The two classes of hybrid classical-quantum dynamics

Understand

Coupling between quantum and classical systems is consistent, provided the evolution is linear in the state space, preserves the split of systems into quantum and classical degrees of freedom, and preserves probabilities.

• The evolution law must be a completely positive and norm preserving map.
• We prove that if the dynamics is memoryless, there are two classes of these dynamics, one which features finite sized jumps in the classical phase space and one which is continuous.
• We find the most general form of each class of classical-quantum master equation.