Space-Time Dynamics in Open and Closed Quantum Systems

Abstract

A fundamental feature of the physics of waves is interference. The forma tion of highly regular spatio-temporal patterns in the quantum mechanical probability density of confined particles is a striking example. The density distributions have been termed “quantum interference patterns”. In this thesis we track down the dynamics of open and closed quantum systems in space and time. For this purpose we construct the initial wave packet and investigate how it evolves in time for such quantum systems. We introduce the concept of quantum revivals which are characterized by initially local ized quantum states that have a short-term, quasi-classical time evolution, which then can spread significantly over several orbits, only to reform later in the form of a quantum revival where the spreading reverses itself, the wave packet relocalizes, and the semi-classical periodicity is once again evident. Relocalization of the initial wave packet into a number of smaller copies of the initial packet (‘minipackets’ or ‘clones’) is also possible, giving rise to fractional revivals. Systems exhibiting such behavior are a fundamental re alization of time-dependent interference phenomena for bound states with quantized energies in quantum mechanics and are therefore of wide inter est in the physics community. We Introduce the concept of autocorrelation function, that measures the overlap (in Hilbert space) of a time-dependent quantum mechanical wave function, with its initial value. The explicit ex pression for the autocorrelation function for the time-dependent Gaussian solution of the Schrodinger equation, in the case of a particle in a box, is evaluated.