# A note on spectrum and quantum dynamics

## TL;DR

This paper investigates the quantum dynamics of the Schrödinger equation, demonstrating that the rate at which solutions escape from finite-dimensional subspaces varies along subsequences of time, highlighting complex temporal behaviors.

## Contribution

It extends the understanding of quantum dynamical systems by analyzing the subsequential escape rates of solutions, inspired by Simon's Wonderland Theorem.

## Key findings

- Escape rates depend on subsequences of time going to infinity
- Solutions typically escape from finite-dimensional subspaces in a Baire generic sense
- The behavior parallels phenomena described by Simon's Wonderland Theorem

## Abstract

We show, in the same vein of Simon's Wonderland Theorem, that, typically in Baire's sense, the rates with whom the solutions of the Schr\"odinger equation escape, in time average, from every finite-dimensional subspace, depend on subsequences of time going to infinite.