Accuracy of the non-relativistic approximation for momentum diffusion

Abstract

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.

Application of molecular dynamics simulations in interface interaction of clay: Current status and perspectives

“…The commonly used quantum chemical calculation methods and simulation methods are based on quantum mechanics theory, namely, Born Oppenheimer approximation, 74 non‐relativistic approximation, 75 single electron approximation, 76 and so forth, and have developed on the basis. Materials Studio can effectively simulate the relationship between atomic and molecular structures of materials.…”

Breakdown of agreement between non-relativistic and relativistic quantum dynamical predictions in the non-relativistic regime

“…However, it is not known whether the non-relativistic time-dependent wave function and quantities derived from it are always close approximation to the relativistic counterparts as conventionally expected [8]. This important fundamental question in quantum physics has not been addressed so farthe accuracy of the non-relativistic approximation to relativistic dynamics in the non-relativistic regime has only been studied in the classical context [9][10][11][12][13][14][15]. Here we present a theoretical argument that the non-relativistic quantum approximation is, generally, not always close to the relativistic quantum dynamics in the non-relativistic regime, and provide supporting numerical evidence for the free rotor and hydrogen atom.…”