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arXiv:math-ph/0110010 · Communications in Mathematical Physics

Gross-Pitaevskii Theory of the Rotating Bose Gas

Robert Seiringer

Published Sep 1, 2002• 80 citations
arXivHTMLPDF
DOI
10.1007/s00220-002-0695-2

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Gross-Pitaevskii Theory of the

Robert Seiringer

We study the Gross-Pitaevskii functional for a rotating two-dimensional Bose gas in a trap. We prove that there is a breaking of the rotational symmetry in the ground state; more precisely, for any value of the angular velocity and for large enough values of the interaction strength, the ground state of the functional is not an eigenfunction of the angular momentum. This has interesting consequences on the Bose gas with spin; in particular, the ground state energy depends non-trivially on the number of spin components, and the different components do not have the same wave function. For the special case of a harmonic trap potential, we give explicit upper and lower bounds on the critical coupling constant for symmetry breaking.

•Jan 1, 2001•0 citations
We consider a strongly interacting Bose-Einstein condensate in a spherical harmonic trap. The system is treated by applying a slave-boson representation for hard-core bosons. A renormalized Gross-Pitaevskii theory is derived for the condensate wave function that describes the dilute regime (like the conventional Gross-Pitaevskii theory) as well as the dense regime. We calculate the condensate density of a rotating condensate for both the vortex-free condensate and the condensate with a single vortex and determine the critical angular velocity for the formation of a stable vortex in a rotating trap.
We study the Gross-Pitaevskii functional for a rotating two-dimensional Bose gas in a trap. We prove that there is a breaking of the rotational symmetry in the ground state; more precisely, for any value of the angular velocity and for large enough values of the interaction strength, the ground state of the functional is not an eigenfunction of the angular momentum. This has interesting consequences on the Bose gas with spin; in particular, the ground state energy depends non-trivially on the number of spin components, and the dierent components do not have the same wave function. For the special case of a harmonic trap potential, we give explicit upper and lower bounds on the critical coupling constant for symmetry breaking. 1
We study the Gross-Pitaevskii functional for a rotating two-dimensional Bose gas in a trap. We prove that there is a breaking of the rotational symmetry in the ground state; more precisely, for any value of the angular velocity and for large enough values of the interaction strength, the ground state of the functional is not an eigenfunction of the angular momentum. This has interesting consequences on the Bose gas with spin; in particular, the ground state energy depends non-trivially on the number of spin components, and the different components do not have the same wave function. For the special case of a harmonic trap potential, we give explicit upper and lower bounds on the critical coupling constant for symmetry breaking.