Vortices and Spontaneous Symmetry Breaking in Rotating Bose Gases

zbMath1156.82396arXiv0801.0427MaRDI QIDQ3596972

Publication date: 9 February 2009

Abstract: We present a rigorous proof of the appearance of quantized vortices in dilute trapped Bose gases with repulsive two-body interactions subject to rotation, which was obtained recently in joint work with Elliott Lieb. Starting from the many-body Schroedinger equation, we show that the ground state of such gases is, in a suitable limit, well described by the nonlinear Gross-Pitaevskii equation. In the case of axially symmetric traps, our results show that the appearance of quantized vortices causes spontaneous symmetry breaking in the ground state.

Full work available at URL: https://arxiv.org/abs/0801.0427

Mathematics Subject Classification ID

NLS equations (nonlinear Schrödinger equations) (35Q55) Symmetry breaking in quantum theory (81R40) Schrödinger operator, Schrödinger equation (35J10) Statistical mechanics of liquids (82D15)

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