Quantum heat engines: Limit cycles and exceptional points.

Area of Science:

• Quantum Thermodynamics
• Statistical Mechanics
• Quantum Information

Background:

• Quantum Otto cycles are theoretical models for quantum heat engines.
• Limit cycles represent stable, repeating operational states in thermodynamic cycles.
• The behavior of quantum systems under cyclic processes is crucial for understanding quantum engines.

Purpose of the Study:

• To investigate the conditions under which a quantum Otto cycle fails to reach a stable limit cycle.
• To identify the quantum mechanical origins of instability in quantum Otto cycles.
• To contrast the behavior of quantum harmonic oscillators with quantum spins as working fluids.

Main Methods:

• Analysis of the quantum Otto cycle using a working fluid of quantum harmonic oscillators.
• Examination of the propagator's compactness and its eigenvalues.
• Identification of non-Hermitian degeneracies (exceptional points) in the propagator's eigenvalues.
• Investigation using the associated Lie algebras for rigorous proof.

Main Results:

• The inability to reach a limit cycle is directly linked to the noncompact nature of the cycle's propagator.
• A third-order exceptional point marks the transition from complex to real eigenvalues, indicating instability.
• A second-order exceptional point is found where the cycle trajectory diverges, associated with eigenvalue modulus > 1.
• The divergence arises from the inability of heat baths to dissipate internally generated heat during adiabatic strokes.

Conclusions:

• Quantum Otto cycles with harmonic oscillators exhibit instabilities characterized by exceptional points, preventing limit cycle attainment.
• Quantum spins, possessing compact Hamiltonians, do not exhibit these exceptional points and are stable.
• The findings highlight the critical role of propagator properties and heat bath dissipation in quantum engine performance.