54 citations · 237 across the 25 of their papers we have counts for
30 papers
Commutator Estimates for Low-Temperature Fermi Gases
Jacky J. Chong, Laurent Lafleche, Jinyeop Lee +1
We investigate the semiclassical regularity of thermal equilibria in the presence of a harmonic potential at low temperature; that is, we obtain the asymptotic behavior of the Scha…
The Semi-Classical Limit from the Dirac Equation with Time-Dependent External Electromagnetic Field to Relativistic Vlasov Equations
François Golse, Nikolai Leopold, Norbert J. Mauser +2
We prove the mathematically rigorous (semi-)classical limit of the Dirac equation with time-dependent external electromagnetic field to relativistic Vlasov equations…
Diffusion Limit of the Low-Density Magnetic Lorentz Gas
Alessia Nota, Dominik Nowak, Chiara Saffirio
We consider the magnetic Lorentz gas proposed by Bobylev et al. [4], which describes a point particle moving in a random distribution of hard-disk obstacles in under…
Semiclassical Limit of the Bogoliubov-de Gennes Equation
Jacky J. Chong, Laurent Lafleche, Chiara Saffirio
In this paper, we rewrite the time-dependent Bogoliubov$\unicode{x2013}$de Gennes equation in an appropriate semiclassical form and establish its semiclassical limit to a two-parti…
Derivation of the Vlasov-Maxwell system from the Maxwell-Schrödinger equations with extended charges
Nikolai Leopold, Chiara Saffirio
We consider the Maxwell-Schrödinger equations in the Coulomb gauge describing the interaction of extended fermions with their self-generated electromagnetic field. They heuristical…
Weakly interacting Fermions: mean-field and semiclassical regimes
Chiara Saffirio
The derivation of effective macroscopic theories approximating microscopic systems of interacting particles is a major question in non-equilibrium statistical mechanics. In these n…
Existence and stability of weak solutions of the Vlasov--Poisson system in localized Yudovich spaces
Gianluca Crippa, Marco Inversi, Chiara Saffirio +1
We consider the Vlasov--Poisson system both in the repulsive (electrostatic potential) and in the attractive (gravitational potential) cases. In our first main theorem, we prove th…
Uniqueness criteria for the Vlasov--Poisson system and applications to semiclassical analysis
Laurent Lafleche, Chiara Saffirio
We review some uniqueness criteria for the Vlasov--Poisson system, emerging as corollaries of stability estimates in strong or weak topologies, and show how they serve as a guideli…
On the semiclassical regularity of thermal equilibria
Jacky J. Chong, Laurent Lafleche, Chiara Saffirio
We study the regularity properties of fermionic equilibrium states at finite positive temperature and show that they satisfy certain semiclassical bounds. As a corollary, we identi…
On the Rate of Convergence in the Limit from the Hartree to the Vlasov$\unicode{x2013}$Poisson Equation
Jacky J. Chong, Laurent Lafleche, Chiara Saffirio
Using a new stability estimate for the difference of the square roots of two solutions of the Vlasov$\unicode{x2013}$Poisson equation, we obtain the convergence in the norm o…
Propagation of moments for large data and semiclassical limit to the relativistic Vlasov equation
Nikolai Leopold, Chiara Saffirio
We investigate the semiclassical limit from the semi-relativistic Hartree-Fock equation describing the time evolution of a system of fermions in the mean-field regime with a relati…
Global-in-time Semiclassical Regularity for the Hartree-Fock Equation
Jacky J. Chong, Laurent Lafleche, Chiara Saffirio
For arbitrarily large times , we prove the uniform-in- propagation of semiclassical regularity for the solutions to the Hartree$\unicode{x2013}$Fock equation with singu…
From many-body quantum dynamics to the Hartree-Fock and Vlasov equations with singular potentials
Jacky J. Chong, Laurent Lafleche, Chiara Saffirio
We obtain the combined mean-field and semiclassical limit from the -body Schrödinger equation for fermions interacting via singular potentials. To obtain the result, we first pr…
From the Hartree to the Vlasov dynamics: conditional strong convergence
Chiara Saffirio
We review the recent results [45, 46] concerning the semiclassical limit from the Hartree dynamics to the Vlasov equation with singular potentials and extend them to the case of mo…
Strong semiclassical limit from Hartree and Hartree-Fock to Vlasov-Poisson equation
Laurent Lafleche, Chiara Saffirio
We consider the semiclassical limit from the Hartree to the Vlasov equation with general singular interaction potential including the Coulomb and gravitational interactions, and we…
Two-dimensional Lorentz process for magnetotransport: Boltzmann-Grad limit
Alessia Nota, Chiara Saffirio, Sergio Simonella
We study a system of charged, noninteracting classical particles moving in a Poisson distribution of hard-disk scatterers in two dimensions, under the effect of a magnetic field pe…
Semiclassical limit to the Vlasov equation with inverse power law potentials
Chiara Saffirio
We consider mixed quasi-free states describing fermions in the mean-field limit. In this regime, the time evolution is governed by the nonlinear Hartree equation. In the large…
From the Hartree equation to the Vlasov-Poisson system: strong convergence for a class of mixed states
Chiara Saffirio
We consider the evolution of fermions interacting through a Coulomb or gravitational potential in the mean-field limit as governed by the nonlinear Hartree equation with Coulom…
Mean-field evolution of fermions with singular interaction
Chiara Saffirio
We consider a system of N fermions in the mean-field regime interacting though an inverse power law potential , for . We prove the convergence of a solutio…
Lagrangian solutions to the Vlasov-Poisson system with a point charge
Gianluca Crippa, Silvia Ligabue, Chiara Saffirio
We consider the Cauchy problem for the repulsive Vlasov-Poisson system in the three dimensional space, where the initial datum is the sum of a diffuse density, assumed to be bounde…
Mean field evolution of fermions with Coulomb interaction
Marcello Porta, Simone Rademacher, Chiara Saffirio +1
We study the many body Schrödinger evolution of weakly coupled fermions interacting through a Coulomb potential. We are interested in a joint mean field and semiclassical scaling,…
Derivation of the Boltzmann equation: hard spheres, short-range potentials and beyond
Chiara Saffirio
We review some results concerning the derivation of the Boltzmann equation starting from the many-body classical Hamiltonian dynamics. In particular, the celebrated paper by O. E.…
From the Hartree dynamics to the Vlasov equation
Niels Benedikter, Marcello Porta, Chiara Saffirio +1
We consider the evolution of quasi-free states describing fermions in the mean field limit, as governed by the nonlinear Hartree equation. In the limit of large , we study t…
Weak dependence for a class of local functionals of Markov chains on
Carlo Boldrighini, Antonella Marchesiello, Chiara Saffirio
In some papers on infinite Markov chains in , and notably in the work of R.A. Minlos and collaborators, one can prove the existence of a spectral gap for a suitable s…