Holographic Vortex Liquids and Superfluid Turbulence

Abstract

Superfluid turbulence, often referred to as quantum turbulence, is a fascinating phenomenon for which a satisfactory theoretical framework is lacking. Holographic duality provides a systematic new approach to studying quantum turbulence by mapping the dynamics of certain quantum theories onto the dynamics of classical gravity. We use this gravitational description to numerically construct turbulent flows in a holographic superfluid in two spatial dimensions. We find that the superfluid kinetic energy spectrum obeys the Kolmogorov −5/3 scaling law, as it does for turbulent flows in normal fluids. We trace this scaling to a direct energy cascade by injecting energy at long wavelengths and watching it flow to a short-distance scale set by the vortex core size, where dissipation by vortex annihilation and vortex drag becomes efficient. This is in sharp contrast with the inverse energy cascade of normal fluid turbulence in two dimensions. We also demonstrate that the microscopic dissipation spectrum has a simple geometric interpretation.

Periodic shedding of vortex dipoles from a moving penetrable obstacle in a Bose-Einstein condensate

“…Dipole-dipole collisions are particularly interesting in that vortex pair annihilation may occur during the collision. Vortex pair annihilation is one of the key issues in the study of 2D quantum turbulence [32][33][34][35][36][37][38][39][40]. Many aspects of the pair annihilation process [41,42], such as the roles of vortex-phonon interactions [43,44], and thermal dissipation [45], have never been directly addressed in experiments.…”

Theory of the vortex-clustering transition in a confined two-dimensional quantum fluid

“…Several works have considered the possibility of an inverse energy cascade in two-dimensional BECs, suggesting that the compressibility of the fluid may be fatal for largescale clustering, instead causing transport of energy to small scales driven by vortex dipole annihilation [56][57][58]. However, these works considered specific scenarios that immediately prohibited clustering, due to either starting from initial conditions dominated by acoustic energy [56,57], or evolving the system according to an overdamped equation of motion [58].…”

“…However, these works considered specific scenarios that immediately prohibited clustering, due to either starting from initial conditions dominated by acoustic energy [56,57], or evolving the system according to an overdamped equation of motion [58]. As shown in a systematic study of energy transport [44], a clear regime exists where energy is transported to large scales via a vortex clustering process.…”

Relaxation of superfluid turbulence in highly oblate Bose-Einstein condensates

“…An interesting question is whether the inverse cascade can occur in an atomic BEC. Since the enstrophy, proportional to the total number of quantized vortices in quantum turbulence, is not conserved in a compressible 2D superfluid due to the vortex-antivortex annihilation, there has been a theoretical controversy on this issue [11][12][13][14][15][16][17][18][19][20]. Recently, Neely et al [21] reported an experimental and numerical study to show that there are conditions for which 2D turbulence in a BEC can dissipatively evolve into large-scale flow.…”