Ballistic flights and random diffusion as building blocks for Hamiltonian kinetics

Area of Science:

• * Physics
• * Statistical Mechanics
• * Dynamical Systems

Background:

• * Hamiltonian systems with mixed phase space exhibit complex transport phenomena.
• * Understanding transport mechanisms is crucial for various physical processes.
• * Existing models may not fully capture the interplay of ordered and chaotic dynamics.

Purpose of the Study:

• * To develop a novel kinetic approach for analyzing transport in Hamiltonian systems.
• * To decompose complex dynamics into simpler, manageable components.
• * To provide a framework for understanding phenomena like anomalous diffusion and chaos-assisted transport.

Main Methods:

• * Decomposing the system's dynamics into ballistic flight and random diffusion components.
• * Developing a kinetic scheme that generates a stochastic process.
• * Comparing the statistical properties of the kinetic model with the original Hamiltonian system.

Main Results:

• * The proposed kinetic scheme generates statistical properties similar to the original Hamiltonian system.
• * The approach offers insights into anomalous diffusion and current rectification.
• * It provides a classical analogue for chaos-assisted tunneling through chaos-assisted exchange.

Conclusions:

• * The kinetic approach offers a powerful tool for studying transport in Hamiltonian systems.
• * It successfully models complex phenomena like anomalous diffusion and chaos-assisted transport.
• * This work bridges classical and quantum mechanics by providing a classical counterpart to chaos-assisted tunneling.