Aging effects in the quantum dynamics of a dissipative free particle: non-ohmic case

We report new results related to the two-time dynamics of the coordinate of a quantum free particle, damped through its interaction with a fractal thermal bath (non-ohmic coupling $\sim\omega^\delta$ with $0<\delta<1$ or $1<\delta<2)$. When the particle is localized, its position does not age. When it undergoes anomalous diffusion, only its displacement may be defined. It is shown to be an aging variable. The finite temperature aging regime is self-similar. It is described by a scaling function of the ratio ${t_w/\tau}$ of the waiting time to the observation time, as characterized by an exponent directly linked to $\delta$.Comment: 4 pages, 3 figures, submitted to PR

Real-Time-RG Analysis of the Dynamics of the Spin-Boson Model

Using a real-time renormalization group method we determine the complete dynamics of the spin-boson model with ohmic dissipation for coupling strengths $\alpha\lesssim 0.1-0.2$. We calculate the relaxation and dephasing time, the static susceptibility and correlation functions. Our results are consistent with quantum Monte Carlo simulations and the Shiba relation. We present for the first time reliable results for finite cutoff and finite bias in a regime where perturbation theory in $\alpha$ or in tunneling breaks down. Furthermore, an unambigious comparism to results from the Kondo model is achieved.Comment: 4 pages, 5 figures, 1 tabl

Thinking about growth : a cognitive mapping approach to understanding small business development

School of Managemen

Modulation of Localized States in Electroconvection

We report on the effects of temporal modulation of the driving force on a particular class of localized states, known as worms, that have been observed in electroconvection in nematic liquid crystals. The worms consist of the superposition of traveling waves and have been observed to have unique, small widths, but to vary in length. The transition from the pure conduction state to worms occurs via a backward bifurcation. A possible explanation of the formation of the worms has been given in terms of coupled amplitude equations. Because the worms consist of the superposition of traveling waves, temporal modulation of the control parameter is a useful probe of the dynamics of the system. We observe that temporal modulation increases the average length of the worms and stabilizes worms below the transition point in the absence of modulation.Comment: 4 pages, 4 figure

Generalized quantum Fokker-Planck, diffusion and Smoluchowski equations with true probability distribution functions

Traditionally, the quantum Brownian motion is described by Fokker-Planck or diffusion equations in terms of quasi-probability distribution functions, e.g., Wigner functions. These often become singular or negative in the full quantum regime. In this paper a simple approach to non-Markovian theory of quantum Brownian motion using {\it true probability distribution functions} is presented. Based on an initial coherent state representation of the bath oscillators and an equilibrium canonical distribution of the quantum mechanical mean values of their co-ordinates and momenta we derive a generalized quantum Langevin equation in $c$-numbers and show that the latter is amenable to a theoretical analysis in terms of the classical theory of non-Markovian dynamics. The corresponding Fokker-Planck, diffusion and the Smoluchowski equations are the {\it exact} quantum analogues of their classical counterparts. The present work is {\it independent} of path integral techniques. The theory as developed here is a natural extension of its classical version and is valid for arbitrary temperature and friction (Smoluchowski equation being considered in the overdamped limit).Comment: RevTex, 16 pages, 7 figures, To appear in Physical Review E (minor revision

Stability of persistent currents in a Bose-Einstein condensate confined in a toroidal trap

Motivated by recent experiments in Bose-Einstein condensed atoms that have been confined in toroidal traps, we examine the stability of persistent currents in such systems. We investigate the extent that the stability of these currents may be tunable, and the possible difficulties in their creation and detection.Comment: 6 pages, 5 figure

Aortic valve calcification volumes and chronic brain infarctions in patients undergoing transcatheter aortic valve implantation

Chronic silent brain infarctions, detected as new white matter hyperintensities on magnetic resonance imaging (MRI) following transcatheter aortic valve implantation (TAVI), are associated with long-term cognitive deterioration. This is the first study to investigate to which extent the calcification volume of the native aortic valve (AV) measured with cardiac computed tomography angiography (CTA) predicts the increase in chronic white matter hyperintensity volume after TAVI. A total of 36 patients (79 ± 5 years, median EuroSCORE II 1.9%, Q1–Q3 1.5–3.4%) with severe AV stenosis underwent fluid attenuation inversion recovery (FLAIR) MRI < 24 h prior to TAVI and at 3 months follow-up for assessment of cerebral white matter hyperintensity volume (mL). Calcification volumes (mm3) of the AV, aortic arch, landing zone and left ventricle were measured on the CTA pre-TAVI. The largest calcification volumes were found in the AV (median 692 mm3) and aortic arch (median 633 mm3), with a large variation between patients (Q1–Q3 482–1297 mm3 and 213–1727 mm3, respectively). The white matter hyperintensity volume increased in 72% of the patients. In these patients the median volume increase was of 1.1 mL (Q1–Q3 0.3–4.6 mL), corresponding with a 27% increase from baseline (Q1–Q3 7–104%). The calcification volume in the AV predicted the increase of white matter hyperintensity volume (Δ%), with a 35% increase of white matter hyperintensity volume, per 100 mm3 of AV calcification volume (SE 8.5, p < 0.001). The calcification volumes in the aortic arch, landing zone and left ventricle were not associated with the increase in white matter hyperintensity volume. In 72% of the patients new chronic white matter hyperintensities developed 3 months after TAVI, with a median increase of 27%. A higher calcification volume in the AV was associated with a larger increase in the white matter hyperintensity volume. These findings show the potential for automated AV calcium screening as an imaging biomarker to predict chronic silent brain infarctions

Convalescent plasma in patients admitted to hospital with COVID-19 (RECOVERY): a randomised controlled, open-label, platform trial

Background: Many patients with COVID-19 have been treated with plasma containing anti-SARS-CoV-2 antibodies. We aimed to evaluate the safety and efficacy of convalescent plasma therapy in patients admitted to hospital with COVID-19. Methods: This randomised, controlled, open-label, platform trial (Randomised Evaluation of COVID-19 Therapy [RECOVERY]) is assessing several possible treatments in patients hospitalised with COVID-19 in the UK. The trial is underway at 177 NHS hospitals from across the UK. Eligible and consenting patients were randomly assigned (1:1) to receive either usual care alone (usual care group) or usual care plus high-titre convalescent plasma (convalescent plasma group). The primary outcome was 28-day mortality, analysed on an intention-to-treat basis. The trial is registered with ISRCTN, 50189673, and ClinicalTrials.gov, NCT04381936. Findings: Between May 28, 2020, and Jan 15, 2021, 11558 (71%) of 16287 patients enrolled in RECOVERY were eligible to receive convalescent plasma and were assigned to either the convalescent plasma group or the usual care group. There was no significant difference in 28-day mortality between the two groups: 1399 (24%) of 5795 patients in the convalescent plasma group and 1408 (24%) of 5763 patients in the usual care group died within 28 days (rate ratio 1·00, 95% CI 0·93–1·07; p=0·95). The 28-day mortality rate ratio was similar in all prespecified subgroups of patients, including in those patients without detectable SARS-CoV-2 antibodies at randomisation. Allocation to convalescent plasma had no significant effect on the proportion of patients discharged from hospital within 28 days (3832 [66%] patients in the convalescent plasma group vs 3822 [66%] patients in the usual care group; rate ratio 0·99, 95% CI 0·94–1·03; p=0·57). Among those not on invasive mechanical ventilation at randomisation, there was no significant difference in the proportion of patients meeting the composite endpoint of progression to invasive mechanical ventilation or death (1568 [29%] of 5493 patients in the convalescent plasma group vs 1568 [29%] of 5448 patients in the usual care group; rate ratio 0·99, 95% CI 0·93–1·05; p=0·79). Interpretation: In patients hospitalised with COVID-19, high-titre convalescent plasma did not improve survival or other prespecified clinical outcomes. Funding: UK Research and Innovation (Medical Research Council) and National Institute of Health Research