Relativistic dynamics of resonantly driven classical and quantum systems

Erind Brahimi

F. Reuse

R. E. Wagner, P. J. Peverly, Qichang C. Su +1 more

We compare the time evolution of the quantum-mechanical spatial probability density obtained by solving the time-dependent Dirac equation with its classical counterpart obtained from the relativistic Liouville equation for the phase-space density in a regime in which the dynamics is essentially relativistic. 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 description matches the quantum evolution remarkably well.

Hsinchen Yu, Zhongzhou Ren, Xin Zhang

We study a non-periodically driven kicked rotor based on the one-dimensional quantum relativistic kicked rotor (QRKR). In our model, we add a small constant to the interval of the one-dimensional QRKR after each kick process. It is found that the momentum spreading is stable in finite kicked times, it then jumps up or down and becomes stable again. This interesting phenomenon is understood by quantum resonance. Moreover, the stable-jump–stable-jump phenomenon persists, even though the interval of kick process is randomly increased. This result means that the quantum resonance is independent of the periodic perturbation in the QRKR model.

Boon Leong Lan, Rui Jian Chu

We show, both analytically and numerically, that the non-relativistic and relativistic quantum predictions for the dynamics of a prototypical driven electron – the periodically kicked rotor – do not always agree in the non-relativistic regime. The surprisingly different quantum predictions could be tested experimentally using ultra-cold fermionic atoms in a periodically-pulsed 1D optical lattice. Similar breakdown of agreement should occur for driven quantum systems in general. Since the relativistic theory should be empirically correct, it must be used instead of the approximate non-relativistic theory to correctly study the quantum dynamics of a driven system after the breakdown time, which could lead to important contributions in a wide range of fields from atomic to molecular, chemical and condensed-matter physics.