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Mixing Rates of Ergodic Algorithms

Sprott Julien C.

In response to the 2024 Snook Prize Problem, this paper compares the mixing rates of six simple numerical algorithms that produce an ergodic Gaussian distribution of position and momentum for a one-dimensional harmonic oscillator. A hundred thousand initial conditions spread uniformly over the co ...

2024 Snook Prize Problem: Ergodic Algorithms’ Mixing Rates

Hoover William G., Hoover Carol G.

In 1984 Shuichi Nosé invented an isothermal mechanics designed to generate Gibbs’ canonical distribution for the coordinates {q} and momenta {p} of classical N-body systems [1, 2]. His approach introduced an additional timescaling variable s that could speed up or slow down the {q, p} motion i ...