Search for: All records

We study the entanglement contour and partial entanglement entropy (PEE) in quantum field theories in 3 and higher dimensions. The entanglement entropy is evaluated from a certain limit of the PEE with a geometric regulator. In the context of the entanglement contour, we classify the geometric regulators, study their difference from the UV regulators. Furthermore, for spherical regions in conformal field theories (CFTs) we find the exact relation between the UV and geometric cutoff, which clarifies some subtle points in the previous literature. We clarify a subtle point of the additive linear combination (ALC) proposal for PEE in higher dimensions. The subset entanglement entropies in the ALC proposal should all be evaluated as a limit of the PEE while excluding a fixed class of local-short-distance correlation. Unlike the 2-dimensional configurations, naively plugging the entanglement entropy calculated with a UV cutoff will spoil the validity of the ALC proposal. We derive the entanglement contour function for spherical regions, annuli and spherical shells in the vacuum state of general-dimensional CFTs on a hyperplane. 

Abstract Long-duration GRB 200829A was detected by Fermi-GBM and Swift-BAT/XRT, and then rapidly observed by other ground-based telescopes. It has a weak γ -ray emission in the very early phase and is followed by a bright spiky γ -ray emission pulse. The radiation spectrum of the very early emission is best fitted by a power-law function with index ∼−1.7. However, the bright spiky γ -ray pulse, especially the time around the peak, exhibits a distinct two-component radiation spectrum, i.e., Band function combined with a blackbody radiation spectrum. We infer the photospheric properties and reveal a medium magnetization at a photospheric position by adopting the initial size of the outflow as r 0 = 10 9 cm. It implies that the Band component in this pulse may be formed during the dissipation of the magnetic field. The power-law radiation spectra found in the very early prompt emission may imply the external-shock origination of this phase. Then, we perform the Markov Chain Monte Carlo method fitting on the light curves of this burst, where the jet corresponding to the γ -ray pulse at around 20 s is used to refresh the external shock. It is shown that the light curves of the very early phase and X-ray afterglow after 40 s, involving the X-ray bump at around 100 s, can be well modeled in the external-shock scenario. For the obtained initial outflow, we estimate the minimum magnetization factor of the jet based on the fact that the photospheric emission of this jet is missed in the very early phase. 

Entanglement entropy satisfies a first law-like relation, whichequates the first order perturbation of the entanglement entropy for theregion A A to the first order perturbation of the expectation value of the modularHamiltonian, \delta S_{A}=\delta \langle K_A \rangle δ S A = δ ⟨ K A ⟩ .We propose that this relation has a finer version which states that, thefirst order perturbation of the entanglement contour equals to the firstorder perturbation of the contour of the modular Hamiltonian,i.e.  \delta s_{A}(\textbf{x})=\delta \langle k_{A}(\textbf{x})\rangle δ s A ( 𝐱 ) = δ ⟨ k A ( 𝐱 ) ⟩ .Here the contour functions s_{A}(\textbf{x}) s A ( 𝐱 ) and k_{A}(\textbf{x}) k A ( 𝐱 ) capture the contribution from the degrees of freedom at \textbf{x} 𝐱 to S_{A} S A and K_A K A respectively. In some simple cases k_{A}(\textbf{x}) k A ( 𝐱 ) is determined by the stress tensor. We also evaluate the quantumcorrection to the entanglement contour using the fine structure of theentanglement wedge and the additive linear combination (ALC) proposalfor partial entanglement entropy (PEE) respectively. The fine structurepicture shows that, the quantum correction to the boundary PEE can beidentified as a bulk PEE of certain bulk region. While the shows thatthe quantum correction to the boundary PEE comes from the linearcombination of bulk entanglement entropy. We focus on holographictheories with local modular Hamiltonian and configurations of quantumfield theories where the applies. 

Background The natural history of disease in patients infected with severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) remained obscure during the early pandemic. Aim Our objective was to estimate epidemiological parameters of coronavirus disease (COVID-19) and assess the relative infectivity of the incubation period. Methods We estimated the distributions of four epidemiological parameters of SARS-CoV-2 transmission using a large database of COVID-19 cases and potential transmission pairs of cases, and assessed their heterogeneity by demographics, epidemic phase and geographical region. We further calculated the time of peak infectivity and quantified the proportion of secondary infections during the incubation period. Results The median incubation period was 7.2 (95% confidence interval (CI): 6.9‒7.5) days. The median serial and generation intervals were similar, 4.7 (95% CI: 4.2‒5.3) and 4.6 (95% CI: 4.2‒5.1) days, respectively. Paediatric cases < 18 years had a longer incubation period than adult age groups (p = 0.007). The median incubation period increased from 4.4 days before 25 January to 11.5 days after 31 January (p < 0.001), whereas the median serial (generation) interval contracted from 5.9 (4.8) days before 25 January to 3.4 (3.7) days after. The median time from symptom onset to discharge was also shortened from 18.3 before 22 January to 14.1 days after. Peak infectivity occurred 1 day before symptom onset on average, and the incubation period accounted for 70% of transmission. Conclusion The high infectivity during the incubation period led to short generation and serial intervals, necessitating aggressive control measures such as early case finding and quarantine of close contacts.