Collective 1/f fluctuation by pseudo-Casimir-invariants

Area of Science:

• Statistical Mechanics
• Dynamical Systems Theory
• Nonlinear Dynamics

Background:

• 1/f fluctuation, or pink noise, is a common phenomenon in various physical systems.
• Hamiltonian dynamical systems with many degrees of freedom and long-range interactions often exhibit complex behavior.
• Understanding the origins of 1/f noise in such systems is crucial for many scientific fields.

Purpose of the Study:

• To propose a universal scenario explaining the emergence of 1/f fluctuations in Hamiltonian dynamical systems.
• To investigate the role of pseudoinvariants in generating quasistationary states and slow dynamics.
• To demonstrate the universality of the observed 1/f fluctuations across different system parameters.

Main Methods:

• Theoretical analysis using the Vlasov equation in the thermodynamic limit.
• Identification of pseudoinvariants in finite systems leading to quasistationary states.
• Direct numerical simulations to confirm the presence of 1/f fluctuations.

Main Results:

• A universal scenario for 1/f fluctuation in Hamiltonian systems with long-range interactions is proposed.
• Pseudoinvariants in finite systems lead to slow dynamics and long-time correlations.
• Numerical simulations confirm the generation of 1/f fluctuations in collective variables.

Conclusions:

• The study provides a unified explanation for 1/f noise in a broad class of Hamiltonian systems.
• The findings highlight the importance of pseudoinvariants and slow dynamics in generating universal 1/f fluctuations.
• The universality is confirmed by varying system parameters like interaction range and particle number.