arXiv subjects

Marnie Smith

Publications and source records attributed to Marnie Smith.

3 recordsLinked to original sources

arXiv2026

The uniform-in-time electrostatic limit of the linearised Vlasov-Maxwell system: the Poisson equilibrium

The Vlasov-Maxwell system with Newtonian particle transport is linearised about the Poisson equilibrium on $\mathbb{R}^3$, with the speed of light $c$ treated as a large parameter. For uniformly controlled initial data, with transverse fields that may remain of order one, the difference between the Vlasov-Maxwell perturbation and its linearised Vlasov-Poisson counterpart is bounded uniformly in time by their initial discrepancy plus a term of order $c^{-1}$. The same estimate holds for their scattering states, and the rate in $c$ is sharp. The longitudinal dynamics are governed by the same Volterra equation as in linearised Vlasov-Poisson and undergo Landau damping. The transverse fields exhibit Klein-Gordon-type dispersion, and control of their accumulated effect along free transport yields the uniform comparison.

math.AP↗

arXiv2026

Phase mixing for the Hartree equation and Landau damping in the semiclassical limit

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, phase-mixing estimates in finite regularity are established. These demonstrate density decay and scattering of solutions in weighted quantum Sobolev spaces, providing a quantum analogue of Landau damping in classical plasma physics. The results hold uniformly in the semiclassical limit, thereby bridging the quantum and classical regimes.

math.AP↗

arXiv2026

The semiclassical limit from Hartree to Vlasov at positive density: strong uniform-in-time convergence and scattering

Strong semiclassical convergence from the Hartree equation to the Vlasov equation is established in three dimensions near Penrose-stable homogeneous steady states at positive density. For sufficiently regular integrable interaction kernels, an $O(\hbar^2)$ convergence rate in weighted Sobolev spaces is proved on finite time intervals. Combining this estimate with earlier uniform-in-$\hbar$ phase-mixing and scattering bounds for the Hartree equation yields global existence and scattering for the corresponding Vlasov solution through the semiclassical limit. If the quantum and classical initial perturbations are aligned, the semiclassical convergence is uniform for all times, and the Wigner transforms of the quantum scattering profiles converge to the classical scattering profile at the explicit rate $O((\ln\hbar^{-1})^{-1/3})$.

math.AP↗