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Title: Bose–Einstein condensates and scalar fields; exploring the similitudes

We analyze the the remarkable analogy between the classical Klein–Gordon equation for a test scalar field in a flat and also in a curved background, and the Gross–Pitaevskii equation for a Bose–Einstein condensate trapped by an external potential. We stress here that the solution associated with the Klein–Gordon equation (KG) in a flat space time has the same mathematical structure, under certain circumstances, to those obtained for the Gross–Pitaevskii equation, that is, a static soliton solution. Additionally, Thomas–Fermi approximation is applied to the 3–dimensional version of this equation, in order to calculate some thermodynamical properties of the system in curved a space–time back ground. Finally, we stress the fact that a gravitational background provides, in some cases, a kind of confining potential for the scalar field, allowing us to remarks even more the possible connection between scalar fields and the phenomenon of Bose–Einstein condensation.
Authors:
 [1] ;  [2] ;  [3]
  1. Departamento de Física, Centro de Investigación y de Estudios Avanzados del IPN, A.P. 14-740, 07000 México D.F. (Mexico)
  2. Departamento de Física, Universidad Autónoma Metropolitana-Iztapalapa, A.P. 55-534, México D.F. 09340 (Mexico)
  3. Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Circuito Exterior C.U., A.P. 70-543, México D.F. 04510 (Mexico)
Publication Date:
OSTI Identifier:
22264059
Resource Type:
Journal Article
Resource Relation:
Journal Name: AIP Conference Proceedings; Journal Volume: 1577; Journal Issue: 1; Conference: 5. Leopoldo Garcia-Colin Mexican meeting on mathematical and experimental physics, Mexico City (Mexico), 9-13 Sep 2013; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; APPROXIMATIONS; EQUATIONS; MATHEMATICAL SOLUTIONS; SCALAR FIELDS; SOLITONS