On the minimizers of the Ginzburg-Landau energy for high kappa : the axially symmetric case
On the multiple overlap function of the SK model.
In this note, we prove an asymptotic expansion and a central limit theorem for the multiple overlap R1, ..., s of the SK model, defined for given N, s ≥ 1 by R1, ..., s = N-1Σi≤N σ1i ... σsi. These results are obtained by a careful analysis of the terms appearing in the cavity derivation formula, as well as some graph induction procedures. Our method could hopefully be applied to other spin glasses models.
On the NLS dynamics for infinite energy vortex configurations on the plane.
On the number of ground states of the Edwards–Anderson spin glass model
Ground states of the Edwards–Anderson (EA) spin glass model are studied on infinite graphs with finite degree. Ground states are spin configurations that locally minimize the EA Hamiltonian on each finite set of vertices. A problem with far-reaching consequences in mathematics and physics is to determine the number of ground states for the model on for any . This problem can be seen as the spin glass version of determining the number of infinite geodesics in first-passage percolation or the number...
On the Plasma-Charge problem
This short report is a review on recent results of S. Caprino, C. Marchioro, E. Miot and the author on the initial value problem associated to the evolution of a continuous distribution of charges (plasma) in presence of a finite number of point charges.
On the regularity of a free boundary for a nonlinear obstacle problem arising in superconductor modelling
On the smallest eigenvalue of the Stokes operator in a domain with fine-grained random boundary.
On the zero-one law and the law of large numbers for random walk in mixing random environment.
One-dimensional vertex models associated with a class of Yangian invariant Haldane-Shastry like spin chains.
Optimal feedback control of Ginzburg-Landau equation for superconductivity via differential inclusion
Slightly below the transition temperatures, the behavior of superconducting materials is governed by the Ginzburg-Landau (GL) equation which characterizes the dynamical interaction of the density of superconducting electron pairs and the exited electromagnetic potential. In this paper, an optimal control problem of the strength of external magnetic field for one-dimensional thin film superconductors with respect to a convex criterion functional is considered. It is formulated as a nonlinear coefficient...
Ordered dissipative structures in exciton systems in semiconductor quantum wells.
Ordering of energy levels for extended Hubbard chain.
Original title unknown
Particle-in-wavelets scheme for the 1D Vlasov-Poisson equations ⋆⋆⋆
A new numerical scheme called particle-in-wavelets is proposed for the Vlasov-Poisson equations, and tested in the simplest case of one spatial dimension. The plasma distribution function is discretized using tracer particles, and the charge distribution is reconstructed using wavelet-based density estimation. The latter consists in projecting the Delta distributions corresponding to the particles onto a finite dimensional linear space spanned by...
Peltier effect of superconductor-semiconductor mesoscopic device.
Periodic sphere packings and the Wulff-shape.
Phénomène de couche limite dans un modèle de ferromagnétisme
Problèmes d’évolution liés à l’énergie de Ginzburg-Landau
Problemi di geometria stocastica nei processi di cristallizzazione di polimeri. Aspetti modellistici, statistici e computazionali
Process-level quenched large deviations for random walk in random environment
We consider a bounded step size random walk in an ergodic random environment with some ellipticity, on an integer lattice of arbitrary dimension. We prove a level 3 large deviation principle, under almost every environment, with rate function related to a relative entropy.