On Deterministic Numerical Methods for the ...
Type de document :
Compte-rendu et recension critique d'ouvrage
Titre :
On Deterministic Numerical Methods for the quantum Boltzmann-Nordheim Equation. I. Spectrally accurate approximations, Bose-Einstein condensation, Fermi-Dirac saturation
Auteur(s) :
Mouton, Alexandre [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Rey, Thomas [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Reliable numerical approximations of dissipative systems [RAPSODI ]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Rey, Thomas [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Reliable numerical approximations of dissipative systems [RAPSODI ]
Titre de la revue :
Journal of Computational Physics
Pagination :
112197
Éditeur :
Elsevier
Date de publication :
2023-09
ISSN :
0021-9991
Mot(s)-clé(s) en anglais :
large time behavior
spectral method
Fermi-Dirac saturation
Bose-Einstein condensation
quantum
Boltzmann-Nordheim equation
spectral method
Fermi-Dirac saturation
Bose-Einstein condensation
quantum
Boltzmann-Nordheim equation
Discipline(s) HAL :
Mathématiques [math]/Analyse numérique [math.NA]
Résumé en anglais : [en]
Spectral methods, thanks to their high accuracy and the possibility to use fast algorithms, represent an effective way to approximate the collisional kinetic equations of Boltzmann type, such as the Boltzmann-Nordheim ...
Lire la suite >Spectral methods, thanks to their high accuracy and the possibility to use fast algorithms, represent an effective way to approximate the collisional kinetic equations of Boltzmann type, such as the Boltzmann-Nordheim equation. This equation, modeled on the seminal Boltzmann equation, describes using a statistical physics formalism the time evolution of a gas composed of bosons or fermions. Using the spectral-Galerkin algorithm introduced in [F. Filbet, J. Hu, and S. Jin, ESAIM: Math. Model. Numer. Anal., 2011], together with some novel parallelization techniques, we investigate some of the conjectured properties of the large time behavior of the solutions to this equation. In particular, we are able to observe numerically both Bose-Einstein condensation and Fermi-Dirac relaxation.Lire moins >
Lire la suite >Spectral methods, thanks to their high accuracy and the possibility to use fast algorithms, represent an effective way to approximate the collisional kinetic equations of Boltzmann type, such as the Boltzmann-Nordheim equation. This equation, modeled on the seminal Boltzmann equation, describes using a statistical physics formalism the time evolution of a gas composed of bosons or fermions. Using the spectral-Galerkin algorithm introduced in [F. Filbet, J. Hu, and S. Jin, ESAIM: Math. Model. Numer. Anal., 2011], together with some novel parallelization techniques, we investigate some of the conjectured properties of the large time behavior of the solutions to this equation. In particular, we are able to observe numerically both Bose-Einstein condensation and Fermi-Dirac relaxation.Lire moins >
Langue :
Anglais
Vulgarisation :
Non
Projet ANR :
Collections :
Source :
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