Accuracy of the non-relativistic approximation for momentum diffusion
Electrical and Computer Systems Engineering, School of Engineering, Monash University, 47500, Bandar Sunway, Malaysia
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Accepted: 24 May 2016
Published online: 29 June 2016
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.
© The Author(s), 2016