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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todo:paper_09534075_v43_n9_p_Calzetta2023-10-03T15:51:03Z Vortex formation in a two-dimensional Bose gas Calzetta, E. Ho, K.-Y. Hu, B.L. 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar 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, E. Ho, K.-Y. Hu, B.L. 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. |
| format |
JOUR |
| author |
Calzetta, E. Ho, K.-Y. Hu, B.L. |
| author_facet |
Calzetta, E. Ho, K.-Y. Hu, B.L. |
| author_sort |
Calzetta, E. |
| 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 |
| url |
http://hdl.handle.net/20.500.12110/paper_09534075_v43_n9_p_Calzetta |
| work_keys_str_mv |
AT calzettae vortexformationinatwodimensionalbosegas AT hoky vortexformationinatwodimensionalbosegas AT hubl vortexformationinatwodimensionalbosegas |
| _version_ |
1807322769290952704 |