Tunneling Time and Wave Packets Evolution

E. H. Hauge, J. P. Falck, Tor A. Fjeldly

Rolf W. Landauer, Th. Martin

Óscar del Barco, M. Ortuño, V. Gasparian

We analyze the tunneling-time problem via the presence time formalism. With this method we reproduce previous results for very long wave packets and we are able to calculate the tunneling time for general wave packets of arbitrary shape and length. The tunneling time for a general wave packet is equal to the average over the energy components of the standard phase time. With this approach we can also calculate the time uncertainty. We have checked that the results obtained with this approach agree extremely well with numerical simulations of the wave packet evolution.

Lijuan Jia, Long Xu, Peng Zhang +1 more

Abstract We investigate the time-dependent electron wave packet in a one-dimensional geometry with the potential bent by a homogeneous external field. Based on the behaviors of the wave packet over time, we observe a crossover time. After this crossover time, the temporal evolution of the wave packet comes into a new regime, where the wave packet evolves in a self-similar structure. To establish the time scale of this crossover quantitatively, we utilize the Loschmidt echo function, through which the time at which the crossover occurs can be extracted. We also find the time of the maximum ionization velocity can be comparable with the semi-classical tunneling delay time.

Jose Tadeu Lunardi, Luiz A. Manzoni, Andrew T. Nystrom +1 more

А. Ж. Хачатрян, Al.G. Alexanyan, V. A. Khoetsyan +1 more

We consider the evolution of a wave packet that is made up of a group of the wave functions describing the stationary scattering process and tunnels through a one-dimensional potential of arbitrary form. As the main characteristics of the time difference of the tunnelling process, use is made of the propagation speed of the wave-packet maximum. We show that the known Hartman formula for the tunnelling time corresponds to the wave packet with a wavenumber-uniform spectral composition in the case, when the phase and transmission coefficient modulus dispersions are taken into account only in the linear approximation. The amplitude of the main peak of the transmitted wave intensity is proven to be independent of the tunnelling time and is determined by the transmission coefficient of the spectral component at the carrier frequency and the spectral width of the wave packet. In the limit of an infinitely wide potential barrier the amplitude of the wave-packet maximum is shown to tend to zero slower than the tunnelling time tends to its asymptotic value, i.e., indeed we deal with the paradox of an infinitely large propagation speed of a wave disturbance through the barrier.