arXiv subjects

Federica Pezzotti

Publications and source records attributed to Federica Pezzotti.

6 recordsLinked to original sources

arXiv2019

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 $α\in (0,1)$ or collide elastically with probability $1-α$. 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.

math-ph↗

arXiv2016

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.

math-ph↗

arXiv2011

Propagation of Chaos in a Coagulation Model

A deterministic coalescing dynamics with constant rate for a particle system in a finite volume with a fixed initial number of particles is considered. It is shown that, in the thermodynamic limit, with the constraint of fixed density, the corresponding coagulation equation is recovered and global in time propagation of chaos holds.

math-ph↗

arXiv2011

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.

cond-mat.quant-gas↗

arXiv2011

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.

math-ph↗

arXiv2008

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.

math-ph↗