Datum
2023-05Autor
Ávila, Andrés I.Schlagwort
004 Informatik 510 Mathematik 530 Physik QuantenmechanikAtomNumerisches VerfahrenBerechnungMetadata
Zur Langanzeige
Habilitation
Computing Ground States for Fermi-Bose Mixtures through Efficient Numerical Methods
Zusammenfassung
In this work, we will first review the Quantum Mechanics theory to derive the main equations. Next, we will analyze these equations by Functional Analysis methods to find conditions for existence, uniqueness, multiplicity, and other properties as positivity. Next, we will review and develop some numerical methods for solving the nonlinear Schrödinger equation, its time version, generalizations with rotational terms, and systems of NLSE (NLSS). We notice that the main problem to run numerical methods is the memory use, which can be a bottleneck for simulations involving very large linear systems. Finally, we will address this problem of Computing Efficiency and learn some techniques and tools to understand code behavior and memory use to improve our methods and study the effect of using numerical libraries.
Zitieren
@phdthesis{doi:10.17170/kobra-202305138021,
author={Ávila, Andrés I.},
title={Computing Ground States for Fermi-Bose Mixtures through Efficient Numerical Methods},
school={Kassel, Universität Kassel, Fachbereich Mathematik und Naturwissenschaften},
month={05},
year={2023}
}
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2023-07-10T11:38:08Z 2023-07-10T11:38:08Z 2023-05 doi:10.17170/kobra-202305138021 http://hdl.handle.net/123456789/14884 eng Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/ Nonlinear Function Analysis Cold Atoms Quantum Mechanics Numerical Methods Computational Efficiency 004 510 530 Computing Ground States for Fermi-Bose Mixtures through Efficient Numerical Methods Habilitation In this work, we will first review the Quantum Mechanics theory to derive the main equations. Next, we will analyze these equations by Functional Analysis methods to find conditions for existence, uniqueness, multiplicity, and other properties as positivity. Next, we will review and develop some numerical methods for solving the nonlinear Schrödinger equation, its time version, generalizations with rotational terms, and systems of NLSE (NLSS). We notice that the main problem to run numerical methods is the memory use, which can be a bottleneck for simulations involving very large linear systems. Finally, we will address this problem of Computing Efficiency and learn some techniques and tools to understand code behavior and memory use to improve our methods and study the effect of using numerical libraries. open access Ávila, Andrés I. 2021-11-10 237 Seiten Kassel, Universität Kassel, Fachbereich Mathematik und Naturwissenschaften Meister, Andreas (Prof. Dr.) Quantenmechanik Atom Numerisches Verfahren Berechnung publishedVersion false
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