Symmetrized Liouvillian Gap in Markovian Open Quantum Systems

Area of Science:

• Quantum Physics
• Open Quantum Systems
• Theoretical Chemistry

Background:

• Markovian open quantum systems exhibit complex relaxation dynamics.
• The Liouvillian spectral gap estimates asymptotic decay rates but can be misleading due to long crossover times.
• Accurate estimation of relaxation times is crucial for understanding quantum system evolution.

Purpose of the Study:

• To develop a rigorous method for bounding transient decay of autocorrelation functions in open quantum systems.
• To introduce and analyze the properties of the symmetrized Liouvillian gap.
• To compare the effectiveness of the symmetrized Liouvillian gap against the standard Liouvillian gap.

Main Methods:

• Introduction of the symmetrized Liouvillian gap.
• Theoretical analysis of the Liouvillian gap and its symmetrized counterpart.
• Numerical simulations to validate the theoretical findings.

Main Results:

• The symmetrized Liouvillian gap provides a rigorous upper bound for transient decay of autocorrelation functions.
• The standard Liouvillian gap does not always provide a correct estimate of relaxation time.
• The symmetrized and standard Liouvillian gaps are identical under equilibrium conditions but differ when detailed balance is absent.

Conclusions:

• The symmetrized Liouvillian gap is a more reliable indicator of relaxation dynamics in non-equilibrium open quantum systems.
• This work offers a refined tool for analyzing the transient behavior and steady-state properties of quantum systems.
• The findings have implications for fields relying on the accurate modeling of quantum dynamics.