Time dependent Stark ladders: Exact propagator and caustic control

TL;DR

This paper introduces an exact propagator for a particle in discrete space under a time-dependent field, enabling control over caustic wavefronts by explicitly relating them to the external field.

Contribution

It provides a new exact propagator formula for discrete quantum systems with time-dependent fields, allowing precise manipulation of wavefront caustics.

Findings

Derived an explicit propagator for time-dependent fields

Demonstrated control over caustic wavefront shapes

Linked wavefront structure directly to external field parameters

Abstract

In this note we present a new propagator for a particle in discrete space under the influence of a time-dependent field. With this result we are able to control the shape of caustics emerging from a point-like source, as the explicit form of the wavefronts can be put in terms of the external field.