Evolution of Quantum Systems from Microscopic to Macroscopic Scales

Even though the static properties of quantum systems have been known since the early days of quantum mechanics, accurate simulation of the dynamical break-up or ionization remains a theoretical challenge despite our complete knowledge of the relevant interactions. Simulations are challenging because of highly oscillatory exponential phase factors in the electronic wave function and the infinitesimally small values of the continuum components of electronic probability density at large times after the collision. The approach we recently developed, the regularized time-dependent Schrodinger equation method, has addressed these difficulties by removing the diverging phase factors and transforming the time-dependent Schrodinger equation to an expanding space. The evolution of the electronic wave function was followed to internuclear distances of R = 100,000 a.u. or 5 microns, which is of the order of the diameter of a human hair. Our calculations also revealed unexpected presence of free vortices in the electronic wave function. The discovered vortices also bring new light on the mechanism of transferring of the angular momentum from an external to internal motion. The connection between the observable momentum distribution and the time-dependent wave function implies that vortices in the wave function at large times are imaged in the momentum distribution.