A Dynamic Uncertainty Principle for Jacobi Operators

TL;DR

This paper establishes a dynamic uncertainty principle for solutions of Schrödinger-type equations involving Jacobi operators, showing that rapid decay at two times implies triviality of the solution.

Contribution

It extends the uncertainty principle to Jacobi operators with asymptotically constant coefficients, a novel result in this context.

Findings

Solutions cannot decay too fast at two different times unless trivial.

The result applies to Schrödinger-type equations with Jacobi operators.

Provides a new uncertainty principle for discrete operators.

Abstract

We prove that a solution of the Schr\"odinger-type equation $\mathrm{i}\partial_t u= Hu$, where $H$ is a Jacobi operator with asymptotically constant coefficients, cannot decay too fast at two different times unless it is trivial.