Vortex formation in a two-dimensional Bose gas

We discuss the stability of a homogeneous two-dimensional Bose gas at finite temperature against the formation of isolated vortices. We consider a patch of several healing lengths in size and compute its free energy using the Euclidean formalism. Since we deal with an open system, which is able to e...

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Autor principal:	Calzetta, Esteban Adolfo
Publicado:	2010
Materias:	Berezinskii-Kosterlitz-Thouless transition Bose gas Dilute gas Euclidean Finite temperatures Imaginary parts Particle numbers Partition functions Positive definite Symmetry-breaking Vortex formation Angular momentum Bosons Electron energy analyzers Free energy Open systems Two dimensional Vortex flow Gases
Acceso en línea:	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_09534075_v43_n9_p_Calzetta http://hdl.handle.net/20.500.12110/paper_09534075_v43_n9_p_Calzetta
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

id	paper:paper_09534075_v43_n9_p_Calzetta
record_format	dspace
spelling	paper:paper_09534075_v43_n9_p_Calzetta2023-06-08T15:55:17Z Vortex formation in a two-dimensional Bose gas Calzetta, Esteban Adolfo Berezinskii-Kosterlitz-Thouless transition Bose gas Dilute gas Euclidean Finite temperatures Imaginary parts Particle numbers Partition functions Positive definite Symmetry-breaking Vortex formation Angular momentum Bosons Electron energy analyzers Free energy Open systems Two dimensional Vortex flow Gases We discuss the stability of a homogeneous two-dimensional Bose gas at finite temperature against the formation of isolated vortices. We consider a patch of several healing lengths in size and compute its free energy using the Euclidean formalism. Since we deal with an open system, which is able to exchange particles and angular momentum with the rest of the condensate, we use the symmetry-breaking (as opposed to the particle number conserving) formalism, and include configurations with all values of angular momenta in the partition function. At finite temperature, there appear sphaleron configurations associated with isolated vortices. The contribution from these configurations to the free energy is computed in the dilute gas approximation. We show that the Euclidean action of linearized perturbations of a vortex is not positive definite. As a consequence the free energy of the 2D Bose gas acquires an imaginary part. This signals the instability of the gas. This instability may be identified with the Berezinskii-Kosterlitz-Thouless transition. © 2010 IOP Publishing Ltd. Fil:Calzetta, E. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2010 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_09534075_v43_n9_p_Calzetta http://hdl.handle.net/20.500.12110/paper_09534075_v43_n9_p_Calzetta
institution	Universidad de Buenos Aires
institution_str	I-28
repository_str	R-134
collection	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic	Berezinskii-Kosterlitz-Thouless transition Bose gas Dilute gas Euclidean Finite temperatures Imaginary parts Particle numbers Partition functions Positive definite Symmetry-breaking Vortex formation Angular momentum Bosons Electron energy analyzers Free energy Open systems Two dimensional Vortex flow Gases
spellingShingle	Berezinskii-Kosterlitz-Thouless transition Bose gas Dilute gas Euclidean Finite temperatures Imaginary parts Particle numbers Partition functions Positive definite Symmetry-breaking Vortex formation Angular momentum Bosons Electron energy analyzers Free energy Open systems Two dimensional Vortex flow Gases Calzetta, Esteban Adolfo Vortex formation in a two-dimensional Bose gas
topic_facet	Berezinskii-Kosterlitz-Thouless transition Bose gas Dilute gas Euclidean Finite temperatures Imaginary parts Particle numbers Partition functions Positive definite Symmetry-breaking Vortex formation Angular momentum Bosons Electron energy analyzers Free energy Open systems Two dimensional Vortex flow Gases
description	We discuss the stability of a homogeneous two-dimensional Bose gas at finite temperature against the formation of isolated vortices. We consider a patch of several healing lengths in size and compute its free energy using the Euclidean formalism. Since we deal with an open system, which is able to exchange particles and angular momentum with the rest of the condensate, we use the symmetry-breaking (as opposed to the particle number conserving) formalism, and include configurations with all values of angular momenta in the partition function. At finite temperature, there appear sphaleron configurations associated with isolated vortices. The contribution from these configurations to the free energy is computed in the dilute gas approximation. We show that the Euclidean action of linearized perturbations of a vortex is not positive definite. As a consequence the free energy of the 2D Bose gas acquires an imaginary part. This signals the instability of the gas. This instability may be identified with the Berezinskii-Kosterlitz-Thouless transition. © 2010 IOP Publishing Ltd.
author	Calzetta, Esteban Adolfo
author_facet	Calzetta, Esteban Adolfo
author_sort	Calzetta, Esteban Adolfo
title	Vortex formation in a two-dimensional Bose gas
title_short	Vortex formation in a two-dimensional Bose gas
title_full	Vortex formation in a two-dimensional Bose gas
title_fullStr	Vortex formation in a two-dimensional Bose gas
title_full_unstemmed	Vortex formation in a two-dimensional Bose gas
title_sort	vortex formation in a two-dimensional bose gas
publishDate	2010
url	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_09534075_v43_n9_p_Calzetta http://hdl.handle.net/20.500.12110/paper_09534075_v43_n9_p_Calzetta
work_keys_str_mv	AT calzettaestebanadolfo vortexformationinatwodimensionalbosegas
_version_	1768543381023096832

Vortex formation in a two-dimensional Bose gas

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