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J. R. Anglin and M. Crescimanno, e-print cond-mat/0210063.
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13
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13544254171
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note
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s(r) inhomogeneities is due to the lowering of the loss of condensation energy (i.e., an increase in condensation energy) when the "normal" vortex core spatially coincides with the material inhomogeneity. Because vortex motion generates electric fields (Josephson relation), vortex pinning is in fact crucial for type-II superconductivity.
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14
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13544265222
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note
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2.
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15
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13544263122
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note
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2 saturates, approaching a constant. This was also independently shown in a complementary Thomas-Fermi approximation by Fischer and Baym [42].
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16
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13544267321
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Gordon Baym and C. J. Pethick, e-print cond-mat/0308325
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Gordon Baym and C. J. Pethick, e-print cond-mat/0308325.
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0000074584
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V. K. Tkachenko, Zh. Eksp. Teor. Fiz. 49, 1875 (1965) [Sov. Phys. JETP 22, 1282 (1966)].
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21
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0001948185
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B. Y. Rubinstein and L. M. Pismen, Physica D 78, 1 (1994); see also L. M. Pismen, Vortices in Nonlinear Fields (Oxford University, New York, 1999).
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Rubinstein, B.Y.1
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0001948185
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Oxford University, New York
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B. Y. Rubinstein and L. M. Pismen, Physica D 78, 1 (1994); see also L. M. Pismen, Vortices in Nonlinear Fields (Oxford University, New York, 1999).
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Vortices in Nonlinear Fields
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Pismen, L.M.1
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1642331498
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31
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13544268235
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note
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The energy density for the Bose condensate can be straightfor-wardly obtained from a standard interacting boson Hamiltonian, with boson operators approximated by a classical condensate field, appropriate for the BEC state. Equivalently, the same result can be obtained from a mean-field approximation to the coherent-state path integral for the partition function for the interacting boson problem.
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32
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13544273723
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note
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s(r)] analysis breaks down near the edge of the condensate, where the corrections to the uniform vortex density and rigid-body superfluid velocity are large.
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35
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13544277281
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note
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We must remark that, since N is a discrete variable, in actuality one expects steps in N as a function of Ω (see, e.g., Fig. 2 of Ref. [33]) which become negligible at large Ω.
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37
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13544256158
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note
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In fact, for a vortex in a finite but homogeneous superfluid (e.g., helium in a "bucket," for which the superfluid density is finite at the boundary, vanishing only over an atomic length scale), the vanishing-current boundary condition is crucial for obtaining the correct single-vortex energy and dynamics (e.g., the precession of an off-axis vortex). These are strongly affected by the interaction of the vortex with its image vortex introduced to enforce the above boundary condition.
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38
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4244078675
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S. Inouye, S. Gupta, T. Rosenband, A. P. Chikkatur, A. Górlitz, T. L. Gustavson, A. E. Leanhardt, D. E. Pritchard, and W. Ketterle, Phys. Rev. Lett. 87, 080402 (2001).
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39
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13544252359
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note
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This is up to a curl-free vector field V(r,π)π with V(r,π) chosen to match onto the inner solution.
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40
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13544277280
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note
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s(r) with a Gauss ian "bump"on top of a uniform profile varying on long length scales, as considered in Sec. V B 3 in the case of many vortices in an inhomogeneous condensate.
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41
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33646668527
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Vinay Ambegaokar, B. I. Halperin, David R. Nelson, and Eric D. Siggia, Phys. Rev. B 21, 1806 (1980).
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43
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13544263123
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note
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For the case of a uniform lattice (u=0), Tkachenko [17] has shown that Eq. (64a) along with Eq. (66) emerges formally from a small-z expansion of his exact expression for the phase gradient of a uniform vortex array written in terms of the Weierstrass zeta function ζ(z).
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46
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13544257939
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note
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T.
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48
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8644280027
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C. B. Hanna, A. J. Sup, J. C. Diaz-Velez, J. Sinova, and A. H. MacDonald, Bull. Am. Phys. Soc. 49, 951 (2004).
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MacDonald, A.H.5
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49
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1642364268
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Y. Shin, M. Saba, T. A. Pasquini, W. Ketterle, D. E. Pritchard, and A. E. Leanhardt, Phys. Rev. Lett. 92, 050405 (2004).
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Shin, Y.1
Saba, M.2
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Ketterle, W.4
Pritchard, D.E.5
Leanhardt, A.E.6
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50
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13544269144
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note
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Quantitative measurement of the rotation rate Ω is in fact quite difficult, as it is typically experimentally determined by the cloud aspect ratio with error bars that grow with decreasing Ω [6,7].
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