On the wellposedness of some McKean models with moderated or singular diffusion coefficient

We investigate the well-posedness problem related to two models of nonlinear McKean Stochastic Differential Equations with some local interaction in the diffusion term. First, we revisit the case of the McKean-Vlasov dynamics with moderate interaction, previously studied by Meleard and Jourdain in [16], under slightly weaker assumptions, by showing the existence and uniqueness of a weak solution using a Sobolev regularity framework instead of a Holder one. Second, we study the construction of a Lagrangian Stochastic model endowed with a conditional McKean diffusion term in the velocity dynamics and a nondegenerate diffusion term in the position dynamics

Spin dynamics in high-TCT_C superconductors

Key features of antiferromagnetic dynamical correlations in high-$T_C$ superconductors cuprates are discussed. In underdoped regime, the sharp resonance peak, occuring exclusively in the SC state, is accompanied by a broader contribution located around $\sim$ 30 meV which remains above $T_C$. Their interplay may induce incommensurate structure in the superconducting state.Comment: HTS99 Proceedings Miami (January 7-11 1999

New excitations in bcc 4^{4}He - an inelastic neutron scattering study

We report neutron scattering measurements on bcc solid $^{4}$% He. We studied the phonon branches and the recently discovered ''optic-like'' branch along the main crystalline directions. In addition, we discovered another, dispersionless "optic-like'' branch at an energy around 1 meV ($\sim$~11K). The properties of the two "optic-like" branches seem different. Since one expects only 3 acoustic phonon branches in a monoatomic cubic crystal, these new branches must represent different type of excitations. One possible interpretation involves localized excitations unique to a quantum solid.Comment: 4 pages, 3 figures, accepted by PRB, Rapid Communication

Static spectroscopy of a dense superfluid

Dense Bose superfluids, as HeII, differ from dilute ones by the existence of a roton minimum in their excitation spectrum. It is known that this roton minimum is qualitatively responsible for density oscillations close to any singularity, such as vortex cores, or close to solid boundaries. We show that the period of these oscillations, and their exponential decrease with the distance to the singularity, are fully determined by the position and the width of the roton minimum. Only an overall amplitude factor and a phase shift are shown to depend on the details of the interaction potential. Reciprocally, it allows for determining the characteristics of this roton minimum from static "observations" of a disturbed ground state, in cases where the dynamics is not easily accessible. We focus on the vortex example. Our analysis further shows why the energy of these oscillations is negligible compared to the kinetic energy, which limits their influence on the vortex dynamics, except for high curvatures.Comment: 14 pages, 4 figures, extended version, published in J. Low Temp. Phy

Quantum Impurities and the Neutron Resonance Peak in YBa2Cu3O7{\bf YBa_2 Cu_3 O_7}: Ni versus Zn

The influence of magnetic (S=1) and nonmagnetic (S=0) impurities on the spin dynamics of an optimally doped high temperature superconductor is compared in two samples with almost identical superconducting transition temperatures: YBa$_2$(Cu$_{0.97}$Ni$_{0.03}$)$_3$O$_7$ (T$_c$=80 K) and YBa$_2$(Cu$_{0.99}$Zn$_{0.01}$)$_3$O$_7$ (T$_c$=78 K). In the Ni-substituted system, the magnetic resonance peak (which is observed at E$_r \simeq$40 meV in the pure system) shifts to lower energy with a preserved E$_r$/T$_c$ ratio while the shift is much smaller upon Zn substitution. By contrast Zn, but not Ni, restores significant spin fluctuations around 40 meV in the normal state. These observations are discussed in the light of models proposed for the magnetic resonance peak.Comment: 3 figures, submitted to PR

High energy spin excitations in YBa_2 Cu_3 O_{6.5}

Inelastic neutron scattering has been used to obtain a comprehensive description of the absolute dynamical spin susceptibility $\chi'' (q,\omega)$ of the underdoped superconducting cuprate YBa_2 Cu_3 O_{6.5} ($T_c = 52 K$) over a wide range of energies and temperatures ($2 meV \leq \hbar \omega \leq 120 meV$ and $5K \leq T \leq 200K$). Spin excitations of two different symmetries (even and odd under exchange of two adjacent CuO_2 layers) are observed which, surprisingly, are characterized by different temperature dependences. The excitations show dispersive behavior at high energies.Comment: 15 pages, 5 figure

A Semi-Lagrangian scheme for a modified version of the Hughes model for pedestrian flow

In this paper we present a Semi-Lagrangian scheme for a regularized version of the Hughes model for pedestrian flow. Hughes originally proposed a coupled nonlinear PDE system describing the evolution of a large pedestrian group trying to exit a domain as fast as possible. The original model corresponds to a system of a conservation law for the pedestrian density and an Eikonal equation to determine the weighted distance to the exit. We consider this model in presence of small diffusion and discuss the numerical analysis of the proposed Semi-Lagrangian scheme. Furthermore we illustrate the effect of small diffusion on the exit time with various numerical experiments

Spin Susceptibility in Underdoped YBa2Cu3O6+x\bf YBa_2Cu_3O_{6+x}

We report a comprehensive polarized and unpolarized neutron scattering study of the evolution of the dynamical spin susceptibility with temperature and doping in three underdoped single crystals of the \YBCO{6+x} high temperature superconductor: \YBCO{6.5} (Tc = 52 K), \YBCO{6.7} (Tc = 67 K), and \YBCO{6.85} (T_c = 87 K). Theoretical implications of these data are discussed, and a critique of recent attempts to relate the spin excitations to the thermodynamics of high temperature superconductors is given.Comment: minor revisions, to appear in PR