Momentum distribution and non-local high order correlation functions of 1D strongly interacting Bose gas

The Lieb-Liniger model is a prototypical integrable model and has been turned into the benchmark physics in theoretical and numerical investigations of low dimensional quantum systems. In this note, we present various methods for calculating local and nonlocal $M$-particle correlation functions, momentum distribution and static structure factor. In particular, using the Bethe ansatz wave function of the strong coupling Lieb-Liniger model, we analytically calculate two-point correlation function, the large moment tail of momentum distribution and static structure factor of the model in terms of the fractional statistical parameter $\alpha =1-2/\gamma$, where $\gamma$ is the dimensionless interaction strength. We also discuss the Tan's adiabatic relation and other universal relations for the strongly repulsive Lieb-Liniger model in term of the fractional statistical parameter.Comment: 17 pages, various methods for calculating high order correlation functions of the Lieb-Liniger mode

From the sinh-Gordon field theory to the one-dimensional Bose gas: exact local correlations and full counting statistics

We derive exact formulas for the expectation value of local observables in a one-dimensional gas of bosons with point-wise repulsive interactions (Lieb-Liniger model). Starting from a recently conjectured expression for the expectation value of vertex operators in the sinh-Gordon field theory, we derive explicit analytic expressions for the one-point K-body correlation functions \u27e8(\u3a8\u2020)K(\u3a8)K\u27e9 in the Lieb-Liniger gas, for arbitrary integer K. These are valid for all excited states in the thermodynamic limit, including thermal states, generalized Gibbs ensembles and non-equilibrium steady states arising in transport settings. Our formulas display several physically interesting applications: most prominently, they allow us to compute the full counting statistics for the particle-number fluctuations in a short interval. Furthermore, combining our findings with the recently introduced generalized hydrodynamics, we are able to study multi-point correlation functions at the Eulerian scale in non-homogeneous settings. Our results complement previous studies in the literature and provide a full solution to the problem of computing one-point functions in the Lieb Liniger model

Nebulized Recombinant Tissue Plasminogen Activator (rt-PA) for Acute COVID-19-Induced Respiratory Failure: An Exploratory Proof-of-Concept Trial

Acute lung injury in COVID-19 results in diffuse alveolar damage with disruption of the alveolar-capillary barrier, coagulation activation, alveolar fibrin deposition and pulmonary capillary thrombi. Nebulized recombinant tissue plasminogen activator (rt-PA) has the potential to facilitate localized thrombolysis in the alveolar compartment and improve oxygenation. In this proof-of-concept safety study, adults with COVID-19-induced respiratory failure and a <300 mmHg PaO2/FiO2 (P/F) ratio requiring invasive mechanical ventilation (IMV) or non-invasive respiratory support (NIRS) received nebulized rt-PA in two cohorts (C1 and C2), alongside standard of care, between 23 April–30 July 2020 and 21 January–19 February 2021, respectively. Matched historical controls (MHC; n = 18) were used in C1 to explore efficacy. Safety co-primary endpoints were treatment-related bleeds and <1.0–1.5 g/L fibrinogen reduction. A variable dosing strategy with clinical efficacy endpoint and minimal safety concerns was determined in C1 for use in C2; patients were stratified by ventilation type to receive 40–60 mg rt-PA daily for ≤14 days. Nine patients in C1 (IMV, 6/9; NIRS, 3/9) and 26 in C2 (IMV, 12/26; NIRS, 14/26) received nebulized rt-PA for a mean (SD) of 6.7 (4.6) and 9.1(4.6) days, respectively. Four bleeds (one severe, three mild) in three patients were considered treatment related. There were no significant fibrinogen reductions. Greater improvements in mean P/F ratio from baseline to study end were observed in C1 compared with MHC (C1; 154 to 299 vs. MHC; 154 to 212). In C2, there was no difference in the baseline P/F ratio of NIRS and IMV patients. However, a larger improvement in the P/F ratio occurred in NIRS patients (NIRS; 126 to 240 vs. IMV; 120 to 188) and fewer treatment days were required (NIRS; 7.86 vs. IMV; 10.5). Nebulized rt-PA appears to be well-tolerated, with a trend towards improved oxygenation, particularly in the NIRS group. Randomized clinical trials are required to demonstrate the clinical effect significance and magnitude

Nebulized Recombinant Tissue Plasminogen Activator (rt-PA) for Acute COVID-19-Induced Respiratory Failure: An Exploratory Proof-of-Concept Trial

Acute lung injury in COVID-19 results in diffuse alveolar damage with disruption of the alveolar-capillary barrier, coagulation activation, alveolar fibrin deposition and pulmonary capillary thrombi. Nebulized recombinant tissue plasminogen activator (rt-PA) has the potential to facilitate localized thrombolysis in the alveolar compartment and improve oxygenation. In this proof-of-concept safety study, adults with COVID-19-induced respiratory failure and a <300 mmHg PaO2/FiO2 (P/F) ratio requiring invasive mechanical ventilation (IMV) or non-invasive respiratory support (NIRS) received nebulized rt-PA in two cohorts (C1 and C2), alongside standard of care, between 23 April–30 July 2020 and 21 January–19 February 2021, respectively. Matched historical controls (MHC; n = 18) were used in C1 to explore efficacy. Safety co-primary endpoints were treatment-related bleeds and <1.0–1.5 g/L fibrinogen reduction. A variable dosing strategy with clinical efficacy endpoint and minimal safety concerns was determined in C1 for use in C2; patients were stratified by ventilation type to receive 40–60 mg rt-PA daily for ≤14 days. Nine patients in C1 (IMV, 6/9; NIRS, 3/9) and 26 in C2 (IMV, 12/26; NIRS, 14/26) received nebulized rt-PA for a mean (SD) of 6.7 (4.6) and 9.1(4.6) days, respectively. Four bleeds (one severe, three mild) in three patients were considered treatment related. There were no significant fibrinogen reductions. Greater improvements in mean P/F ratio from baseline to study end were observed in C1 compared with MHC (C1; 154 to 299 vs. MHC; 154 to 212). In C2, there was no difference in the baseline P/F ratio of NIRS and IMV patients. However, a larger improvement in the P/F ratio occurred in NIRS patients (NIRS; 126 to 240 vs. IMV; 120 to 188) and fewer treatment days were required (NIRS; 7.86 vs. IMV; 10.5). Nebulized rt-PA appears to be well-tolerated, with a trend towards improved oxygenation, particularly in the NIRS group. Randomized clinical trials are required to demonstrate the clinical effect significance and magnitude

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

Dimethyl fumarate (DMF) inhibits inflammasome-mediated inflammation and has been proposed as a treatment for patients hospitalised with COVID-19. This randomised, controlled, open-label platform trial (Randomised Evaluation of COVID-19 Therapy [RECOVERY]), is assessing multiple treatments in patients hospitalised for COVID-19 (NCT04381936, ISRCTN50189673). In this assessment of DMF performed at 27 UK hospitals, adults were randomly allocated (1:1) to either usual standard of care alone or usual standard of care plus DMF. The primary outcome was clinical status on day 5 measured on a seven-point ordinal scale. Secondary outcomes were time to sustained improvement in clinical status, time to discharge, day 5 peripheral blood oxygenation, day 5 C-reactive protein, and improvement in day 10 clinical status. Between 2 March 2021 and 18 November 2021, 713 patients were enroled in the DMF evaluation, of whom 356 were randomly allocated to receive usual care plus DMF, and 357 to usual care alone. 95% of patients received corticosteroids as part of routine care. There was no evidence of a beneficial effect of DMF on clinical status at day 5 (common odds ratio of unfavourable outcome 1.12; 95% CI 0.86-1.47; p = 0.40). There was no significant effect of DMF on any secondary outcome

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

Dimethyl fumarate (DMF) inhibits inflammasome-mediated inflammation and has been proposed as a treatment for patients hospitalised with COVID-19. This randomised, controlled, open-label platform trial (Randomised Evaluation of COVID-19 Therapy [RECOVERY]), is assessing multiple treatments in patients hospitalised for COVID-19 (NCT04381936, ISRCTN50189673). In this assessment of DMF performed at 27 UK hospitals, adults were randomly allocated (1:1) to either usual standard of care alone or usual standard of care plus DMF. The primary outcome was clinical status on day 5 measured on a seven-point ordinal scale. Secondary outcomes were time to sustained improvement in clinical status, time to discharge, day 5 peripheral blood oxygenation, day 5 C-reactive protein, and improvement in day 10 clinical status. Between 2 March 2021 and 18 November 2021, 713 patients were enroled in the DMF evaluation, of whom 356 were randomly allocated to receive usual care plus DMF, and 357 to usual care alone. 95% of patients received corticosteroids as part of routine care. There was no evidence of a beneficial effect of DMF on clinical status at day 5 (common odds ratio of unfavourable outcome 1.12; 95% CI 0.86-1.47; p = 0.40). There was no significant effect of DMF on any secondary outcome

One-particle density matrix of a trapped Lieb\u2013Liniger anyonic gas

We provide a thorough characterisation of the zero-temperature one-particle density matrix of trapped interacting anyonic gases in one dimension, exploiting recent advances in the field theory description of spatially inhomogeneous quantum systems. We first revisit homogeneous anyonic gases with point-wise interactions. In the harmonic Luttinger liquid expansion of the one-particle density matrix for finite interaction strength, the non-universal field amplitudes were not yet known. We extract them from the Bethe Ansatz formula for the field form factors, providing an exact asymptotic expansion of this correlation function, thus extending the available results in the Tonks\u2013Girardeau limit. Next, we analyse trapped gases with non-trivial density profiles. By applying recent analytic and numerical techniques for inhomogeneous Luttinger liquids, we provide exact expansions for the one-particle density matrix. We present our results for different confining potentials, highlighting the main differences with respect to bosonic gases