We show that the usual sum of R ÿ6 contributions from elements separated by distance R can give qualitatively wrong results for the electromagnetically nonretarded van der Waals interaction between nonoverlapping bodies. This occurs for anisotropic nanostructures that have a zero electronic energy gap, such as metallic nanotubes or nanowires, and nanolayered systems including metals and graphene planes. In all these cases our analytic microscopic calculations give an interaction falling off with a power of separation different from the conventional value. We discuss implications for van der Waals energy functionals. The new nanotube interaction might be directly observable at submicron separations. The vdW physics that we expose here could be relevant in predicting the energetics of bundles of metallic nanowires or nanotubes, layered metallic systems, -conjugated systems including graphite, intercalated graphite, graphitic hydrogen storage systems and pi-stacked biomolecules, and other weakly bound (''soft'') layered and striated nanosystems. Standard local (LDA) and gradient (GGA) density functionals for the electronic energy do not obtain any distant dispersion interaction, but density functionals have been derived recently that obtain, in a natural fashion, both distant dispersion interactions and their saturation at small distances. These and other numerically practicable vdW energy schemes available to date [1][2][3][4][5][6][7][8] for the above systems (in the electromagnetically nonretarded regime) have a ''universal'' feature: the distant vdW interaction energy between sufficiently separated subsystems is given qualitatively by a sum of contributions of form R ÿ6 between microscopic elements separated by distance R. This leads to ''standard'' power laws E / ÿD ÿp for the interaction energy between various macroscopic bodies separated by distance D (column 3 of Table I). Although these universal asymptotic results are indeed valid for most macroscopic systems, we show below that they fail for the anisotropic nanostructures mentioned above. Column 2 of Table I summarizes the asymptotic (D ! 1) benchmarks that we propose below for the vdW energy of two parallel nanostructures of infinite extent.To analyze these situations, we use the correlation energy E RPA c D from the random phase approximation (RPA) [12 -17], a basic microscopic theory that does not rely on assumptions of locality, additivity, nor R ÿ6 contributions. Going beyond the RPA does not change the asymptotic power laws predicted here, unless the exchange-correlation kernel f xc [17][18][19] has a slower spatial decay than the bare Coulomb interaction, an unprecedented and unlikely scenario.Where the separated subsystems exhibit lightly damped long-wavelength plasmons, we note [20] that the principal contribution to E RPA c D comes from the sum of coupledplasmon zero-point energies: otherwise we use the full RPA. Some essential common features of these systems will be abstracted from these specific calculations. We obtain analytic results for t...

In a recent experiment Paoletti [Phys. Rev. Lett. 101, 154501 (2008)]10.1103/PhysRevLett.101.154501 monitored the motion of tracer particles in turbulent superfluid helium and inferred that the velocity components do not obey the Gaussian statistics observed in ordinary turbulence. Motivated by their experiment, we create a small 3D turbulent state in an atomic Bose-Einstein condensate, compute directly the velocity field, and find similar nonclassical power-law tails. We obtain similar results in 2D trapped and 3D homogeneous condensates, and in classical 2D vortex points systems. This suggests that non-Gaussian turbulent velocity statistics describe a fundamental property of quantum turbulence. We also track the decay of the vortex tangle in the presence of the thermal cloud.

We introduce a primary thermometer which measures the temperature of a Bose-Einstein Condensate in the sub-nK regime. We show, using quantum Fisher information, that the precision of our technique improves the state-of-the-art in thermometry in the sub-nK regime. The temperature of the condensate is mapped onto the quantum phase of an atomic dot that interacts with the system for short times. We show that the highest precision is achieved when the phase is dynamical rather than geometric and when it is detected through Ramsey interferometry. Standard techniques to determine the temperature of a condensate involve an indirect estimation through mean particle velocities made after releasing the condensate. In contrast to these destructive measurements, our method involves a negligible disturbance of the system.

We show that a moving obstacle, in the form of an elongated paddle, can create vortices that are dispersed, or induce clusters of like-signed vortices in 2D Bose-Einstein condensates. We propose new statistical measures of clustering based on Ripley's K-function which are suitable to the small size and small number of vortices in atomic condensates, which lack the huge number of length scales excited in larger classical and quantum turbulent fluid systems. The evolution and decay of clustering is analyzed using these measures. Experimentally it should prove possible to create such an obstacle by a laser beam and a moving optical mask. The theoretical techniques we present are accessible to experimentalists and extend the current methods available to induce 2D quantum turbulence in Bose-Einstein condensates.

After more than a decade of experiments generating and studying the physics of quantized vortices in atomic gas Bose-Einstein condensates, research is beginning to focus on the roles of vortices in quantum turbulence, as well as other measures of quantum turbulence in atomic condensates. Such research directions have the potential to uncover new insights into quantum turbulence, vortices, and superfluidity and also explore the similarities and differences between quantum and classical turbulence in entirely new settings. Here we present a critical assessment of theoretical and experimental studies in this emerging field of quantum turbulence in atomic condensates.vortex dynamics | vortex tangle | Kolmorogov cascade | inverse energy cascade Since Onsager's groundbreaking theoretical work linking turbulence and point vortex dynamics in a 2D fluid (1), it has been hoped that the simple nature of quantum vortices in superfluids will aid in understanding the nature of turbulence. After many years of research with superfluid helium systems, the field of quantum turbulence (QT) is now well established and has led to numerous new insights and developments regarding QT and the universality of turbulence (2). The discovery of links between classical turbulence and QT remains a strong motivating factor for QT research, particularly in the emerging field of QT studies with BoseEinstein condensates (BECs). BECs present a new platform for QT studies due to their compressibility, weak interatomic interactions, and availability of new experimental methods for probing and studying superfluid flow (3). The relationship between QT and vortex dynamics in these systems is consequently an inherently interesting new research topic as well.Classical turbulence is composed of eddies of continuous vorticity and size, and it is necessary to solve the Navier-Stokes equation to mathematically describe viscous fluid dynamics (4). For turbulent fluid flow, which consists of scale-invariant flow dynamics across a wide range of length scales, this procedure becomes difficult to tackle from first principles. In comparison, QT is comprised of vortices of less complexity, each with a localized and well-defined vortex core structure and quantized circulation. Superfluid flow is inviscid, and vortices cannot decay by viscous diffusion of vorticity: a quantized vortex cannot simply "spin down" and dissipate energy via viscosity in the same way a classical vortex can. Incompressible kinetic energy is instead diffused through emission of sound waves and then dissipated due to the presence of a thermal cloud in BECs or the normal fluid component in superfluid He.Despite the differences arising from the nature of vortices, classical and quantum turbulence share profound similarities that underscore the universality of turbulence. We briefly illustrate this idea with the structure of kinetic energy spectra in 3D turbulence. At locations in the fluid far from vortex cores, and for length scales greater than the average intervortex spacing, vortex core stru...