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Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level
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Published on: September 26, 2016

Stochastic models for relativistic diffusion.

Boris Baeumer1, Mark M Meerschaert, Mark Naber

  • 1Department of Mathematics and Statistics, University of Otago, Dunedin, New Zealand. bbaeumer@maths.otago.ac.nz

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 28, 2010
PubMed
Summary
This summary is machine-generated.

This study links the Schrödinger equation to a relativistic diffusion equation using analytic continuation. It introduces stochastic models for relativistic diffusion, avoiding fractional calculus for broader applications.

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Area of Science:

  • Theoretical Physics
  • Mathematical Physics
  • Stochastic Processes

Background:

  • The Schrödinger equation describes quantum mechanics, while diffusion equations model particle movement.
  • Analytic continuation is a mathematical technique to extend functions to new domains.
  • Relativistic effects become significant at high speeds and energies.

Purpose of the Study:

  • To explore the relationship between quantum mechanics and diffusion phenomena.
  • To develop a relativistic diffusion model.
  • To investigate stochastic processes in relativistic diffusion.

Main Methods:

  • Analytic continuation of the Schrödinger equation to derive a relativistic diffusion equation.
  • Development of stochastic models for relativistic diffusion.
  • Formulation of equivalent differential equations without fractional derivatives.

Main Results:

  • A relativistic diffusion equation derived via analytic continuation, incorporating fractional calculus.
  • Stochastic models providing an alternative framework for relativistic diffusion.
  • Differential equations equivalent to fractional relativistic diffusion but without fractional derivatives.

Conclusions:

  • The study establishes a formal link between quantum mechanics and relativistic diffusion.
  • The developed stochastic models offer a new perspective on anomalous diffusion.
  • The findings pave the way for exploring relativistic phenomena using diffusion-based approaches.