The Whitham approach to Generalized Hydrodynamics

The formation of dispersive shock waves in the one-dimensional Bose gas represents a limitation of Generalized Hydrodynamics (GHD) due to the coarse-grained nature of the theory. Nevertheless, GHD accurately captures the long wavelength behavior indicating an implicit knowledge of the underlying microscopic physics. Such representation are already known through the Whitham modulation theory, where dispersion-less equations describe the evolution of the slowly varying shock wave parameters. Here we study the correspondence between Whithams approach to the Gross-Pitaevskii equation and GHD in the semi-classical limit. Our findings enable the recovery of the shock wave solution directly from GHD simulations, which we demonstrate for both zero and finite temperature. Additionally, we study how free expansion protocols affect the shock wave density and their implications for experimental detection. The combined picture of Whitham and GHD lends itself to additional physical interpretation regarding the formation of shock waves. Further, this picture exhibits clear analogies to the theory of Quantum GHD, and we discuss possible routes to establish an explicit connection between them.Comment: 17 pages, 9 figure

Nationwide study on SARS-CoV-2 transmission within households from lockdown to reopening, Denmark, 27 February 2020 to 1 August 2020

BACKGROUND: The COVID-19 pandemic is one of the most serious global public health threats of recent times. Understanding SARS-CoV-2 transmission is key for outbreak response and to take action against the spread of disease. Transmission within the household is a concern, especially because infection control is difficult to apply within this setting. AIM: The objective of this observational study was to investigate SARS-CoV-2 transmission in Danish households during the early stages of the COVID-19 pandemic. METHODS: We used comprehensive administrative register data from Denmark, comprising the full population and all COVID-19 tests from 27 February 2020 to 1 August 2020, to estimate household transmission risk and attack rate. RESULTS: We found that the day after receiving a positive test result within the household, 35% (788/2,226) of potential secondary cases were tested and 13% (98/779) of these were positive. In 6,782 households, we found that 82% (1,827/2,226) of potential secondary cases were tested within 14 days and 17% (371/2,226) tested positive as secondary cases, implying an attack rate of 17%. We found an approximate linear increasing relationship between age and attack rate. We investigated the transmission risk from primary cases by age, and found an increasing risk with age of primary cases for adults (aged ≥ 15 years), while the risk seems to decrease with age for children (aged < 15 years). CONCLUSIONS: Although there is an increasing attack rate and transmission risk of SARS-CoV-2 with age, children are also able to transmit SARS-CoV-2 within the household