Effective Dynamics of a Tracer Particle Interacting with an Ideal Bose Gas

We study a system consisting of a heavy quantum particle, called tracer particle, coupled to an ideal gas of light Bose particles, the ratio of masses of the tracer particle and a gas particle being proportional to the gas density. All particles have non-relativistic kinematics. The tracer particle is driven by an external potential and couples to the gas particles through a pair potential. We compare the quantum dynamics of this system to an effective dynamics given by a Newtonian equation of motion for the tracer particle coupled to a classical wave equation for the Bose gas. We quantify the closeness of these two dynamics as the mean-field limit is approached (gas density $\to\infty$). Our estimates allow us to interchange the thermodynamic with the mean-field limit.Comment: 27 pages, typos corrected, a few more explanations adde

Dynamics of Sound Waves in an Interacting Bose Gas

We consider a non-relativistic quantum gas of $N$ bosonic atoms confined to a box of volume $\Lambda$ in physical space. The atoms interact with each other through a pair potential whose strength is inversely proportional to the density, $\rho=\frac{N}{\Lambda}$, of the gas. We study the time evolution of coherent excitations above the ground state of the gas in a regime of large volume $\Lambda$ and small ratio $\frac{\Lambda}{\rho}$. The initial state of the gas is assumed to be close to a \textit{product state} of one-particle wave functions that are approximately constant throughout the box. The initial one-particle wave function of an excitation is assumed to have a compact support independent of $\Lambda$. We derive an effective non-linear equation for the time evolution of the one-particle wave function of an excitation and establish an explicit error bound tracking the accuracy of the effective non-linear dynamics in terms of the ratio $\frac{\Lambda}{\rho}$. We conclude with a discussion of the dispersion law of low-energy excitations, recovering Bogolyubov's well-known formula for the speed of sound in the gas, and a dynamical instability for attractive two-body potentials.Comment: 42 page

Absence of Embedded Mass Shells: Cerenkov Radiation and Quantum Friction

We show that, in a model where a non-relativistic particle is coupled to a quantized relativistic scalar Bose field, the embedded mass shell of the particle dissolves in the continuum when the interaction is turned on, provided the coupling constant is sufficiently small. More precisely, under the assumption that the fiber eigenvectors corresponding to the putative mass shell are differentiable as functions of the total momentum of the system, we show that a mass shell could exist only at a strictly positive distance from the unperturbed embedded mass shell near the boundary of the energy-momentum spectrum.Comment: Revised version: a remark added at the end of Section

Absence of Ground States for a Class of Translation Invariant Models of Non-relativistic QED

We consider a class of translation invariant models of non-relativistic QED with net charge. Under certain natural assumptions we prove that ground states do not exist in the Fock space

Towards a construction of inclusive collision cross-sections in the massless Nelson model

The conventional approach to the infrared problem in perturbative quantum electrodynamics relies on the concept of inclusive collision cross-sections. A non-perturbative variant of this notion was introduced in algebraic quantum field theory. Relying on these insights, we take first steps towards a non-perturbative construction of inclusive collision cross-sections in the massless Nelson model. We show that our proposal is consistent with the standard scattering theory in the absence of the infrared problem and discuss its status in the infrared-singular case.Comment: 23 pages, LaTeX. As appeared in Ann. Henri Poincar\'

Centralising acute stroke care within clinical practice in the Netherlands: lower bounds of the causal impact

BACKGROUND Authors in previous studies demonstrated that centralising acute stroke care is associated with an increased chance of timely Intra-Venous Thrombolysis (IVT) and lower costs compared to care at community hospitals. In this study we estimated the lower bound of the causal impact of centralising IVT on health and cost outcomes within clinical practice in the Northern Netherlands. METHODS We used observational data from 267 and 780 patients in a centralised and decentralised system, respectively. The original dataset was linked to the hospital information systems. Literature on healthcare costs and Quality of Life (QoL) values up to 3 months post-stroke was searched to complete the input. We used Synthetic Control Methods (SCM) to counter selection bias. Differences in SCM outcomes included 95% Confidence Intervals (CI). To deal with unobserved heterogeneity we focused on recently developed methods to obtain the lower bounds of the causal impact. RESULTS Using SCM to assess centralising acute stroke 3 months post-stroke revealed healthcare savings of $US 1735 (CI, 505 to 2966) while gaining 0.03 (CI, − 0.01 to 0.73) QoL per patient. The corresponding lower bounds of the causal impact are$US 1581 and 0.01. The dominant effect remained stable in the deterministic sensitivity analyses with $US 1360 (CI, 476 to 2244) as the most conservative estimate. CONCLUSIONS In this study we showed that a centralised system for acute stroke care appeared both cost-saving and yielded better health outcomes. The results are highly relevant for policy makers, as this is the first study to address the issues of selection and unobserved heterogeneity in the evaluation of centralising acute stroke care, hence presenting causal estimates for budget decisions

Impact of PWM Voltage Waveforms in High-Speed Drives: A Survey on High-Frequency Motor Models and Partial Discharge Phenomenon

The insulation system’s dielectric of the electric motor is very often subjected to severe electrical stress generated by the high dv/dt seen at the machine’s terminals. The electrical stress and high reflected wave transient overvoltage are even more evident in case of high-speed machines fed by high-frequency (HF) converters featuring very fast wide-bandgap devices. They are promoting the occurrence of partial discharges and consequently accelerate ageing. As this is serious issue and the main cause of the drive failure, it is important to analyse and characterise the surges at the motor terminals. Several HF models of motors have been proposed in the literature for this purpose. This article presents a survey on HF motor models, which is crucial in understanding and studying the most critical parameter identification and overvoltage mitigation techniques. Moreover, it offers a comparison of the models’ main features as well as a comparison with the experimental voltage waveform at motor terminals. A general overview of the partial discharge (PD) phenomenon is also provided, as it is favoured by HF operation and together with HF motor modelling provides key insights to the insulation ageing issue. In particular, an analysis of the effects of PWM waveform affecting insulation is given, as well as useful methods for developing strategies for the inspection and maintenance of winding insulation

First imaging of corotating interaction regions using the STEREO spacecraft

Plasma parcels are observed propagating from the Sun out to the large coronal heights monitored by the Heliospheric Imagers (HI) instruments onboard the NASA STEREO spacecraft during September 2007. The source region of these out-flowing parcels is found to corotate with the Sun and to be rooted near the western boundary of an equatorial coronal hole. These plasma enhancements evolve during their propagation through the HI cameras’ fields of view and only becoming fully developed in the outer camera field of view. We provide evidence that HI is observing the formation of a Corotating Interaction Region(CIR) where fast solar wind from the equatorial coronal hole is interacting with the slow solar wind of the streamer belt located on the western edge of that coronal hole. A dense plasma parcel is also observed near the footpoint of the observed CIR at a distance less than 0.1AU from the Sun where fast wind would have not had time to catch up slow wind. We suggest that this low-lying plasma enhancement is a plasma parcel which has been disconnected from a helmet streamer and subsequently becomes embedded inside the corotating interaction region

Deep LOFAR observations of the merging galaxy cluster CIZA J2242.8+5301

Previous studies have shown that CIZA J2242.8+5301 (the 'Sausage' cluster, z = 0.192) is a massive merging galaxy cluster that hosts a radio halo and multiple relics. In this paper, we present deep, high-fidelity, low-frequency images made with the LOw-Frequency Array (LOFAR) between 115.5 and 179 MHz. These images, with a noise of 140 μJy beam- 1 and a resolution of θbeam = 7.3 arcsec × 5.3 arcsec, are an order of magnitude more sensitive and five times higher resolution than previous low-frequency images of this cluster. We combined the LOFAR data with the existing Giant Metrewave Radio Telescope (GMRT) (153, 323, 608 MHz) and Westerbork Synthesis Radio Telescope (WSRT) (1.2, 1.4, 1.7, 2.3 GHz) data to study the spectral properties of the radio emission from the cluster. Assuming diffusive shock acceleration (DSA), we found Mach numbers of Mn=2.7{}_{-0.3}^{+0.6} and Ms=1.9_{-0.2}^{+0.3} for the northern and southern shocks. The derived Mach number for the northern shock requires an acceleration efficiency of several percent to accelerate electrons from the thermal pool, which is challenging for DSA. Using the radio data, we characterized the eastern relic as a shock wave propagating outwards with a Mach number of Me=2.4_{-0.3}^{+0.5}, which is in agreement with MeX=2.5{}_{-0.2}^{+0.6} that we derived from Suzaku data. The eastern shock is likely to be associated with the major cluster merger. The radio halo was measured with a flux of 346 ± 64 mJy at 145 MHz. Across the halo, we observed a spectral index that remains approximately constant (α ^{145 MHz-2.3 GHz}_{{across ˜ 1 Mpc}^2}=-1.01± 0.10) after the steepening in the post-shock region of the northern relic. This suggests a generation of post-shock turbulence that re-energies aged electrons