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Kelvin mode of a vortex in a nonuniform Bose-Einstein condensate | | Alexander L. Fetter
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7 Feb 2004 | | Subject: | Soft Condensed Matter | cond-mat.soft | | Abstract: | In a uniform fluid, a quantized vortex line with circulation h/M can support long-wavelength helical traveling waves proportional to e^{i(kz-omega_k t)} with the well-known Kelvin dispersion relation omega_k approx (hbar k^2/2M) ln(1/|k|xi), where xi is the vortex-core radius. This result is extended to include the effect of a nonuniform harmonic trap potential, using a quantum generalization of the Biot-Savart law that determines the local velocity V of each element of the vortex line. The normal-mode eigenfunctions form an orthogonal Sturm-Liouville set. Although the line’s curvature dominates the dynamics, the transverse and axial trapping potential also affect the normal modes of a straight vortex on the symmetry axis of an axisymmetric Thomas-Fermi condensate. The leading effect of the nonuniform condensate density is to increase the amplitude along the axis away from the trap center. Near the ends, however, a boundary layer forms to satisfy the natural Sturm-Liouville boundary conditions. For a given applied frequency, the next-order correction renormalizes the local wavenumber k(z) upward near the trap center, and k(z) then increases still more toward the ends. | | Source: | arXiv, cond-mat/0402208 | | Services: | Forum | Review | PDF | Favorites | |
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