Single molecule counting statistics for systems with periodic driving.

Area of Science:

• Physical Chemistry
• Spectroscopy
• Theoretical Chemistry

Background:

• Single molecule spectroscopy provides detailed insights into molecular dynamics.
• Analyzing systems under time-dependent perturbations is computationally challenging.
• Existing methods struggle with explicitly time-dependent and periodic driving forces.

Purpose of the Study:

• To extend the generating function approach for calculating event statistics in single molecule spectroscopy.
• To incorporate explicitly time-dependent and periodic perturbations into the analysis.
• To provide a versatile and accurate computational methodology.

Main Methods:

• Utilized Floquet theory to transform time-dependent generating function equations into time-independent effective equations.
• Applied the methodology to systems with both simple stochastic dynamics and quantum dynamics.
• Demonstrated the numerical accuracy and versatility of the extended approach.

Main Results:

• Successfully adapted the generating function approach for periodically driven single molecule systems.
• The use of Floquet theory effectively removes explicit time-dependence from the governing equations.
• Validated the method's accuracy and broad applicability through two distinct dynamic examples.

Conclusions:

• The extended generating function approach, incorporating Floquet theory, offers a powerful tool for analyzing complex single molecule spectroscopy data.
• This methodology significantly simplifies the treatment of time-dependent and periodic perturbations.
• The approach is versatile, applicable to both stochastic and quantum dynamics, paving the way for advanced molecular studies.