Mean-field limit and Semiclassical Expansion of a Quantum Particle System

We consider a quantum system constituted by $N$ identical particles interacting by means of a mean-field Hamiltonian. It is well known that, in the limit $N\to\infty$, the one-particle state obeys to the Hartree equation. Moreover, propagation of chaos holds. In this paper, we take care of the $\hbar$ dependence by considering the semiclassical expansion of the $N$-particle system. We prove that each term of the expansion agrees, in the limit $N\to\infty$, with the corresponding one associated with the Hartree equation. We work in the classical phase space by using the Wigner formalism, which seems to be the most appropriate for the present problem.Comment: 44 pages, no figure

A Kac model for kinetic annihilation

In this paper we consider the stochastic dynamics of a finite system of particles in a finite volume (Kac-like particle system) which annihilate with probability $\alpha \in (0,1)$ or collide elastically with probability $1-\alpha$. We first establish the well-posedness of the particle system which exhibits no conserved quantities. We rigorously prove that, in some thermodynamic limit, a suitable hierarchy of kinetic equations is recovered for which tensorized solution to the homogenous Boltzmann with annihilation is a solution. For bounded collision kernels, this shows in particular that propagation of chaos holds true. Furthermore, we make conjectures about the limit behaviour of the particle system when hard-sphere interactions are taken into account.Comment: 40 page

Derivation of the Fick's Law for the Lorentz Model in a low density regime

We consider the Lorentz model in a slab with two mass reservoirs at the boundaries. We show that, in a low density regime, there exists a unique stationary solution for the microscopic dynamics which converges to the stationary solution of the heat equation, namely to the linear profile of the density. In the same regime the macroscopic current in the stationary state is given by the Fick's law, with the diffusion coefficient determined by the Green-Kubo formula.Comment: 33 pages, 7 figure

Analytical approach to relaxation dynamics of condensed Bose gases

The temporal evolution of a perturbation of the equilibrium distribution of a condensed Bose gas is investigated using the kinetic equation which describes collision between condensate and noncondensate atoms. The dynamics is studied in the low momentum limit where an analytical treatment is feasible. Explicit results are given for the behavior at large times in different temperature regimes.Comment: 25 pages, 3 figures. Typos corrected. Final version to appear in Annals of Physic

Semiclassical Propagation of Coherent States for the Hartree equation

In this paper we consider the nonlinear Hartree equation in presence of a given external potential, for an initial coherent state. Under suitable smoothness assumptions, we approximate the solution in terms of a time dependent coherent state, whose phase and amplitude can be determined by a classical flow. The error can be estimated in $L^2$ by C \sqrt {\var}, \var being the Planck constant. Finally we present a full formal asymptotic expansion

Diagnosis of Imported Dengue and Zika Virus Infections in Italy from November 2015 to November 2022: Laboratory Surveillance Data from a National Reference Laboratory

Dengue (DENV) and Zika (ZIKV) viruses are mosquito-borne human pathogens. In Italy, the presence of the competent vector Aedes albopictus increases the risk of autochthonous transmission, and a national plan for arboviruses prevention, surveillance, and response (PNA 2020–2025) is in place. The results of laboratory diagnosis of both viruses by the National Reference Laboratory for arboviruses (NRLA) from November 2015 to November 2022 are presented. Samples from 655 suspected cases were tested by both molecular and serological assays. Virus and antibody kinetics, cross-reactivity, and diagnostic performance of IgM ELISA systems were analysed. Of 524 cases tested for DENV, 146 were classified as confirmed, 7 as probable, while 371 were excluded. Of 619 cases tested for ZIKV, 44 were classified as confirmed, while 492 were excluded. All cases were imported. Overall, 75.3% (110/146) of DENV and 50% (22/44) of ZIKV cases were confirmed through direct virus detection methods. High percentages of cross reactivity were observed between the two viruses. The median lag time from symptoms onset to sample collection was 7 days for both DENV molecular (range 0–20) and NS1 ELISA (range 0–48) tests, with high percentages of positivity also after 7 days (39% and 67%, respectively). For ZIKV, the median lag time was 5 days (range 0–22), with 16% positivity after 7 days. Diagnostic performance was assessed with negative predictive values ranging from 92% to 95% for the anti-DENV systems, and of 97% for the ZIKV one. Lower positive predictive values were seen in the tested population (DENV: 55% to 91%, ZIKV: 50%). DENV and ZIKV diagnosis by molecular test is the gold standard, but sample collection time is a limitation. Serological tests, including Plaque Reduction Neutralization Test, are thus necessary. Co-circulation and cross-reactivity between the two viruses increase diagnostic difficulty. Continuous evaluation of diagnostic strategies is essential to improve laboratory testing

Measurement of the inclusive isolated-photon cross section in pp collisions at √s = 13 TeV using 36 fb−1 of ATLAS data

The differential cross section for isolated-photon production in pp collisions is measured at a centre-of-mass energy of 13 TeV with the ATLAS detector at the LHC using an integrated luminosity of 36.1 fb. The differential cross section is presented as a function of the photon transverse energy in different regions of photon pseudorapidity. The differential cross section as a function of the absolute value of the photon pseudorapidity is also presented in different regions of photon transverse energy. Next-to-leading-order QCD calculations from Jetphox and Sherpa as well as next-to-next-to-leading-order QCD calculations from Nnlojet are compared with the measurement, using several parameterisations of the proton parton distribution functions. The predictions provide a good description of the data within the experimental and theoretical uncertainties. [Figure not available: see fulltext.

A Kac model for fermions

We introduce a stochastic $N$-particle system and show that, as $N\to \infty$, an effective description ruled by the homogeneous fermionic Uehling-Uhlenbeck equation is recovered. The particle model we consider is the same as the Kac model for the homogeneous Boltzmann equation with an additional exclusion constraint taking into account the Pauli Exclusion Principle.Comment: 46 page