No phase transition for Gaussian fields with bounded spins

Let a<b, \Omega=[a,b]^{\Z^d} and H be the (formal) Hamiltonian defined on \Omega by H(\eta) = \frac12 \sum_{x,y\in\Z^d} J(x-y) (\eta(x)-\eta(y))^2 where J:\Z^d\to\R is any summable non-negative symmetric function (J(x)\ge 0 for all x\in\Z^d, \sum_x J(x)<\infty and J(x)=J(-x)). We prove that there is a unique Gibbs measure on \Omega associated to H. The result is a consequence of the fact that the corresponding Gibbs sampler is attractive and has a unique invariant measure.Comment: 7 page

Ground states of quantum kagome antiferromagnets in a magnetic field

We study the ground state properties of a quantum antiferromagnet in the kagome lattice in the presence of a magnetic field, paying particular attention to the stability of the plateau at magnetization 1/3 of saturation. While the plateau is reinforced by certain deformations of the lattice, like the introduction of structural defect lines and against an Ising anisotropy, ground state correlations are seen to be quite different and the undistorted SU(2) case appears to be rather special.Comment: 3 pages, 3 figures, contribution to the Japanese-French symposium on "Quantum magnetism in spin, charge and orbital systems", Paris 1-4 October 200

Non-linear spectroscopy of rubidium: An undergraduate experiment

In this paper, we describe two complementary non-linear spectroscopy methods which both allow to achieve Doppler-free spectra of atomic gases. First, saturated absorption spectroscopy is used to investigate the structure of the $5{\rm S}_{1/2}\to 5{\rm P}_{3/2}$ transition in rubidium. Using a slightly modified experimental setup, Doppler-free two-photon absorption spectroscopy is then performed on the $5{\rm S}_{1/2}\to 5{\rm D}_{5/2}$ transition in rubidium, leading to accurate measurements of the hyperfine structure of the $5{\rm D}_{5/2}$ energy level. In addition, electric dipole selection rules of the two-photon transition are investigated, first by modifying the polarization of the excitation laser, and then by measuring two-photon absorption spectra when a magnetic field is applied close to the rubidium vapor. All experiments are performed with the same grating-feedback laser diode, providing an opportunity to compare different high resolution spectroscopy methods using a single experimental setup. Such experiments may acquaint students with quantum mechanics selection rules, atomic spectra and Zeeman effect.Comment: 16 pages, 8 figure

Exact multipoint and multitime correlation functions of a one-dimensional model of adsorption and evaporation of dimers

In this work, we provide a method which allows to compute exactly the multipoint and multi-time correlation functions of a one-dimensional stochastic model of dimer adsorption-evaporation with random (uncorrelated) initial states. In particular explicit expressions of the two-point noninstantaneous/instantaneous correlation functions are obtained. The long-time behavior of these expressions is discussed in details and in various physical regimes.Comment: 6 pages, no figur

Solution of a class of one-dimensional reaction-diffusion models in disordered media

We study a one-dimensional class of reaction-diffusion models on a $10-$parameters manifold. The equations of motion of the correlation functions close on this manifold. We compute exactly the long-time behaviour of the density and correlation functions for {\it quenched} disordered systems. The {\it quenched} disorder consists of disconnected domains of reaction. We first consider the case where the disorder comprizes a superposition, with different probabilistic weights, of finite segments, with {\it periodic boundary conditions}. We then pass to the case of finite segments with {\it open boundary conditions}: we solve the ordered dynamics on a open lattice with help of the Dynamical Matrix Ansatz (DMA) and investigate further its disordered version.Comment: 11 pages, no figures. To appear in Phys.Rev.

Diffusion-limited Reactions of hard-core Particles in one-dimension

We investigate three different methods to tackle the problem of diffusion-limited reactions (annihilation) of hard-core classical particles in one dimension. We first extend an approach devised by Lushnikov and calculate for a single species the asymptotic long-time and/or large distance behavior of the two-point correlation function. Based on a work by Grynberg et al., which was developed to treat stochastic adsorption-desorption models, we provide in a second step the exact two-point correlation function (both for one and two-time) of Lushnikov's model. We then propose a new formulation of the problem in terms of path integrals for pseudo-fermions. This formalism can be used to advantage in the multi-species case, specially when applying perturbative renormalization group techniques.Comment: 15 pages, no figure, to appear in PR