Perturbations of eigenvalues embedded at threshold: one, two and three dimensional solvable models

We examine perturbations of eigenvalues and resonances for a class of multi-channel quantum mechanical model-Hamiltonians describing a particle interacting with a localized spin in dimension $d=1,2,3$. We consider unperturbed Hamiltonians showing eigenvalues and resonances at the threshold of the continuous spectrum and we analyze the effect of various type of perturbations on the spectral singularities. We provide algorithms to obtain convergent series expansions for the coordinates of the singularities.Comment: 20 page

The NLS equation in dimension one with spatially concentrated nonlinearities: the pointlike limit

In the present paper we study the following scaled nonlinear Schr\"odinger equation (NLS) in one space dimension: $$i\frac{d}{dt} \psi^{\varepsilon}(t) =-\Delta\psi^{\varepsilon}(t) + \frac{1}{\epsilon}V\left(\frac{x}{\epsilon}\right)|\psi^{\varepsilon}(t)|^{2\mu}\psi^{\varepsilon}(t) \quad \quad \epsilon>0\ ,\quad V\in L^1(\mathbb{R},(1+|x|)dx) \cap L^\infty(\mathbb{R}) \ .$$ This equation represents a nonlinear Schr\"odinger equation with a spatially concentrated nonlinearity. We show that in the limit $\epsilon\to 0$, the weak (integral) dynamics converges in $H^1(\mathbb{R})$ to the weak dynamics of the NLS with point-concentrated nonlinearity: $$i\frac{d}{dt} \psi(t) =H_{\alpha}\psi(t) .$$ where $H_{\alpha}$ is the laplacian with the nonlinear boundary condition at the origin $\psi'(t,0+)-\psi'(t,0-)=\alpha|\psi(t,0)|^{2\mu}\psi(t,0)$ and $\alpha=\int_{\mathbb{R}}Vdx$. The convergence occurs for every $\mu\in \mathbb{R}^+$ if $V \geq 0$ and for every $\mu\in (0,1)$ otherwise. The same result holds true for a nonlinearity with an arbitrary number $N$ of concentration pointsComment: 10 page

The role of small specimen creep testing within a life assessment framework for high temperature power plant

The safe operation of components operating at high temperature and pressure faces numerous challenges associated with ageing materials and maintaining commercial viability whilst economies transition to a lower carbon future as part of their climate change commitments. Due to these challenges the plant operator faces increasing pressure to ensure that any capital or operational expenditures are optimised and must ensure that they duly recognise plant age, condition, operating regime and ultimately the planned closure date. This review, for the first time, describes how small specimen creep testing can be applied within a practical and deployable life assessment framework and in conjunction with other assessment techniques. The current state of the art for small specimen creep testing is critically reviewed; this also includes a review of traditional techniques used on site for the metallurgical assessment of material condition, with examples from site investigations and assessment campaigns in both conventional and nuclear plant applications. In order to enhance the current practice for assessing the condition of creep ageing components this review proposes the more proactive use of small specimen testing methods for the in-service condition assessment of power plant materials, notably earlier in the plant lifecycle and within a holistic life assessment framework. This is intended to provide a means of calibrating the time dependent response of the component or system being monitored, thereby providing a key reference in-service strain rate measurement, or material property evaluation, that can subsequently be used with other traditionally deployed assessment methods to define a more targeted and cost-effective forward inspection plan. The review describes how small specimen creep testing methods and other complementary tools can be use in a new and structured approach to life management. The current status of small specimen testing methods, for both conventional and nuclear applications, is described along with a detailed discussion on current practice for in-service creep life assessment, with a case study used to illustrate the main principals. A case study is presented for ageing CMV (0.5%Cr0.5%Mo0.25%V) main steam pipework due to the extensive amount of through life data available, which highlights the particular challenges associated with the interpretation of various types of site outage inspection data, in conjunction with on-load plant operational data. The current approach to the assessment of component condition follows well established inspection based practices defined in various industry good practice guides, with expert elicitation and experience used to judge the condition of the component, system and operational risk on return to service. This review proposes a new approach to the holistic life assessment of high temperature plant, with a particular emphasis on more proactive use of small specimen testing. In addition, the review has highlighted other aspects of the current approach to in-service condition assessment that could be improved to support the plant owner. This specifically refers to the potential to develop and implement novel life assessment models that can take advantage of the significant amount of site data currently routinely acquired during plant outage overhauls. There is a clear need to provide the plant owner with more reliable and effective life prediction tools, based on earlier and more rigorous assessment of life consumption. The proposed application of small specimen testing described in this paper is equally applicable to both conventional and nuclear plant applications and a range of components, from static pressure systems to high temperature turbine rotors

Determination of the Newtonian Gravitational Constant Using Atom Interferometry

We present a new measurement of the Newtonian gravitational constant G based on cold atom interferometry. Freely falling samples of laser-cooled rubidium atoms are used in a gravity gradiometer to probe the field generated by nearby source masses. In addition to its potential sensitivity, this method is intriguing as gravity is explored by a quantum system. We report a value of G=6.667 10^{-11} m^{3} kg^{-1} s^{-2}, estimating a statistical uncertainty of $\pm$ 0.011 10^{-11} m^{3} kg^{-1} s^{-2} and a systematic uncertainty of $\pm$ 0.003 10^{-11} m^{3} kg^{-1} s^{-2}. The long-term stability of the instrument and the signal-to-noise ratio demonstrated here open interesting perspectives for pushing the measurement accuracy below the 100 ppm level.Comment: 4 figure

Point interactions in acoustics: one dimensional models

A one dimensional system made up of a compressible fluid and several mechanical oscillators, coupled to the acoustic field in the fluid, is analyzed for different settings of the oscillators array. The dynamical models are formulated in terms of singular perturbations of the decoupled dynamics of the acoustic field and the mechanical oscillators. Detailed spectral properties of the generators of the dynamics are given for each model we consider. In the case of a periodic array of mechanical oscillators it is shown that the energy spectrum presents a band structure.Comment: revised version, 30 pages, 2 figure

Atom interferometry gravity-gradiometer for the determination of the Newtonian gravitational constant G

We developed a gravity-gradiometer based on atom interferometry for the determination of the Newtonian gravitational constant \textit{G}. The apparatus, combining a Rb fountain, Raman interferometry and a juggling scheme for fast launch of two atomic clouds, was specifically designed to reduce possible systematic effects. We present instrument performances and show that the sensor is able to detect the gravitational field induced by source masses. A discussion of projected accuracy for \textit{G} measurement using this new scheme shows that the results of the experiment will be significant to discriminate between previous inconsistent values.Comment: 9 pages,9 figures, Submitte

Spin dependent point potentials in one and three dimensions

We consider a system realized with one spinless quantum particle and an array of $N$ spins 1/2 in dimension one and three. We characterize all the Hamiltonians obtained as point perturbations of an assigned free dynamics in terms of some ``generalized boundary conditions''. For every boundary condition we give the explicit formula for the resolvent of the corresponding Hamiltonian. We discuss the problem of locality and give two examples of spin dependent point potentials that could be of interest as multi-component solvable models.Comment: 15 pages, some misprints corrected, one example added, some references modified or adde

Characterization and control of phase fluctuations in elongated Bose-Einstein condensates

Quasi one dimensional Bose-Einstein condensates (BECs) in elongated traps exhibit significant phase fluctuations even at very low temperatures. We present recent experimental results on the dynamic transformation of phase fluctuations into density modulations during time-of-flight and show the excellent quantitative agreement with the theoretical prediction. In addition we confirm that under our experimental conditions, in the magnetic trap density modulations are strongly suppressed even when the phase fluctuates. The paper also discusses our theoretical results on control of the condensate phase by employing a time-dependent perturbation. Our results set important limitations on future applications of BEC in precision atom interferometry and atom optics, but at the same time suggest pathways to overcome these limitations.Comment: 9 pages, 7 figure

Dynamics and Lax-Phillips scattering for generalized Lamb models

This paper treats the dynamics and scattering of a model of coupled oscillating systems, a finite dimensional one and a wave field on the half line. The coupling is realized producing the family of selfadjoint extensions of the suitably restricted self-adjoint operator describing the uncoupled dynamics. The spectral theory of the family is studied and the associated quadratic forms constructed. The dynamics turns out to be Hamiltonian and the Hamiltonian is described, including the case in which the finite dimensional systems comprises nonlinear oscillators; in this case the dynamics is shown to exist as well. In the linear case the system is equivalent, on a dense subspace, to a wave equation on the half line with higher order boundary conditions, described by a differential polynomial $p(\partial_x)$ explicitely related to the model parameters. In terms of such structure the Lax-Phillips scattering of the system is studied. In particular we determine the incoming and outgoing translation representations, the scattering operator, which turns out to be unitarily equivalent to the multiplication operator given by the rational function $-p(i\kappa)^*/p(i\kappa)$, and the Lax-Phillips semigroup, which describes the evolution of the states which are neither incoming in the past nor outgoing in the future

Precision measurements of gravity using cold atom sensors

We present a synthetic view of experiments we are performing using atom interferometry to determine the gravitational constant G and to test the Newtonian gravitational law at micrometric distances. Accurate gravity measurements with atom interferometry also find applications in geophysical studies and in satellite missions for the geoid mapping. Experiments in progress, using ultracold atom devices, for applications in geophyiscal and space monitoring will be also described