A quantum decay model with exact explicit analytical solution

Abstract

A simple decay model is introduced. The model comprises of a point potential well, which experiences an abrupt change. Due to the temporal variation the initial quantum state can either escape from the well or stay localized as a new bound state. The model allows for an exact analytical solution while having the necessary features of a decay process. The results show that the decay is never exponential, as classical dynamics predicts. Moreover, at short times the decay has a \textit{fractional} power law, which differs from perturbation quantum methods predictions.

4 pages, 3 figures

References in corpus (4)

• Effect of optical disorder and single defects on the expansion of a Bose-Einstein condensate in a one-dimensional waveguide
• Generic Short-Time Propagation of Sharp-Boundaries Wave Packets
• The role of initial state reconstruction in short and long time deviations from exponential decay
• Scatterer that leaves "footprints" but no "fingerprints"

Cited by in corpus (9)

• Long-time behavior of many-particle quantum decay
• Timescales of tunneling decay of a localized state
• Analytical study of quadratic and non-quadratic short-time behavior of quantum decay
• Quantum particle displacement by a moving localized potential trap
• Transfer and scattering of wave packets by a nonlinear trap
• Spin dynamics in tunneling decay of a metastable state
• Acceleration of trapped particles and beams
• Trapping of quantum particles and light beams by switchable potential wells
• Bound Eigenstate dynamics under a sudden shift of the well's wall