Fractional behavior in multidimensional Hamiltonian systems describing reactions

Area of Science:

• Chemical Dynamics
• Statistical Mechanics
• Nonlinear Systems

Background:

• Reaction processes are often modeled using Hamiltonian systems.
• Understanding anomalous diffusion and non-standard decay patterns is crucial in chemical dynamics.

Purpose of the Study:

• To investigate the fractional behavior in a three-degree-of-freedom Hamiltonian system modeling reaction processes.
• To analyze the statistical properties of trajectories within a double-well potential with a nonuniform Arnold web.

Main Methods:

• Simulation of a minimal Hamiltonian system with a double-well potential.
• Analysis of survival probability, trajectory spectra (1/f and Lorentzian), and diffusion types (subdiffusion and normal diffusion).
• Wavelet analysis to extract transient features of resonances.

Main Results:

• Survival probability exhibits both power-law and exponential decay.
• Power-law decay trajectories show subdiffusion and 1/f spectra.
• Exponential decay trajectories exhibit normal diffusion and Lorentzian spectra.
• Transient features link trajectory behavior to the Arnold web and potential saddle.

Conclusions:

• Fractional behavior in reaction processes is linked to resonance junctions, including higher-order resonances.
• The interplay between different decay patterns and diffusion types provides insights into dynamical origins.
• Wavelet analysis is effective in revealing transient resonant features.