Time dependent phenomena in quantum mechanics
Solutions to explicit time-dependent Hamiltonians are rare. Specific propagators are known only for Hamiltonians that are quadratic in position and momentum, or that possess an additional invariant which allows to map the time-dependent problem to a related stationary problem.
Especially the description of decaying (or metastable) states requires the analysis of non-stationary systems. We analyzed the survival rate of states in a model, where we lower a barrier that confined the particle for t<0 [10]. These models are related to the Moshinsky shutter, which is a prime example for transient effects in the time-evolution of a quantum state.
The Floquet series for periodically driven systems is well known, but what about the description of a system with a quasiperiodic (Fibonacci sequence) driving? Surprisingly also this case contains invariants of the motion [20].
Recently, we have studied revivals of wavepackets in graphene in a magnetic field [22]. Check out the movies !
References
| [22] | Revivals of quantum wave-packets in graphene | ||
| V. Krueckl and T. Kramer | |||
| New Journal of Physics, 11, 093010 (2009) [Open Access] | article | arxiv | |
| [20] | Quasiperiodic propagation in time of some classical/quantum systems: Nielsen’s conserved quantity and Floquet properties | ||
| P. Kramer, T. Kramer, and V.I. Man’ko | |||
| Physica Scripta, 79 , 055006 (2009) | article | arxiv | |
| [11] | Transient effects in two channel interactions and an application to the behaviour of a time-dependent shutter | ||
| T. Kramer and M. Moshinsky | |||
| Revista Mexicana de Física, 51, 407-414, (2005) | article | Open Access | |
| [10] | Tunnelling out of a time-dependent well | ||
| T. Kramer and M. Moshinsky | |||
| J. Phys. A, 38, 5993-6003, (2005), AMS Review MR2167958 | article | arxiv | |