Quantum work relations and response theory in parity-time-symmetric quantum systems

Area of Science:

• Quantum Thermodynamics
• Quantum Information Theory
• Condensed Matter Physics

Background:

• The universal quantum work relation governs energy exchange in quantum systems driven far from equilibrium.
• Parity-time- (PT-) symmetry offers unique properties in quantum mechanics, particularly in non-Hermitian systems.
• Understanding the applicability of fundamental thermodynamic relations in non-equilibrium quantum systems is crucial.

Purpose of the Study:

• To investigate the extension of the universal quantum work relation to parity-time- (PT-) symmetric quantum systems.
• To explore the implications of unbroken and broken PT symmetry on quantum work relations.
• To demonstrate the recovery of established theories as special cases within this framework.

Main Methods:

• Analysis of a quantum system driven arbitrarily far from equilibrium.
• Application of the universal quantum work relation to PT-symmetric Hamiltonians.
• Investigation of system dynamics under conditions of both unbroken and broken PT symmetry.

Main Results:

• The universal quantum work relation is shown to extend to PT-symmetric quantum systems with unbroken PT symmetry.
• Microscopic reversibility is identified as the underlying principle for this extension.
• The quantum Jarzynski equality, linear response theory, and Onsager reciprocal relations are recovered as special cases.
• The universal quantum work relation fails to hold in the regime of broken PT symmetry due to non-preservation of the norm.

Conclusions:

• The study establishes the validity of the universal quantum work relation in a significant class of PT-symmetric quantum systems.
• The findings highlight the critical role of PT symmetry preservation in maintaining fundamental thermodynamic relations in quantum dynamics.
• This work bridges quantum thermodynamics and the study of PT-symmetric systems, offering new theoretical insights.