Geometrical approach to hydrodynamics and low-energy excitations of spinor condensates
- 21 July 2009
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review B
- Vol. 80 (2), 024420
- https://doi.org/10.1103/physrevb.80.024420
Abstract
In this work, we derive the equations of motion governing the dynamics of spin- spinor condensates. We pursue a description based on standard physical variables (total density and superfluid velocity), alongside “spin nodes:” unit vectors that describe the spin- state and also exhibit the point-group symmetry of a spinor condensate’s mean-field ground state. In the first part of our analysis, we derive the hydrodynamic equations of motion, which consist of a mass continuity equation, Landau-Lifshitz equations for the spin nodes, and a modified Euler equation. In particular, we provide a generalization of the Mermin-Ho relation to spin one and find an analytic solution for the skyrmion texture in the incompressible regime of a spin-half condensate. In the second part, we study the linearized dynamics of spinor condensates. We provide a general method to linearize the equations of motion based on the symmetry of the mean-field ground state using the local stereographic projection of the spin nodes. We also provide a simple construction to extract the collective modes from symmetry considerations alone akin to the analysis of vibrational excitations of polyatomic molecules. Finally, we present a mapping between the spin-wave modes, and the wave functions of electrons in atoms, where the spherical symmetry is degraded by a crystal field. These results demonstrate the beautiful geometrical structure that underlies the dynamics of spinor condensates.
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