Quantum statistical ensemble for emissive correlated systems.

Area of Science:

• Quantum mechanics
• Statistical mechanics
• Many-body systems

Background:

• Relaxation dynamics in complex quantum systems are crucial for statistical mechanics.
• The canonical ensemble and Boltzmann distribution typically rely on detailed balance for steady states.
• Open quantum systems interacting with an environment are fundamental to understanding thermalization.

Purpose of the Study:

• To investigate the steady-state properties of an open correlated quantum system in contact with a vacuum reservoir.
• To determine the nature of the stationary probability distribution in such an 'emissive' system.
• To explore the emergence of Boltzmann-like distributions in the absence of detailed balance.

Main Methods:

• Modeling an open correlated quantum system interacting with a vacuum reservoir.
• Analyzing the relaxation dynamics towards the steady state.
• Investigating transition rates between system eigenstates.
• Examining the stationary probability distribution across different N-particle sectors.

Main Results:

• The steady state exhibits a Boltzmann-like probability distribution over stable eigenstates within each N-particle sector.
• This Boltzmann distribution emerges despite the absence of detailed balance.
• The system's quantum statistical ensemble is characterized by sector-dependent temperatures, differing from the Gibbs ensemble.
• Transition rates show an exponential dependence on transition energy.

Conclusions:

• The Boltzmann distribution can arise in emissive quantum systems even without detailed balance.
• Sector-specific temperatures characterize the steady state of these systems.
• The findings suggest a generic property for a broad class of emissive quantum many-body systems.