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Physics Letters A

Tunneling times in complex potentials

S. Lj. S. KOČINAC, V. Milanović

Published Jul 19, 2007• 14 citations
Publisher
DOI
10.1016/j.physleta.2007.07.021

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We study the dynamics of multidimensional quantum tunneling by introducing a complex absorbing potential into a two-dimensional model for spontaneous fission. We first diagonalize the Hamiltonian with the complex potential to determine a resonance state as well as its lifetime. We then solve the time-dependent Schr\"odinger equation with such basis in order to investigate the tunneling path. We compare this method with the semiclassical method for multidimensional tunneling with imaginary time. A good agreement is found both for the lifetime and for the tunneling path.
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.
The times spent by an electron in a scattering event or tunnelling through a potential barrier are investigated using a method based on the absorption probabilities. The reflection and transmission times derived from this method are equal to the local Larmor times if the transmission and reflection probability amplitudes are complex analytic functions of the complex potential. The numerical results show that they coincide with the phase times except as the incident electron energy approaches zero or when the transmission probability is too small. If the imaginary potential covers the whole space the tunnelling times are again equal to the phase times. The results show that the tunnelling times based on absorption probabilities are the best of the various candidates.