Construction of Ground-State Solutions of the Gross–Pitaevskii–Poisson System Using Genetic Algorithms

We present the construction of the ground state of the Gross–Pitaevskii–Poisson equations using genetic algorithms. By employing numerical solutions, we develop an empirical formula for the density that works within the considered parameter space. Through the analysis of both numerical and empirical...

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Bibliographic Details
Published in:Universe (Basel) 2024-08, Vol.10 (8), p.309
Main Authors: Tena-Contreras, Carlos, Alvarez-Ríos, Iván, Guzmán, Francisco S.
Format: Article
Language:English
Subjects:
Algorithms
Bose condensates
Boundary conditions
Dark matter
Eigenvalues
Electrons
Genetic algorithms
Numerical analysis
self-gravitating systems
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Summary:We present the construction of the ground state of the Gross–Pitaevskii–Poisson equations using genetic algorithms. By employing numerical solutions, we develop an empirical formula for the density that works within the considered parameter space. Through the analysis of both numerical and empirical solutions, we investigate the stability of these ground-state solutions. Our findings reveal that while the numerical solution outperforms the empirical formula, both solutions lead to similar oscillation modes. We observe that the stability of the solutions depends on specific values of the central density and the nonlinear self-interaction term and establish an empirical criterion delineating the conditions under which the solutions exhibit stability or instability.
ISSN:2218-1997
2218-1997
DOI:10.3390/universe10080309