Statevector reduction in discrete time: A random walk in Hilbert space

A simple model is presented in which the statevector evolves every seconds in one of two ways, according to a particular probability rule. It is shown that this random walk in Hilbert space results in reduction of the statevector. It is also shown how the continuous spontaneous localization (CSL) theory of statevector reduction is achieved as a limiting case of this model, exactly as Brownian motion is a limiting case of ordinary random walk. Finally, a slightly different but completely equivalent form of the CSL equations suggested by the simple model given here is discussed.     

Jupiter's Great Red Spot and zonal winds as a self-consistent,one-layer,quasigeostrophic flow

We present the point of view that both the vortices and the east-west zonal winds of Jupiter are confined to the planet's shallow weather layer and that their dynamics is completely described by the weakly dissipated, weakly forced quasigeostrophic (QG) equation. The weather layer is the region just below the tropopause and contains the visible clouds. The forcing mimics the overshoot of fluid from an underlying convection zone. The late-time solutions of the weakly forced and dissipated QG equations appear to be a small subset of the unforced and undissipated equations and are robust attractors. We illustrate QG vortex dynamics and attempt to explain the important features of Jupiter's Great Red Spot and other vortices: their shapes, locations with respect to the extrema of the east-west winds, stagnation points, numbers as a function of latitude, mergers, break-ups, cloud morphologies, internal distributions of vorticity, and signs of rotation with respect to both the planet's rotation and the shear of their surrounding east-west winds. Initial-value calculations in which the weather layer starts at rest produce oscillatory east-west winds. Like the Jovian winds, the winds are east-west asymmetric and have Karman vortex streets located only at the west-going jets. From numerical calculations we present an empirically derived energy criterion that determines whether QG vortices survive in oscillatory zonal flows with nonzero potential vorticity gradients. We show that a recent proof that claims that all QG vortices decay when embedded in oscillatory zonal flows is too restrictive in its assumptions. We show that the asymmetries in the cloud morphologies and numbers of cyclones and anticyclones can be accounted for by a QG model of the Jovian atmosphere, and we compare the QG model with competing models.