Under the Barrier Wave Packet Tunneling Dynamics

V. V. Dodonov, A. B. Klimov, Vladimir I. Man’ko

Joachim Ankerhold

Yu. E. Lozovik, Alexey V. Filinov

The transmission of wave packets through barriers by tunneling is studied in detail by the method of quantum molecular dynamics. The distribution of the arrival times of a tunneling packet in front of and behind a barrier and the momentum distribution function of the packet are calculated. The average position and average momentum of the packet and their spread are investigated. It is found that below the barrier a part of the packet is reflected, and a Gaussian barrier increases the average momentum of the transmitted packet and its spread in momentum space.

M. Alkhateeb, X. Gutiérrez de la Cal, M. Ll. Pons +2 more

Recent results on electron tunneling across a potential barrier, inferred from observations or obtained from theoretical models, have suggested superluminal or instantaneous barrier traversal times. In this work we investigate relativistic wave-packet dynamics for an electron tunneling through a potential barrier employing space-time resolved solutions to relativistic quantum field theory (QFT) equations. We prove by linking the QFT property of microcausality to the wave-packet behavior that the tunneling dynamics is fully causal, precluding instantaneous or superluminal effects. We illustrate these results by performing numerical computations for an electron tunneling through a potential barrier for standard tunneling as well for Klein tunneling. In all cases (Klein tunneling or regular tunneling across a standard or a supercritical potential) the transmitted wave packet remains in the causal envelope of the propagator, even when its average position lies ahead of the average position of the corresponding freely propagated wave packet.

Pedro Pereyra

Markus Saltzer, Joachim Ankerhold

We study to what extent propagation of wave packets through potential barriers can be described semiclassically in real time. By analyzing the semiclassical approximation to the exact path-integral representation of the quantum-mechanical time evolution operator, we show that in the long-time sector it is dominated by quasiclassical fluctuations associated with caustics. Contrary to the description of tunneling in imaginary times, simple tunneling paths even for complex energies do not exist. Our findings lead to an extended semiclassical propagation scheme for wave-packet dynamics which is numerical efficient and accurately describes deep incoherent tunneling through static and externally driven barrier potentials.