Abstract.
The accuracy of the non-relativistic approximation, which is calculated using the same parameter and the same initial ensemble of trajectories, to relativistic momentum diffusion at low speed is studied numerically for a prototypical nonlinear Hamiltonian system -the periodically delta-kicked particle. We find that if the initial ensemble is a non-localized semi-uniform ensemble, the non-relativistic approximation to the relativistic mean square momentum displacement is always accurate. However, if the initial ensemble is a localized Gaussian, the non-relativistic approximation may not always be accurate and the approximation can break down rapidly.
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Liang, SN., Lan, B.L. Accuracy of the non-relativistic approximation for momentum diffusion. Eur. Phys. J. Plus 131, 218 (2016). https://doi.org/10.1140/epjp/i2016-16218-0
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DOI: https://doi.org/10.1140/epjp/i2016-16218-0