Relativistic analysis of stochastic kinematics

Area of Science:

• * Physics
• * Statistical Mechanics
• * Relativistic Kinematics

Background:

• * Stochastic kinematics describes random particle motion.
• * Understanding diffusion in inertial frames is crucial for various physical phenomena.
• * Previous models often simplified relativistic effects on diffusion.

Purpose of the Study:

• * To develop a relativistic analysis of stochastic kinematics.
• * To determine the transformation of the effective diffusivity tensor in inertial frames.
• * To investigate the impact of relativistic effects on diffusion processes.

Main Methods:

• * Analysis of Poisson-Kac stochastic processes.
• * Examination of one-dimensional and higher-dimensional spatial models.
• * Application of discrete space-time diffusion processes.
• * Confirmation through simulation experiments.

Main Results:

• * Effective diffusion coefficient is inversely proportional to the third power of the Lorentz factor in 1D.
• * The diffusivity tensor becomes nonisotropic in moving frames for higher dimensions.
• * Diffusivities parallel and orthogonal to motion scale differently with the Lorentz factor.
• * A general transformation theory for tensor diffusivity was established.

Conclusions:

• * Relativistic effects significantly alter diffusion tensor properties in inertial frames.
• * The derived transformation theory provides a framework for understanding anisotropic diffusion.
• * Findings have implications for modeling transport phenomena in high-energy physics and cosmology.