Motion of vortices implies chaos in Bohmian mechanics

Bohmian mechanics is a causal interpretation of quantum mechanics in which particles describe trajectories guided by the wave function. The dynamics in the vicinity of nodes of the wave function, usually called vortices, is regular if they are at rest. However, vortices generically move during time evolution of the system. We show that this movement is the origin of chaotic behavior of quantum trajectories. As an example, our general result is illustrated numerically in the two-dimensional isotropic harmonic oscillator.Comment: 7 pages 5 figure

Lagrangian statistics in fully developed turbulence

The statistics of Lagrangian particles transported by a three-dimensional fully developed turbulent flow is investigated by means of high-resolution direct numerical simulations. The analysis of single trajectories reveals the existence of strong trapping events vortices at the Kolmogorov scale which contaminates inertial range statistics up to 10 t¿. For larger time separations, we find that Lagrangian structure functions display intermittency in agreement with the prediction of the multifractal model of turbulence. The study of two-particle dispersion shows that the probability density function of pair separation is very close to the original prediction of Richardson of 1926. Nevertheless, moments of relative dispersion are strongly affected by finite Reynolds effects, thus limiting the possibility to measure numerical prefactors, such as the Richardson constant g. We show how, by using an exit time statistics, it is possible to have a precise estimation of g which is consistent with recent laboratory measurements

Lagrangian statistics in fully developed turbulence

The statistics of Lagrangian particles transported by a three-dimensional fully developed turbulent flow is investigated by means of high-resolution direct numerical simulations. The analysis of single trajectories reveals the existence of strong trapping events vortices at the Kolmogorov scale which contaminates inertial range statistics up to 10 t¿. For larger time separations, we find that Lagrangian structure functions display intermittency in agreement with the prediction of the multifractal model of turbulence. The study of two-particle dispersion shows that the probability density function of pair separation is very close to the original prediction of Richardson of 1926. Nevertheless, moments of relative dispersion are strongly affected by finite Reynolds effects, thus limiting the possibility to measure numerical prefactors, such as the Richardson constant g. We show how, by using an exit time statistics, it is possible to have a precise estimation of g which is consistent with recent laboratory measurements