A Central Limit Theorem in Many-Body Quantum Dynamics

We study the many body quantum evolution of bosonic systems in the mean field limit. The dynamics is known to be well approximated by the Hartree equation. So far, the available results have the form of a law of large numbers. In this paper we go one step further and we show that the fluctuations around the Hartree evolution satisfy a central limit theorem. Interestingly, the variance of the limiting Gaussian distribution is determined by a time-dependent Bogoliubov transformation describing the dynamics of initial coherent states in a Fock space representation of the system.     

The structure and possible catalytic sites of Mo(3)S(9) as a model of amorphous molybdenum trisulfide: a computational study

The structure and reactivity of Mo(3)S(9) clusters, taken as a model for amorphous molybdenum trisulfide, have been investigated at the B3LYP density functional level of theory. Two computed ground-state cluster structures are close in energy and have similar structural parameters and vibrational modes. These values agree well with the available experimental data. These cluster structures are considered to be formed simultaneously during the preparation process of catalysts. Their catalytic activity has been analyzed on the basis of frontier molecular orbital properties (FMO). It is mainly due to 4d-type orbitals of the unsaturated molybdenum centers without terminal sulfur coordination. The small HOMO-LUMO gaps suggest that Mo(3)S(9) clusters can act as Lewis acids or Lewis bases.     

Novel Copolymers of Difluoro Ring-substituted 2-Phenyl-1,1-dicyanoethylenes with 4-Fluorostyrene: Synthesis,Structure and Dielectric Study

Copolymerization of fluorine ring-substituted 2-phenyl-1,1-dicyanoethenes, RC₆H₃CH?C(CN)₂ (R is 2,3-F,F, 2,4-F,F, 2,5-F,F, 2,6-F,F, and 4-CF₃) with 4-fluorostyrene were prepared in the presence of a radical initiator (ABCN) at 70°C. The composition of the copolymers was calculated from nitrogen analysis, and the copolymers were characterized by IR, ¹H and ¹³C-NMR, GPC, DSC, and TGA. The monomer reactivity ratios for 4-fluorostyrene (M₁), r₁ = 0.6 and 2-(2,4-difluorophenyl)-1,1-dicyanoethene (M₂), r₂ = 0 were determined from Fineman-Ross plot. The order of relative reactivity (1/r₁) for difluoro-substituted monomers is 2,4-F,F (0.31) > 2,3-F,F (0.25) > 2,5-F,F (0.22) > 2,6-F,F (0.10). DSC curves showed that the copolymers were amorphous with high T _g in comparison with that poly(4-fluorostyrene) indicating a substantial decrease in chain mobility of the copolymer due to the high dipolar character of the trisubstituted ethylene monomer units. From the thermogravimetric analysis, the copolymers began to degrade in the range 214–260°C. The copolymer of 4-fluorostyrene and 2-(2,4-difluorophenyl)-1,1-dicyanoethene and poly(4-fluorostyrene) were dielectrically characterized in the range 25–200°C. The dominating relaxation process detected in both materials was the α-relaxation, associated with the dynamic glass transition. The relationship polarity-permittivity was discussed.     

Super-Diffusivity in a Shear Flow Model¶from Perpetual Homogenization

This paper is concerned with the asymptotic behavior solutions of stochastic differential equations dy _t =dω _t −∇Γ(y _t ) dt, y ₀=0 and d=2. Γ is a 2 &\times; 2 skew-symmetric matrix associated to a shear flow characterized by an infinite number of spatial scales Γ₁₂=−Γ₂₁=h(x ₁), with h(x ₁)=∑ _{n =0} ^∞γ _n h ⁿ (x ₁/R _n ), where h ⁿ are smooth functions of period 1, h ⁿ (0)=0, γ _n and R _n grow exponentially fast with n. We can show that y ^t has an anomalous fast behavior (?[|y ^t |²]∼t ^1+ν with ν > 0) and obtain quantitative estimates on the anomaly using and developing the tools of homogenization. Received: 1 June 2001 / Accepted: 11 January 2002     

The construction of thed+1-dimensional gaussian droplet

The aim of this note is to study the asymptotic behavior of a gaussian random field, under the condition that the variables are positive and the total volume under the variables converges to some fixed numberv>0. In the context of Statistical Mechanics, this corresponds to the problem of constructing a droplet on a hard wall with a given volume. We show that, properly rescaled, the profile of a gaussian configuration converges to a smooth hypersurface, which solves a quadratic variational problem. Our main tool is a scaling dependent large deviation principle for random hypersurfacesDedicated to the memory of Roland Dobrushin, who passed away on 13 November 1995     

Synergy in selective catalytic oxidation

Summary A strong synergy between separate oxide phases A and B is observed in the oxidation of isobutylene to methacrolein. This is explained by the continuous activation of potential centers on A by spill-over oxygen emitted by B (remote control). This activation corresponds to the creation of Brönsted sites in the case where A is MoO₃. We discuss some details of the mechanism and the consequences with respect to catalyst design and process.     

Aging in two-dimensional Bouchaud's model

Let E _x be a collection of i.i.d. exponential random variables. Symmetric Bouchaud's model on ℤ² is a Markov chain X(t) whose transition rates are given by w _xy = ν exp (−βE _x ) if x, y are neighbours in ℤ². We study the behaviour of two correlation functions: ℙ[X(t _w +t) = X(t _w )] and ℙ[X(t') = X(t _w ) ∀ t'∈ [t _w , t _w + t]]. We prove the (sub)aging behaviour of these functions when β > 1.