arXiv subjects

Gaia Marangon

Publications and source records attributed to Gaia Marangon.

2 recordsLinked to original sources

arXiv2026

From Klein-Gordon-Wave to Schrödinger-Wave: a Normal Form Approach

We consider a Klein-Gordon-Wave system, describing the evolution of a massive field and a massless one interacting through a Yukawa-like coupling, and we explicitly derive its Hamiltonian normal form to first and second order. To the first-order approximation, the normal form results in a Schrödinger-Wave system, which reduces to the Schrödinger-Poisson one in the singular limit of vanishing perturbative parameter. The second-order approximation provides the successive corrections to the Schrödinger-Wave system, and is presented in order to show that higher-order approximations to all orders can be obtained by iterating our constructive procedure. The normal form technique adopted here formally extends the standard Birkhoff normal form procedure for harmonic oscillators to include a set of free particles in the unperturbed problem. The mathematical result obtained here might explain, for example, the "cooling" process of ultra-light dark matter, the approximate validity of the Schrödinger-Poisson system describing its dynamics and the long term conservation of the total dark matter mass.

math-ph↗

arXiv2025

Scaling of highly excited Schrödinger-Poisson eigenstates and universality of their rotation curves

This work provides a comprehensive numerical characterization of the excited spherically symmetric stationary states of the Schrödinger-Poisson problem. Through numerical computation of highly excited eigenstates, novel heuristic laws are proposed, which describe how their fundamental features scale with the excitation index $n$. Key characteristics of the eigenfunctions include: the effective support, which exhibits a parabolic dependence on the excitation index; the distances between adjacent nodes, whose pattern varies regularly with $n$; and the oscillation amplitude, which follows a power law with an exponent approaching $-1$ for large $n$. Based on the eigenfunctions, eigenvelocities are conveniently defined. They exhibit a mid-range oscillatory region with an average linear trend, whose slope approaches zero in the large $n$ limit; and they are characterized by heuristic scaling relationships with the excitation index $n$, revealing an intrinsic universal behavior.

math-ph↗