Hitting a ball on a spring: a simple model for understanding decoherence with wavefunctions

Abstract

The typical approach to studying decoherence begins by examining a combined system and interacting environment (termed bath), and then deriving a master equation to examine the behaviour of the density matrix after tracing over the bath, typically by invoking the Markovian approximation. This approach is quite successful for a large variety of systems however is frequently a non-intuitive picture that can mask the fundamental behaviour of the system. We examine here a simple model that captures the essence of decoherence and study it using the wavefunction picture, invoking the analytic concepts of the correspondence principle, the method of images, the phase jitter concept, and the scattering matrix formalism. We complement this with a numerical study using the split-operator FFT method, the forced harmonic oscillator method, and the thawed Gaussian approximation.

Polar inelastic profiles in fast-atom diffraction at surfaces

“…A major weakness of the QBCM is that surface vibration are treated only through the local Debye oscillator thus neglecting the phonons mode which are the genuine eigenstates of vibrations at surfaces. Only few authors have developed approaches where phonons are explicit, most are adapted to TEAS [34,[50][51][52] but also to grazing incidences [53,54].…”

“…Of course, even at zero temperature, the surface atoms are not standing still at equilibrium positions but quantum mechanics indicates that position and momentum cannot be treated as independent (see e.g. ref [34] for a ball hitting a harmonic oscillator). In single scattering conditions such as X-ray, TEAS, or neutron diffraction, the equilibrium position reappears because it is the only one where large scale coherence can build up.…”