On the Mean-Field Limit of Bosons with Coulomb Two-Body Interaction

In the mean-field limit the dynamics of a quantum Bose gas is described by a Hartree equation. We present a simple method for proving the convergence of the microscopic quantum dynamics to the Hartree dynamics when the number of particles becomes large and the strength of the two-body potential tends to 0 like the inverse of the particle number. Our method is applicable for a class of singular interaction potentials including the Coulomb potential. We prove and state our main result for the Heisenberg-picture dynamics of "observables", thus avoiding the use of coherent states. Our formulation shows that the mean-field limit is a "semi-classical" limit.Comment: Corrected typos and included an elementary proof of the Kato smoothing estimate (Lemma 6.1

Justification of the coupled-mode approximation for a nonlinear elliptic problem with a periodic potential

Coupled-mode systems are used in physical literature to simplify the nonlinear Maxwell and Gross-Pitaevskii equations with a small periodic potential and to approximate localized solutions called gap solitons by analytical expressions involving hyperbolic functions. We justify the use of the one-dimensional stationary coupled-mode system for a relevant elliptic problem by employing the method of Lyapunov--Schmidt reductions in Fourier space. In particular, existence of periodic/anti-periodic and decaying solutions is proved and the error terms are controlled in suitable norms. The use of multi-dimensional stationary coupled-mode systems is justified for analysis of bifurcations of periodic/anti-periodic solutions in a small multi-dimensional periodic potential.Comment: 18 pages, no figure

Non-equilibrium states of a photon cavity pumped by an atomic beam

We consider a beam of two-level randomly excited atoms that pass one-by-one through a one-mode cavity. We show that in the case of an ideal cavity, i.e. no leaking of photons from the cavity, the pumping by the beam leads to an unlimited increase in the photon number in the cavity. We derive an expression for the mean photon number for all times. Taking into account leaking of the cavity, we prove that the mean photon number in the cavity stabilizes in time. The limiting state of the cavity in this case exists and it is independent of the initial state. We calculate the characteristic functional of this non-quasi-free non-equilibrium state. We also calculate the energy flux in both the ideal and open cavity and the entropy production for the ideal cavity.Comment: Corrected energy production calculations and made some changes to ease the readin

Coupled-mode equations and gap solitons in a two-dimensional nonlinear elliptic problem with a separable periodic potential

We address a two-dimensional nonlinear elliptic problem with a finite-amplitude periodic potential. For a class of separable symmetric potentials, we study the bifurcation of the first band gap in the spectrum of the linear Schr\"{o}dinger operator and the relevant coupled-mode equations to describe this bifurcation. The coupled-mode equations are derived by the rigorous analysis based on the Fourier--Bloch decomposition and the Implicit Function Theorem in the space of bounded continuous functions vanishing at infinity. Persistence of reversible localized solutions, called gap solitons, beyond the coupled-mode equations is proved under a non-degeneracy assumption on the kernel of the linearization operator. Various branches of reversible localized solutions are classified numerically in the framework of the coupled-mode equations and convergence of the approximation error is verified. Error estimates on the time-dependent solutions of the Gross--Pitaevskii equation and the coupled-mode equations are obtained for a finite-time interval.Comment: 32 pages, 16 figure

Finite-temperature Fermi-edge singularity in tunneling studied using random telegraph signals

We show that random telegraph signals in metal-oxide-silicon transistors at millikelvin temperatures provide a powerful means of investigating tunneling between a two-dimensional electron gas and a single defect state. The tunneling rate shows a peak when the defect level lines up with the Fermi energy, in excellent agreement with theory of the Fermi-edge singularity at finite temperature. This theory also indicates that defect levels are the origin of the dissipative two-state systems observed previously in similar devices.Comment: 5 pages, REVTEX, 3 postscript figures included with epsfi

Radical chemistry and ozone production at a UK coastal receptor site

OH, HO2, total and partially speciated RO2, and OH reactivity (kOH′) were measured during the July 2015 ICOZA (Integrated Chemistry of OZone in the Atmosphere) project that took place at a coastal site in north Norfolk, UK. Maximum measured daily OH, HO2 and total RO2 radical concentrations were in the range 2.6–17 × 106, 0.75–4.2 × 108 and 2.3–8.0 × 108 molec. cm−3, respectively. kOH′ ranged from 1.7 to 17.6 s−1, with a median value of 4.7 s−1. ICOZA data were split by wind direction to assess differences in the radical chemistry between air that had passed over the North Sea (NW–SE sectors) and that over major urban conurbations such as London (SW sector). A box model using the Master Chemical Mechanism (MCMv3.3.1) was in reasonable agreement with the OH measurements, but it overpredicted HO2 observations in NW–SE air in the afternoon by a factor of ∼ 2–3, although slightly better agreement was found for HO2 in SW air (factor of ∼ 1.4–2.0 underprediction). The box model severely underpredicted total RO2 observations in both NW–SE and SW air by factors of ∼ 8–9 on average. Measured radical and kOH′ levels and measurement–model ratios displayed strong dependences on NO mixing ratios, with the results suggesting that peroxy radical chemistry is not well understood under high-NOx conditions. The simultaneous measurement of OH, HO2, total RO2 and kOH′ was used to derive experimental (i.e. observationally determined) budgets for all radical species as well as total ROx (i.e. OH + HO2 + RO2). In NW–SE air, the ROx budget could be closed during the daytime within experimental uncertainty, but the rate of OH destruction exceeded the rate of OH production, and the rate of HO2 production greatly exceeded the rate of HO2 destruction, while the opposite was true for RO2. In SW air, the ROx budget analysis indicated missing daytime ROx sources, but the OH budget was balanced, and the same imbalances were found with the HO2 and RO2 budgets as in NW–SE air. For HO2 and RO2, the budget imbalances were most severe at high-NO mixing ratios, and the best agreement between HO2 and RO2 rates of production and destruction rates was found when the RO2 + NO rate coefficient was reduced by a factor of 5. A photostationary-steady-state (PSS) calculation underpredicted daytime OH in NW–SE air by ∼ 35 %, whereas agreement (∼ 15 %) was found within instrumental uncertainty (∼ 26 % at 2σ) in SW air. The rate of in situ ozone production (P(Ox)) was calculated from observations of ROx, NO and NO2 and compared to that calculated from MCM-modelled radical concentrations. The MCM-calculated P(Ox) significantly underpredicted the measurement-calculated P(Ox) in the morning, and the degree of underprediction was found to scale with NO

Measurement of the Bottom-Strange Meson Mixing Phase in the Full CDF Data Set

We report a measurement of the bottom-strange meson mixing phase \beta_s using the time evolution of B0_s -> J/\psi (->\mu+\mu-) \phi (-> K+ K-) decays in which the quark-flavor content of the bottom-strange meson is identified at production. This measurement uses the full data set of proton-antiproton collisions at sqrt(s)= 1.96 TeV collected by the Collider Detector experiment at the Fermilab Tevatron, corresponding to 9.6 fb-1 of integrated luminosity. We report confidence regions in the two-dimensional space of \beta_s and the B0_s decay-width difference \Delta\Gamma_s, and measure \beta_s in [-\pi/2, -1.51] U [-0.06, 0.30] U [1.26, \pi/2] at the 68% confidence level, in agreement with the standard model expectation. Assuming the standard model value of \beta_s, we also determine \Delta\Gamma_s = 0.068 +- 0.026 (stat) +- 0.009 (syst) ps-1 and the mean B0_s lifetime, \tau_s = 1.528 +- 0.019 (stat) +- 0.009 (syst) ps, which are consistent and competitive with determinations by other experiments.Comment: 8 pages, 2 figures, Phys. Rev. Lett 109, 171802 (2012

Learning from multimedia and hypermedia

Computer-based multimedia and hypermedia resources (e.g., the world wide web) have become one of the primary sources of academic information for a majority of pupils and students. In line with this expansion in the field of education, the scientific study of learning from multimedia and hypermedia has become a very active field of research. In this chapter we provide a short overview with regard to research on learning with multimedia and hypermedia. In two review sections, we describe the educational benefits of multiple representations and of learner control, as these are the two defining characteristics of hypermedia. In a third review section we describe recent scientific trends in the field of multimedia/hypermedia learning. In all three review sections we will point to relevant European work on multimedia/hypermedia carried out within the last 5 years, and often carried out within the Kaleidoscope Network of Excellence. According to the interdisciplinary nature of the field this work might come not only from psychology, but also from technology or pedagogy. Comparing the different research activities on multimedia and hypermedia that have dominated the international scientific discourse in the last decade reveals some important differences. Most important, a gap seems to exist between researchers mainly interested in a “serious” educational use of multimedia/ hypermedia and researchers mainly interested in “serious” experimental research on learning with multimedia/hypermedia. Recent discussions about the pros and cons of “design-based research” or “use-inspired basic research” can be seen as a direct consequence of an increasing awareness of the tensions within these two different cultures of research on education