相关论文: Phase mixing estimates for the nonlinear Hartree e…

The asymptotic behaviour of the Hartree equation is studied near translation-invariant steady states. For short-range interaction kernels satisfying a uniform Penrose stability condition, including the screened Coulomb interaction,…

In this paper, we establish derivative estimates for the Vlasov-Poisson system with screening interactions around Penrose-stable equilibria on the phase space $\mathbb{R}^d_x\times \mathbb{R}_v^d$, with dimension $d\ge 3$. In particular, we…

The formalism for exactly calculating the retarded and advanced Green's functions of strongly correlated lattice models in a uniform electric field is derived within dynamical mean-field theory. To illustrate the method, we solve for the…

We prove a scattering result near certain steady states for a Hartree equation for a random field. This equation describes the evolution of a system of infinitely many particles. It is an analogous formulation of the usual Hartree equation…

An efficient implementation of the nonequilibrium Green function (NEGF) method combined with the density functional theory (DFT) using localized pseudo-atomic orbitals (PAOs) is presented for electronic transport calculations of a system…

We prove quantitative estimates on the the parabolic Green function and the stationary invariant measure in the context of stochasic homogenization of elliptic equations in nondivergence form. We consequently obtain a quenched, local CLT…

In this paper, we consider the Hartree equation with smooth but long-range interaction in the semi-classical regime, in three-dimensional space. We show that the density function of small-data solution decays at the optimal rate. When the…

We study the dynamics of perturbations around an inhomogeneous stationary state of the Vlasov-HMF (Hamiltonian Mean-Field) model, satisfying a linearized stability criterion (Penrose criterion). We consider solutions of the linearized…

Consider the linear transport equation in $1$D under an external confining potential $\Phi$: \begin{equation*} \partial_t f + v \partial_x f - \partial_x \Phi \partial_v f = 0. \end{equation*} For $\Phi = \frac{x^2}{2} + \frac{\epsilon…

We carry out a comprehensive linear stability analysis of active Brownian particle systems around a constant homogeneous state. These scalar models, being important prototypes for the continuous description of active matter, are…

The UV/IR mixing in the \lambda \phi^4 model on a non-commutative (NC) space leads to new predictions in perturbation theory, including Hartree-Fock type approximations. Among them there is a changed phase diagram and an unusual behavior of…

This paper investigates quantitative estimates in elliptic homogenization of non-divergence form with unbounded drift and an interface, which continues the study of the previous work by Hairer and Manson [Ann. Probab. 39(2011) 648-682],…

We consider a Hartree equation for a random variable, which describes the temporal evolution of infinitely many Fermions. On the Euclidean space, this equation possesses equilibria which are not localised. We show their stability through a…

We study mixed finite element methods for the rotating shallow water equations with linearized momentum terms but nonlinear drag. By means of an equivalent second-order formulation, we prove long-time stability of the system without energy…

This paper presents a novel approach for estimating the modes of an observed non-stationary mixture signal. A link is first established between the short-time Fourier transform and the sparse sampling theory, where the observations are…

We study solutions of the collisionless Boltzmann equation (CBE) in a functional Koopman representation. This facilitates the use of linear spectral techniques characteristic of the analysis of Schrodinger-type equations. For illustrative…

We present a new proof of global existence and long range scattering, from small initial data, for the one-dimensional cubic gauge invariant nonlinear Schr\"odinger equation, and for Hartree equations in dimension $n \geq 2$. The proof…

We present a method to perform stability analysis of nonequilibrium fixed points appearing in self-consistent electron transport calculations. The nonequilibrium fixed points are given by the self-consistent solution of stationary,…

In this paper, we present a series of applications of the pointwise estimates of the (unrestricted) Green tensor of the nonstationary Stokes system in the half space, established in our previous work [CMP 2023]. First, we show the…

We consider nonlinear Schr\"odinger equation with a Hartree-type nonlocal nonlinearity. The case where a nonlinear interaction potential grows at the spatial infinity is studied. By virtue of an effective decomposition of the nonlinearity…