On Markovianity and classicality in multilevel spin-boson models

Area of Science:

• Quantum mechanics
• Statistical physics
• Quantum optics

Background:

• Quantum systems coupled to bosonic fields are fundamental in many areas of physics.
• Understanding the transition from quantum to classical behavior is a key challenge.
• Hamiltonian models with rotating-wave interaction are commonly used to describe such systems.

Purpose of the Study:

• To investigate the unitary and reduced evolution of a multilevel quantum system interacting with a multimode boson field.
• To determine conditions under which this quantum evolution becomes Markovian and classical.

Main Methods:

• Analysis of Hamiltonian models for multilevel systems coupled to boson fields.
• Application of the rotating-wave interaction approximation.
• Investigation of system evolution under sharp measurements in arbitrary bases.
• Derivation of conditions for Markovianity and classical stochastic process equivalence.

Main Results:

• Explicit proof of Markovian evolution in the flat coupling limit.
• Identification of necessary and sufficient conditions for the process to be classical.
• Demonstration that classical probability distributions satisfy the Kolmogorov consistency condition.

Conclusions:

• The quantum evolution of these systems can exhibit Markovian behavior under specific approximations and measurement schemes.
• A clear link is established between quantum dynamics and classical stochastic processes.
• This work provides a framework for understanding quantum-classical transitions in open quantum systems.