Mixing Rates of Ergodic Algorithms

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 constant energy surface are used for each of the six systems. The time-dependent kurtosis serves as a measure of the mixing rate. By this criterion, the most rapid mixing occurs for the signum thermostat system with an optimally chosen parameter value.

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Opracowanie rekordu ze środków MNiSW, umowa nr POPUL/SP/0154/2024/02 w ramach programu "Społeczna odpowiedzialność nauki II" - moduł: Popularyzacja nauki (2025).