Classical versus quantum dynamics for a driven relativistic oscillator - art. no. 035402

We compare the time evolution of the quantum-mechanical spatial probability density obtained by solving the time-dependent Dirac equation with its cla ssical counterpart obtained from the relativistic Liouville equation for th e phase-space density in a regime in which the dynamics is essentially rela tivistic. For a resonantly driven one-dimensional harmonic oscillator, the simplest nontrivial model system to perform this comparison, we find that, despite the nonlinearity induced by relativity, the classical ensemble desc ription matches the quantum evolution remarkably well.