Quantum Evolution and Anticipation

TL;DR

This paper extends the analysis of quantum anticipation effects to general quantum evolutions, characterizing conditions for orthogonal evolution and providing tools for further theoretical and experimental exploration.

Contribution

It introduces a comprehensive framework for analyzing quantum anticipation in general evolutions and links orthogonal evolution to positive joint spectral measures.

Findings

Quantum evolutions with embedded orthogonal evolution have positive joint spectral measures.

The paper categorizes quantum evolution and assesses anticipation strength.

Provides analytic tools for future experimental verification.

Abstract

In a previous paper we have investigated quantum states evolving into mutually orthogonal states at equidistant times, and the quantum anticipation effect exhibited by measurements at one half step. Here we extend our analyzes of quantum anticipation to general type quantum evolutions and spectral measures and prove that quantum evolutions possessing an embedded orthogonal evolution are characterized by positive joint spectral measure. Furthermore, we categorize quantum evolution, assess anticipation strength and provide a framework of analytic tools and results, thus preparing for further investigation and experimental verification of anticipation in concrete physical situations such as the H-atom, which we have found to exhibit anticipation.