Semiclassical analysis for Hartree equation

Semiclassical analysis for pseudo-relativistic Hartree equations

In this paper we study the semiclassical limit for the pseudo-relativistic Hartree equation √ −ε2∆ +m2u+ V u = (Iα ∗ |u|) |u|p−2u, in R , where m > 0, 2 ≤ p < 2N N−1 , V : R N → R is an external scalar potential, Iα(x) = cN,α |x|N−α is a convolution kernel, cN,α is a positive constant and (N − 1)p−N < α < N . For N = 3, α = p = 2, our equation becomes the pseudo-relativistic Hartree equation wi...

Semiclassical wave packet dynamics for Hartree equations

We study the propagation of wave packets for nonlinear nonlocal Schrödinger equations in the semi-classical limit. When the kernel is smooth, we construct approximate solutions for the wave functions in subcritical, critical and supercritical cases (in terms of the size of the initial data). The validity of the approximation is proved up to Ehrenfest time. For homogeneous kernels, we establish ...

A Semiclassical Hartree-fock Method

We present a semiclassical approach, the partial fi resummation method, to calculate nuclear ground state properties in a selfconsistent way starting from an effective nucleon-nucleon interaction. This method is shown to be easily generalized tu describe excited nuclear systems. Selfconsistent semiclassical densities can be further used as an optimal starting point for the calculation of nuclea...

Semiclassical Analysis for the Kramers–Fokker–Planck Equation

In certain applications one is interested in the long-time behavior of systems described by a linear partial differential equation. For example, in kinetic equations one studies the decay to equilibrium of various linear and nonlinear systems. For the Kramers–Fokker–Planck equation, which will be studied here, exponential decay was shown in Talay (1999) and an explicit rate was given in Hérau a...

Dirac's equation in semiclassical physics.