Power spectra for both interrupted and perennial aging processes

Area of Science:

• Complex Systems
• Statistical Physics
• Non-equilibrium Physics

Background:

• Random telegraphic noise (RTN) is characterized by waiting time distributions.
• The ergodic hypothesis is crucial for applying the Wiener-Khintchine theorem to power spectrum analysis.
• Deviations from ergodicity (mu<2) require careful consideration of spectrum evaluation.

Purpose of the Study:

• To theoretically and numerically study the power spectrum of RTN with a power-law waiting time distribution (psi(tau) ~ 1/tau^mu).
• To analyze the behavior of the power spectrum S(f) = K/f^eta, particularly near the ergodic-non-ergodic boundary (mu approx 2).
• To investigate the influence of finite sequence length (L) on the power spectrum, considering different truncation effects.

Main Methods:

• Theoretical analysis of RTN power spectrum.
• Numerical simulations to validate theoretical predictions.
• Application of a generalized Onsager principle.
• Consideration of finite sequence length (L) and truncation effects (physical and observation-induced).

Main Results:

• The power spectrum follows S(f) = K/f^eta, with eta = 3-mu, bridging ergodic (mu>2) and non-ergodic (mu<2) regimes.
• For mu<2, the Wiener-Khintchine theorem is validated by truncation effects.
• The coefficient K depends on L (K ~ 1/L^(2-mu)) in the L<
• A transition from 1/f^eta to 1/f^2 regimes is predicted and observed in experiments.

Conclusions:

• The study provides a unified theoretical framework for understanding the power spectrum of RTN across different ergodic conditions.
• The findings explain experimental observations in blinking quantum dots and intermittent molecular fluorescence.
• The work offers criteria to distinguish between different truncation regimes (L<>T(max)) in experimental data.