Roton creation and vortex nucleation in superfluids

The nonlocal nonlinear Schrodinger equation is used to analyze the superfluid flow around an impurity. The differences ̈ between the processes of vortex nucleation and roton creation are elucidated. It is argued that vortices are nucleated when the velocity around the ion exceeds the velocity of sound. q 2000 Elsevier Science B.V. All rights reserved. PACS: 67.40.Vs; 67.55; 02.60; 05.45.-a A half a century has passed since the discovery of superfluidity and superfluid vortices, but the mechanisms of vortex nucleation are still not properly understood. The main reason is that there is no truly microscopic picture of superfluid helium available, so the appearance of vortices Afrom nothingB, or intrinsic nucleation, cannot be derived from first principles. In the absence of such theory the dynamics of vortices are quite often derived from the Ginzburg– Ž . w x Pitaevskii GP model 1,2 which is assumed to be linked to the condensate fraction of the superfluid. This model has been extensively studied particularly for the motion of ions in a dilute Bose condensate w x 3,4 . The main conclusion of the numerical integration and asymptotic analysis of the GP equation is that the vortices nucleate when the velocity somewhere on the surface of the moving object exceeds ) Corresponding author. Fax: q1-310-206-2679. Ž . E-mail addresses: [email protected] N.G. Berloff , Ž . [email protected] P.H. Roberts . the speed of sound. The condensate escapes the formation of a shock wave through the breakdown of the healing layer, resulting in vortex nucleation. Unfortunately, there are many shortcomings of the GP model, so that the model can claim only a qualitative significance for actual superfluid helium. The dispersion relation of the GP model has no roton minimum, which is held responsible for many of the properties of the superfluid. The velocity, c, of long 1 2 wavelength sound is proportional to r where r is the density, while experiments evaluating the Ž . Gruneisen constant U s rE crcEr , show that, in ̈ G T Ž the bulk i.e., on lengthscales long compared with . the healing length, krc , the fluid behaves as a Ž g . barotropic fluid pAr , where p is the pressure w x with gs2.8 5 . Finally, the healing length and correlation length in real helium are known to be quite different. For some time there has been a belief that, as soon as a realistic two-particle interaction potential, V, that leads to a phonon–roton-like spectra is introduced in the GP model, the properties of superfluid w x helium will be well represented 6–11 . The mini0375-9601r00r$ see front matter q 2000 Elsevier Science B.V. All rights reserved. Ž . PII: S0375-9601 00 00516-8 ( ) N.G. Berloff, P.H. RobertsrPhysics Letters A 274 2000 69–74 70 mum requirements on such a potential would be the correct position of the roton minimum and the corŽ . rect bulk normalization see below . Unfortunately, w x as was shown in Ref. 12 , such a model is not applicable since it has nonphysical solutions, having catastrophic mass concentrations. To remedy this, we w x adopted 13 a density–functional theory approach w x 14,15 and included short-range correlations into the total energy in the simplest way. This allowed us to correct the nonphysical features of the model, while retaining not only an adequate representation of the Landau dispersion relation, but also simplicity in the analytical and numerical studies. We used this model, which is a nonlocal nonlinear Schrodinger equation ̈ Ž . NNLSE , to elucidate the properties of vortex rings. For this model we showed that the vortex core parameter and the healing length can be brought into agreement, so that the energy of large vortex rings w x agrees with experimental observations 16 . The goal of this Letter is to use the NNLSE model to elucidate vortex nucleation from, and roton emission by, mov-