Structure of quantum mean force Gibbs states for coupled harmonic systems

Area of Science:

• Quantum Mechanics
• Statistical Mechanics
• Condensed Matter Physics

Background:

• Open quantum systems interact with environments (heat baths).
• The steady state is typically the mean force Gibbs (MFG) state, differing from the system Gibbs state when coupling is significant.
• Understanding these states is crucial for quantum thermodynamics and information.

Purpose of the Study:

• To derive the exact mean force Gibbs (MFG) state for coupled quantum harmonic oscillators interacting with multiple thermal baths.
• To develop a nonperturbative method for calculating system covariances in the MFG state.
• To investigate the impact of system-bath coupling strength and its spatial dependence.

Main Methods:

• Path integral method to derive the exact MFG state.
• Nonperturbative calculation of system covariances.
• Analysis of coupling effects in the ultrastrong coupling limit.

Main Results:

• The exact MFG state for coupled quantum harmonic oscillators was derived.
• A novel nonperturbative method for calculating covariances was developed.
• The effect of system-bath coupling was found to decay exponentially with distance from the boundary, analogous to the quantum skin effect.
• The ultrastrong coupling limit was analyzed, connecting to broader quantum system results.

Conclusions:

• The study provides an exact solution for the MFG state in a relevant quantum system.
• The observed exponential decay of coupling effects highlights a quantum skin effect in open quantum harmonic oscillators.
• The findings offer insights into quantum system behavior under strong environmental interactions.