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Relativistic Lévy processes.

Lucas G B de Souza1,2, M G E da Luz3, E P Raposo4

  • 1Universidade Federal do Rio Grande do Norte, Departamento de Física Teórica e Experimental, Natal 59078-970, Brazil.

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Summary
This summary is machine-generated.

Researchers explored sums of random velocities in special relativity, discovering a new class of relativistic Lévy processes. These processes help identify relativistic regimes and assess stochastic relativistic effects in experiments.

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Area of Science:

  • Physics
  • Mathematics
  • Statistical Mechanics

Background:

  • Stochastic processes are fundamental in physics.
  • Special relativity governs high-velocity phenomena.
  • Understanding random velocity distributions is key in relativistic systems.

Purpose of the Study:

  • To investigate sums of independent and identically distributed random velocities in special relativity.
  • To introduce and characterize a new class of stochastic processes: relativistic Lévy processes.
  • To develop a method for identifying relativistic regimes and assessing stochastic relativistic effects.

Main Methods:

  • Mathematical analysis of velocity distributions under relativistic velocity addition.
  • Characterization of the new processes based on distribution concavity and measurement probabilities.
  • Comparison with experimental data from heavy-ion diffusion and antiproton cooling.

Main Results:

  • The one-dimensional velocity distributions are stable under relativistic velocity addition.
  • A new class of stochastic processes, relativistic Lévy processes, has been defined.
  • Relativistic regimes can be identified by distribution concavity and measurement probabilities.
  • Findings align with heavy-ion diffusion and antiproton cooling momentum deviations.

Conclusions:

  • Relativistic Lévy processes represent a novel framework for stochastic phenomena in special relativity.
  • The study provides a protocol to evaluate the significance of relativistic stochastic effects in experiments.
  • The results offer insights into particle behavior in high-energy physics and accelerator experiments.