Semi-Markov processes in open quantum systems. III. Large deviations of first-passage-time statistics

Area of Science:

• Quantum Mechanics
• Statistical Physics

Background:

• Open quantum systems exhibit complex dynamics, including quantum jumps.
• First passage time statistics are crucial for understanding system evolution and relaxation.
• Scaled generating functions (SCGFs) provide insights into statistical properties.

Purpose of the Study:

• To develop a method for calculating large deviations of first passage time statistics in open quantum systems.
• To derive SCGFs for counting statistics in these systems.
• To investigate the applicability and limitations of the semi-Markov process for different types of variables.

Main Methods:

• Utilizing the semi-Markov process to model open quantum systems with finite collapsed states.
• Employing an equation of poles to determine SCGFs.
• Analyzing the roots of the equation with respect to the z-transform parameter.
• Investigating current-like variables and their associated transform convergence issues.

Main Results:

• Analytical solutions for SCGFs of first passage time statistics were obtained for simple counting variables.
• The method's limitations were identified for current-like variables due to root non-uniqueness.
• The approach was successfully illustrated using a resonantly driven two-level quantum system.
• Quantum violations of classical kinetic and thermodynamic uncertainty relations were explored.

Conclusions:

• The semi-Markov process offers a robust framework for analyzing first passage time statistics in specific open quantum systems.
• The derived SCGFs provide valuable tools for characterizing quantum system dynamics.
• Understanding the limitations of the method is crucial for its accurate application.
• The findings contribute to the study of quantum thermodynamics and uncertainty relations.