14 citations · 43 across the 10 of their papers we have counts for
13 papers
A Gauge-Covariant Semiclassical Limit from the magnetic Hartree--Fock equation to the magnetic Vlasov--Poisson equation
Jacky J. Chong, Zhuohui You
We study the semiclassical limit from the magnetic Hartree--Fock equation to the magnetic Vlasov--Poisson equation in three spatial dimensions in the presence of a nonuniform, pure…
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…
Kinetic localization via Poincaré-type inequalities and applications to the condensation of Bose gases
Jacky J. Chong, Hao Liang, Phan Thành Nam
We propose a simplified localization method for Bose gases, based on a Poincare-type inequality, which leads to a new derivation of Bose--Einstein condensation for dilute Bose gase…
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…
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…
Global uniform in estimates for solutions of a system of Hartree-Fock-Bogoliubov type in the case
Jacky Chong, Xin Dong, Manossos Grillakis +2
We extend the results of the 2019 paper by the third and fourth author globally in time. More precisely, we prove uniform in estimates for the solutions , and of a c…
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…
Global estimates for the Hartree-Fock-Bogoliubov equations
Jacky Jia Wei Chong, Manoussos G. Grillakis, Matei Machedon +1
We prove that certain Sobolev-type norms, slightly stronger than those given by energy conservation, stay bounded uniformly in time and . This allows one to extend the local exi…
Dynamical Hartree-Fock-Bogoliubov Approximation of Interacting Bosons
Jacky Jia Wei Chong, Zehua Zhao
We consider a many-body Boson system with pairwise particle interaction given by for and a non-negative spherically-symmetric function. Our main resul…
Uniform in Global Well-posedness of the Time-Dependent Hartree-Fock-Bogoliubov Equations in
Jacky J. Chong
In this article, we prove the global well-posedness of the time-dependent Hartree-Fock-Bogoliubov (TDHFB) equations in with two-body interaction potentials of th…
Dynamics of Large Boson Systems with Attractive Interaction and a Derivation of the Cubic Focusing NLS in
Jacky Jia Wei Chong
We consider a system of bosons where the particles experience a short range two-body interaction given by where ,…