TITLE:
Persistence Exponent for the Simple Diffusion Equation: The Exact Solution for Any Integer Dimension
AUTHORS:
Devashish Sanyal
KEYWORDS:
Non-Equilibrium Statistical Mechanics, Diffusion Equation, Persistence Exponent, Probability Theory
JOURNAL NAME:
Journal of Modern Physics,
Vol.12 No.10,
August
4,
2021
ABSTRACT: The persistence exponent for the simple diffusion equation , with random Gaussian initial condition, has been calculated exactly using a method known as selective averaging. The probability that the value of the field at a specified spatial coordinate remains positive throughout for a certain time t behaves as for asymptotically large time t. The value of , calculated here for any integer dimension d, is for and 1 otherwise. This exact theoretical result is being reported possibly for the first time and is not in agreement with the accepted values for respectively.