for evaluating statistical dependence. HSIC is based on computing the Hilbert-Schmidt norm of the cross-covariance operator of mapped samples in the corresponding Hilbert spaces. The HSIC empirical estimator is very easy to compute and has good theoretical and practical properties. We exploit the capabilities of HSIC to explain nonlinear dependences in two remote sensing problems: temperature estimation and chlorophyll concentration prediction from spectra. Results show that, when the relationship between random variables is nonlinear or when few data are available, the HSIC criterion outperforms other standard methods, such as the linear correlation or mutual information.

Colloidal assembly on magnetically vibrated stripes

We investigate the collective organization of paramagnetic colloidal particles externally driven above the periodic stripes of a uniaxial ferrimagnetic garnet film. An external field modulation induces vibration of the stripe walls and produces random motion of the particles. Defects in the stripe pattern break the symmetry of the potential and favor particle nucleation into large clusters above a critical density. Mismatch between particle size and pattern wavelength generates assemblies with different morphological order. At even higher field strengths, repulsive dipolar interactions between the particles induce cluster melting. We propose a novel approach to generate and externally control a variety of colloidal assemblies.