Five approaches to exact open-system dynamics: Complete positivity, divisibility, and time-dependent observables

Area of Science:

• Quantum mechanics
• Open quantum systems
• Quantum dynamics

Background:

• Classical Markovianity is extended to open quantum systems via divisibility concepts.
• Different theoretical frameworks exist to analyze quantum system dynamics.

Purpose of the Study:

• Analyze divisibility of open quantum system dynamics using five complementary approaches.
• Investigate the impact of divisibility on observable level occupation and transport currents.
• Quantify the system's footprint on its environment via information measures.

Main Methods:

• Equations of motion
• Real-time diagrammatics
• Kraus-operator sums
• Time-local and nonlocal quantum master equations (Nakajima-Zwanzig)
• Exactly solvable fermionic resonant level model

Main Results:

• Loss of semigroup-divisibility causes reentrant behavior: temporary increase in level occupation, implying transport current reversal.
• Loss of completely positive divisibility prohibits current reversals in specific time intervals.
• Exact time-dependent environmental state and information measures (entropy, exchange entropy, coherent information) are determined.

Conclusions:

• Divisibility is crucial for understanding non-Markovian quantum dynamics.
• Reentrant behavior and current reversals are key signatures of lost divisibility.
• The study provides a framework for experimental detection and environmental impact quantification.