Solving the Schrodinger Poisson System using the coordinate Adaptive Moving Mesh method

TL;DR

This paper introduces an adaptive moving mesh method to efficiently solve the Schrödinger-Poisson system, enabling dynamic resolution adjustment for complex quantum and astrophysical simulations.

Contribution

The paper adapts the coordinate-based AMM to the Schrödinger-Poisson system, demonstrating its effectiveness on test problems and dark matter scenarios.

Findings

Successfully solves stationary Schrödinger-Poisson problems.

Enables dynamic resolution in complex astrophysical simulations.

Improves computational efficiency for quantum systems.

Abstract

In this paper, we implement the Adaptive Moving Mesh method (AMM) to the solution of initial value problems involving the Schr\"odinger equation, and more specifically the Schr\"odinger-Poisson system of equations. This method is based on the solution of the problem on a discrete domain, whose resolution is coordinate and time-dependent, and allows to dynamically assign numerical resolution in terms of desired refinement criteria. We apply the method to solve various test problems involving stationary solutions of the SP system, and toy scenarios related to the disruption of subhalo s made of ultralight bosonic dark matter traveling on top of host galaxies.