# Vestiges of quantum oscillations in the open evolution of semiclassical states

## TL;DR

This paper investigates how quantum oscillations, detectable via local wave function correlations, persist in open quantum systems undergoing Markovian decoherence, revealing residual quantum features beyond classical descriptions.

## Contribution

It introduces a semiclassical framework for analyzing local wave function correlations in open quantum systems and demonstrates the persistence of quantum oscillations after decoherence.

## Key findings

- Quantum oscillations can be detected through local correlations.
- Spectral lines corresponding to classical momenta remain visible after decoherence.
- Quantum features persist even when the Wigner function becomes positive.

## Abstract

A single wave component of a quantum particle can in principle be detected by the way that it interferes with itself, that is, through the local wave function correlation. The interpretation as the expectation of a local translation operator allows this measure of quantum wavyness to be followed through the process of decoherence in open quantum systems. This is here assumed to be Markovian, determined by Lindblad operators that are linear in position and momentum. The limitation of small averaging windows and even smaller correlation lengths simplifies the semiclassical theory for the evolving local correlation. Its spectrum has a peak for each classical momentum, subjected to Gaussian broadening with decoherence. These spectral lines can be clearly resolved even after the Wigner function has become positive: The correlations located far from caustics seem to be the last vestige of quantum oscilations.