Construction and evolution of equilibrium configurations of the Schr\"odinger-Poisson system in the Madelung frame

TL;DR

This paper constructs and analyzes equilibrium configurations of the Schr"odinger-Poisson system in the Madelung frame, comparing their evolution and conservation properties using finite volume methods.

Contribution

It introduces a method to construct ground state configurations in the Madelung frame and compares their evolution with traditional SP formulations.

Findings

Equilibrium configurations are successfully constructed in the Madelung frame.

Conservation of mass and energy is analyzed during evolution.

Numerical issues in the Madelung frame are discussed.

Abstract

We present the construction of ground state equilibrium configurations of the Schr\"odinger-Poisson (SP) system in the Madelung frame and evolve such configuration using finite volume methods. We compare the behavior of these configurations when evolved within the SP and Madelung frames, in terms of conservation of mass and energy. We also discuss the issues of the equations in the Madelung frame and others inherent to the numerical methods used to solve them.