Tunnelling in double-minimum potentials

Yong Yang

Quantum tunneling across double potential barriers is studied. With the assumption that the real space is a continuum, it is rigorously proved that large barriers of arbitrary shapes can be penetrated by low-energy particles with a probability of unity, i.e., realization of resonant tunneling (RT), by simply tuning the interbarrier spacing. The results are demonstrated by tunneling of electrons and protons, in which resonant and sequential tunneling are distinguished. The critical dependence of tunneling probabilities on the barrier positions not only demonstrates the crucial role of phase factors but also points to the possibility of ultrahigh accuracy measurements near resonance. By contrast, the existence of a nonzero minimum length puts upper bounds on the barrier size and particle mass, beyond which effective RT ceases. A scheme is suggested for dealing with the practical difficulties arising from the delocalization of particle position due to the uncertainty principle. This work opens a possible avenue for experimental tests of the existence of a minimum length based on atomic systems. Published by the American Physical Society 2024

S. Lj. S. KOČINAC, V. Milanović

Christian Bracher, M. Kleber, Mustafa Riza

Tunneling problems are characterized by different quantum time scales of motion. In this paper, we identify a tunneling time scale, which is based on a simple variational principle. The method utilizes the stationary eigenfunctions for a given one-dimensional potential structure, and it provides a truly local definition of the tunneling time, independent of the asymptotic shape of the potential. We express the minimum tunneling time in terms of the more common time scales obtained from the Larmor clock setup. Asymptotic formulas for both the extreme quantum and the semiclassical limit are presented. As an experimental verification of the variational approach we demonstrate that the minimum tunneling time governs the time a particle requires to traverse the barrier in a symmetric double-well structure.

Oscar J. Riveros

Xiao Qu

First,resolving the Schroinger equation for the boundary condition,we got the tunneling time of one and double delta complex potentials.Then,we also analyzed the effection of the related aspects to the phase time by using the Matlab and Origin.The research we got that,the phase time under the two conditions,was different for the effection of the real and imaginary part,as well as the projectile energy. Reserching the signal delta complex potentials,we got the maximum,while the double delta complex potentials having the minimum.Lastly,the two different potentials were simulated and analyzed.

Sourendu Gupta A