Deformation Quantization of a Certain Type of Open Systems

TL;DR

This paper presents a method for quantizing certain classical open quantum systems using deformation quantization, ensuring the preservation of complete positivity in their quantum evolution.

Contribution

It introduces a systematic approach to quantize classical open systems into quantum open systems while maintaining their physical properties.

Findings

Successfully quantized classical open systems preserving complete positivity

Applied method to linearly coupled harmonic oscillators

Demonstrated the approach's effectiveness in a standard example

Abstract

We give an approach to open quantum systems based on formal deformation quantization. It is shown that classical open systems of a certain type can be systematically quantized into quantum open systems preserving the complete positivity of the open time evolution. The usual example of linearly coupled harmonic oscillators is discussed.