The Fokker-Planck equation for bosons in 2D: Well-posedness and asymptotic behavior

We show that solutions of the 2D Fokker-Planck equation for bosons are defined globally in time and converge to equilibrium, and this convergence is shown to be exponential for radially symmetric solutions. The main observation is that a variant of the Hopf-Cole transformation relates the 2D equatio...

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Publicado:	2016
Materias:	Bose-Einstein Entropy method Long-time asymptotics Bosons Linear transformations Mathematical transformations Statistical mechanics Timing jitter Asymptotic behaviors Convergence to equilibrium Entropy functional Entropy methods Hopf-cole transformations Radially symmetric solution Fokker Planck equation
Acceso en línea:	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0362546X_v137_n_p291_Canizo http://hdl.handle.net/20.500.12110/paper_0362546X_v137_n_p291_Canizo
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

id	paper:paper_0362546X_v137_n_p291_Canizo
record_format	dspace
spelling	paper:paper_0362546X_v137_n_p291_Canizo2023-06-08T15:35:13Z The Fokker-Planck equation for bosons in 2D: Well-posedness and asymptotic behavior Bose-Einstein Entropy method Long-time asymptotics Bosons Linear transformations Mathematical transformations Statistical mechanics Timing jitter Asymptotic behaviors Bose-Einstein Convergence to equilibrium Entropy functional Entropy methods Hopf-cole transformations Long-time asymptotics Radially symmetric solution Fokker Planck equation We show that solutions of the 2D Fokker-Planck equation for bosons are defined globally in time and converge to equilibrium, and this convergence is shown to be exponential for radially symmetric solutions. The main observation is that a variant of the Hopf-Cole transformation relates the 2D equation in radial coordinates to the usual linear Fokker-Planck equation. Hence, radially symmetric solutions can be computed analytically, and our results for general (non radially symmetric) solutions follow from comparison and entropy arguments. In order to show convergence to equilibrium we also prove a version of the Csiszár-Kullback inequality for the Bose-Einstein-Fokker-Planck entropy functional. © 2015 Elsevier Ltd. All rights reserved. 2016 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0362546X_v137_n_p291_Canizo http://hdl.handle.net/20.500.12110/paper_0362546X_v137_n_p291_Canizo
institution	Universidad de Buenos Aires
institution_str	I-28
repository_str	R-134
collection	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic	Bose-Einstein Entropy method Long-time asymptotics Bosons Linear transformations Mathematical transformations Statistical mechanics Timing jitter Asymptotic behaviors Bose-Einstein Convergence to equilibrium Entropy functional Entropy methods Hopf-cole transformations Long-time asymptotics Radially symmetric solution Fokker Planck equation
spellingShingle	Bose-Einstein Entropy method Long-time asymptotics Bosons Linear transformations Mathematical transformations Statistical mechanics Timing jitter Asymptotic behaviors Bose-Einstein Convergence to equilibrium Entropy functional Entropy methods Hopf-cole transformations Long-time asymptotics Radially symmetric solution Fokker Planck equation The Fokker-Planck equation for bosons in 2D: Well-posedness and asymptotic behavior
topic_facet	Bose-Einstein Entropy method Long-time asymptotics Bosons Linear transformations Mathematical transformations Statistical mechanics Timing jitter Asymptotic behaviors Bose-Einstein Convergence to equilibrium Entropy functional Entropy methods Hopf-cole transformations Long-time asymptotics Radially symmetric solution Fokker Planck equation
description	We show that solutions of the 2D Fokker-Planck equation for bosons are defined globally in time and converge to equilibrium, and this convergence is shown to be exponential for radially symmetric solutions. The main observation is that a variant of the Hopf-Cole transformation relates the 2D equation in radial coordinates to the usual linear Fokker-Planck equation. Hence, radially symmetric solutions can be computed analytically, and our results for general (non radially symmetric) solutions follow from comparison and entropy arguments. In order to show convergence to equilibrium we also prove a version of the Csiszár-Kullback inequality for the Bose-Einstein-Fokker-Planck entropy functional. © 2015 Elsevier Ltd. All rights reserved.
title	The Fokker-Planck equation for bosons in 2D: Well-posedness and asymptotic behavior
title_short	The Fokker-Planck equation for bosons in 2D: Well-posedness and asymptotic behavior
title_full	The Fokker-Planck equation for bosons in 2D: Well-posedness and asymptotic behavior
title_fullStr	The Fokker-Planck equation for bosons in 2D: Well-posedness and asymptotic behavior
title_full_unstemmed	The Fokker-Planck equation for bosons in 2D: Well-posedness and asymptotic behavior
title_sort	fokker-planck equation for bosons in 2d: well-posedness and asymptotic behavior
publishDate	2016
url	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0362546X_v137_n_p291_Canizo http://hdl.handle.net/20.500.12110/paper_0362546X_v137_n_p291_Canizo
_version_	1768542084164222976

The Fokker-Planck equation for bosons in 2D: Well-posedness and asymptotic behavior

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