68 citations · 577 across the 31 of their papers we have counts for
8 papers · 1 filter
The second order Huang-Yang approximation to the Fermi thermodynamic pressure
Xuwen Chen, Jiahao Wu, Zhifei Zhang
We consider a dilute Fermi gas in the thermodynamic limit with interaction potential scattering length at temperature . We prove the 2nd order Huang-Yang appr…
The second order Huang-Yang formula to the 3D Fermi gas: the Gross-Pitaevskii regime
Xuwen Chen, Jiahao Wu, Zhifei Zhang
For a system of Fermions of spin , with its interaction potential of scattering length , the classical Huang-Yang formula states that the energy density is of th…
The Second Order 2D Behaviors of a 3D Bose Gases in the Gross-Pitaevskii Regime
Xuwen Chen, Jiahao Wu, Zhifei Zhang
We consider a system of bosons interacting in a three-dimensional box endowed with periodic boundary condition that is strongly confined in one direction such that the normaliz…
The Derivation of the Boltzmann Equation from Quantum Many-body Dynamics
Xuwen Chen, Justin Holmer
We consider the quantum many-body dynamics at the weak-coupling scaling. We derive rigorously the quantum Boltzmann equation, which contains the classical hard sphere model and, ef…
On the Rigorous Derivation of the 3D Cubic Nonlinear Schrödinger Equation with A Quadratic Trap
Xuwen Chen
We consider the dynamics of the 3D N-body Schrödinger equation in the presence of a quadratic trap. We assume the pair interaction potential is N^{3β-1}V(N^{β}x). We justify the me…
Collapsing Estimates and the Rigorous Derivation of the 2d Cubic Nonlinear Schrödinger Equation with Anisotropic Switchable Quadratic Traps
Xuwen Chen
We consider the 2d and 3d many body Schrödinger equations in the presence of anisotropic switchable quadratic traps. We extend and improve the collapsing estimates in Klainerman-Ma…
Second order corrections to mean field evolution for weakly interacting Bosons in the case of 3-body interactions
Xuwen Chen
In this paper, we consider the Hamiltonian evolution of N weakly interacting Bosons. Assuming triple collisions, its mean field approximation is given by a quintic Hartree equation…
The Grillakis-Machedon-Margetis Second order corrections to mean field evolution for weakly interacting Bosons in the case of 3-body interactions
Xuwen Chen
This note shows that, with a little modification, the results in arXiv:0904.0158 hold in the 3-body interactions case.