Dynamics of a quantum wave emitted by a decaying and evanescent point source

TL;DR

This paper models a decaying, evanescent quantum point source in 1D, analyzing wave dynamics, characteristic times, and quantum phenomena like diffraction and decay deviations, revealing optimal conditions for observation.

Contribution

It introduces a simplified model for quantum wave emission from a point source, capturing key dynamics without detailed inner-region modeling.

Findings

Identifies a generalized tunneling time for wave maximum arrival

Discovers an optimal injection frequency for observing diffraction and decay deviations

Analyzes wave dynamics and characteristic times in a 1D quantum decay model

Abstract

We put forward a model that describes a decaying and evanescent point source of non-interacting quantum waves in 1D. This point-source assumption allows for a simple description that captures the essential aspects of the dynamics of a wave traveling through a classically forbidden region without the need to specify the details of the inner region. The dynamics of the resulting wave is examined and several characteristic times are identified. One of them generalizes the tunneling time-scale introduced by B\"uttiker and Landauer and it characterizes the arrival of the maximum of the wave function. Diffraction in time and deviations from exponential decay are also studied. Here we show that there exists an optimal injection frequency and detection point for the observation of these two quantum phenomena.