A Probability Distribution for Quantum Tunneling Times

Abstract

We propose a general expression for the probability distribution of real-valued tunneling times of a localized particle, as measured by the Salecker-Wigner-Peres quantum clock. This general expression is used to obtain the distribution of times for the scattering of a particle through a static rectangular barrier and for the tunneling decay of an initially bound state after the sudden deformation of the potential, the latter case being relevant to understand tunneling times in recent attosecond experiments involving strong field ionization.

How to understand the tunneling in attosecond experiment?

“…Importantly, Winful showed that the contribution of the first term is disentangled from the barrier time delay[13]. And in their work Lunardi et al used the so-called Salecker-Wigner-Peres quantum-clock (SWP-QC) with MC-simulation[14,15], they found that the tunneling time in the attoclock is given by the form 6. The first term, called well-time, is according to the authors the time delay spent before reaching the barrier and the second term corresponds to the barrier time delay.…”

Soft self-healing resistive-based sensors inspired by sensory transduction in biological systems

“…If the interparticle distance between the particles of the secondary phase is small enough, tunneling paths form and electrons move between the conductive particles [76]. However, when the interparticle distance increases, the probability for tunneling paths to form decreases [77]. For larger interparticle distance, the percolation theory is dominant.…”

Electron interaction with the environment in tunnel ionization

“…Though a direct measurement of such small times is difficult, the advent of intense laser fields has made measurements [13][14][15] on the tunneling of bound electrons [16] from atoms possible. In this field ionization process, the electron tunnels through the potential created by a superposition of the atomic Coulomb potential and the laser field.…”