Deformation Quantization of a Certain Type of Open Systems

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.

Major update. Improved main statements. 21 pages

References in corpus (8)

• Concepts and methods in the theory of open quantum systems
• Quantization of non-Hamiltonian and Dissipative Systems
• States and representations in deformation quantization
• Canonical quantization of so-called non-Lagrangian systems
• The damped harmonic oscillator in deformation quantization
• Deformation quantization of linear dissipative systems
• Hermitian star products are completely positive deformations
• Complete Positivity of Rieffel's Deformation Quantization by Actions of ${\mathbb{R}}^d$