# Equilibrium properties and decoherence of an open harmonic oscillator

## TL;DR

This paper investigates the equilibrium behavior and decoherence mechanisms of an open harmonic oscillator, introducing generalized operators, a Heisenberg framework, and analyzing quantum fluctuations at critical damping thresholds.

## Contribution

It extends the theory of open harmonic oscillators by generalizing creation/destruction operators, applying the Heisenberg representation to identify decoherence, and analyzing quantum fluctuations at damping boundaries.

## Key findings

- Decoherence can be characterized without specific system states.
- Quantum fluctuations lead to non-continuous limits at damping boundaries.
- Generalized operators facilitate analysis of open quantum systems.

## Abstract

The equilibrium properties of an open harmonic oscillator are considered in three steps: First the creation and destruction operators are generalized for open dynamics and the creation operator is used to construct coherent states. The second step consists of the introduction of the Heisenberg representation where the dynamical decoherence can be identified without making reference to the state of the system. Finally it is pointed out that the quantum fluctuations generate non-continuous limit for infinitesimal system-environment interactions and at the border of the under- and over-damped oscillator.