Relativistic Heat Equation via Lévy stable distributions: Exact Solutions
arXiv:1610.05605 · doi:10.1002/andp.201700374
Abstract
We introduce and study an extension of the heat equation relevant to relativistic energy formula involving square root of differential operators. We furnish exact solutions of corresponding Cauchy (initial) problem using the operator formalism invoking one-sided Lévy stable distributions. We note a natural appearance of Bessel polynomials which allow one the obtention of closed form solutions for a number of initial conditions. The resulting relativistic diffusion is slower than the non-relativistic one, although it still can be termed a normal one. Its detailed statistical characterization is presented in terms of exact evaluation of arbitrary moments and is compared with the non-relativistic case.
References in corpus (8)
- Relativistic Brownian Motion
- Exact and explicit probability densities for one-sided Levy stable distributions
- Superpositions of Probability Distributions
- Superstatistics approach to path integral for a relativistic particle
- Nonlinear heat conduction equations with memory: physical meaning and analytical results
- Relativistic equations with fractional and pseudo-differential operators
- Relativistic dynamics, Green function and pseudodifferential operators
- Theory of relativistic heat polynomials and one-sided Lévy distributions