Correlation functions of the one-dimensional attractive Bose gas

The zero-temperature correlation functions of the one-dimensional attractive Bose gas with a delta-function interaction are calculated analytically for any value of the interaction parameter and number of particles, directly from the integrability of the model. We point out a number of interesting features, including zero recoil energy for a large number of particles, analogous to the M?ssbauer effect.     

Unexpected stability of phospholipid langmuir monolayers deposited on Triton X-100 aqueous solutions

We studied at the molecular level the interaction between neutral detergent Triton X-100 aqueous solution and a phospholipid Langmuir monolayer deposited on top using surface pressure measurement and grazing incidence X-ray diffraction (GIXD). Macroscopically, the detergent-phospholipid system follows the Gibbs law. However, GIXD shows that the detergent and the phospholipid segregate at the interface. The molecular organization of pure phospholipid domains is imposed by the detergent through surface pressure. Compression and expansion of the surface monolayer system in its final state reveal the stability of the phospholipids domains against dissolution by the detergent in the subphase, even above the detergent cmc. This resistance to dissolution is suppressed by an expansion of the monolayer.     

Tracking the effects of interactions on spinons in gapless Heisenberg chains

We consider the effects of interactions on spinon excitations in Heisenberg spin-1/2 chains. We compute the exact two-spinon part of the longitudinal structure factor of the infinite chain in zero field for all values of anisotropy in the gapless antiferromagnetic regime, via an exact algebraic approach. Our results allow us to quantitatively describe the behavior of these fundamental excitations throughout the observable continuum, for cases ranging from free to fully coupled chains, thereby explicitly mapping the effects of "turning on the interactions" in a strongly correlated system.     

Setup of a scanning near field infrared microscope (SNIM): imaging of sub-surface nano-structures in gallium-doped silicon

We have realized a scanning near-field infrared microscope in the 3-4 microm wavelength range. As a light source, a tunable high power continuous wave infrared optical parametric oscillator with an output power of up to 2.9 W in the 3-4 microm range has been set up. Using scanning near field infrared microscopy (SNIM) imaging we have been able to obtain a lateral resolution of < or =30 nm at a wavelength of 3.2 microm, which is far below the far-field resolution limit of lambda/2. Using this "chemical nanoscope" we could image a sub-surface structure of implanted gallium ions in a topographically flat silicon wafer giving evidence for a near-field contrast. The observed contrast is explained in terms of the effective infrared reflection as a function of the sub-surface gallium doping concentration. The future use of the setup for nm imaging in the chemically important OH, N-H and C-H stretching vibration is discussed.     

A stochastic gradient type algorithm for closed-loop problems

We focus on the numerical solution of closed-loop stochastic problems, and propose a perturbed gradient algorithm to achieve this goal. The main hurdle in such problems is the fact that the control variables are infinite-dimensional, due to, e.g., the information constraints. Alternatively said, control variables are feedbacks, i.e., functions. Such controls have hence to be represented in a finite way in order to solve the problem numerically. In the same way, the gradient of the criterion is itself an infinite-dimensional object. Our algorithm replaces this exact (and unknown) gradient by a perturbed one, which consists of the product of the true gradient evaluated at a random point and a kernel function which extends this gradient to the neighbourhood of the random point. Proceeding this way, we explore the whole space iteration after iteration through random points. Since each kernel function is perfectly known by a small number of parameters, say N, the control at iteration k is perfectly known as an infinite-dimensional object by at most N × k parameters. The main strength of this method is that it avoids any discretization of the underlying space, provided that we can sample as many points as needed in this space. Moreover, our algorithm can take into account the possible measurability constraints of the problem in a new way. Finally, the randomized strategy implemented by the algorithm causes the most probable parts of the space to be the most explored ones, which is a priori an interesting feature. In this paper, we first prove two convergence results of this algorithm in the strongly convex and convex cases, and then give some numerical examples showing the interest of this method for practical stochastic optimization problems. In Memoriam: Jean-Sébastien Roy passed away July 04, 2007. He was 33 years old.     

Synthesis of zirconium, hafnium, and tantalum complexes with sterically demanding hydrazide ligands

The bulky hydrazine t-BuN(H)NMe2 was synthesized via hydrazone and t-BuN(H)N(H)Me intermediates as the major component in a 90:5:5 mixture consisting of t-BuN(H)NMe2, t-BuN(Me)N(H)Me, and t-BuN(Me)NMe2. Reacting the mixture with n-BuLi followed by distillation and fractional crystallization led to the isolation of the ligand precursor LiN(t-Bu)NMe2. Lithium hydrazides, LiN(R)NMe2, were reacted with metal chlorides to afford the hydrazide complexes M(N(Et)NMe2)4 (M = Zr or Hf), MCl(N(R)NMe2)3 (M = Zr, R = i-Pr or t-Bu; M = Hf, R = t-Bu), and TaCl3(N(i-Pr)NMe2)2. The X-ray crystal structures of [LiN(i-Pr)NMe2]4, [LiN(t-Bu)NMe2.THF]2, ZrCl(N(R)NMe2)3 (R = i-Pr or t-Bu), and TaCl3(N(i-Pr)NMe2)2 were determined. The structural analyses revealed that the hydrazide ligands in ZrCl(N(R)NMe2)3 (R = i-Pr or t-Bu) and TaCl3(N(i-Pr)NMe2)2 are eta2 coordinated.     

Dynamics of Citrate Coordination on Gold Nanoparticles Under Low Specific Power Laser-Induced Heating

SERS evolution recorded over a drop-coated coffee-ring pattern of citrate-capped gold colloids was investigated as a function of time under low-specific laser power. Spectral changes caused by plasmon-induced reaction could not be detected, but a long-term transient original spectral profile showing additional lines was observed. We performed deep qualitative and quantitative SERS intensity variation analysis based on the complementary use of extreme deviation and cross-correlation statistics, which provided further insights on the behavior of citrate-capping layers of gold nanoparticles upon laser illumination. More precisely, the cross-correlation analysis made possible to follow the so-called individual events denoting particular resonance structures, in which groups of modes were assigned to an evolution of citrate coordination on gold surface driven by photo-activation. As a consequence, the detection limit was increased and new lines were related to the presence of a very low amount of dicarboxy-acetone (DCA), which was already present in the system.     

Bottom-Up Synthesis,Dispersion and Properties of Rectangular-Shaped Graphene Quantum Dots

Carbon nanomaterials have attracted the attention of the scientific community for more than 30 years now; first with fullerene, then with nanotubes and now with graphene and graphene related materials. Graphene quantum dots (GQDs) are nanoparticles of graphene that can be synthesized following two approaches, namely top-down and bottom-up methods. The top-down synthesis used harsh chemical and/or physical treatments of macroscopic graphitic materials to obtain nanoparticles, while the second is based on organic chemistry through the synthesis of polycyclic aromatic hydrocarbons exhibiting various sizes and shapes that are perfectly controlled. The main drawback of this approach is related to the low solubility of carbon materials that prevents the synthesis of nanoparticles containing more than few hundreds of sp² carbon atoms. Here we report on the synthesis of a family of rectangular-shaped graphene quantum dots containing up to 162 sp² carbon atoms. These graphene quantum dots are not functionalized on their periphery in order to keep the maximum similarity with nanoparticles of pure graphene. We chose water with sodium deoxycholate surfactant to study their dispersion and their optical properties (absorption, photoluminescence and photoluminescence excitation). The electronic structure of the particles and of their aggregates are studied using Tight-Binding (TB). We observe that the larger particles ( GQD 3 and GQD 4 ) present a slightly better dispensability than the smaller ones, probably because the larger GQDs can accommodate more surfactant molecules on each side, which helps to stabilize their dispersion in water.