Related papers: Tunnelling of plane waves through a square barrier
We analytically compute the time evolution of an initial infinite plane wave in the presence of a 1-dimensional square quantum barrier. This calculation generalizes the analysis of the shutter problem and sets the basis for the calculation…
The quantum shutter approach to tunneling time scales (G. Garc\'{\i }a-Calder\'{o}n and A. Rubio, Phys. Rev. A \textbf{55}, 3361 (1997)), which uses a cutoff plane wave as the initial condition, is extended in such a way that a certain type…
The particle approach to one-dimensional potential scattering is applied to non relativistic tunnelling between two, three and four identical barriers. We demonstrate as expected that the infinite sum of particle contributions yield the…
The assisted tunneling of a wave packet between square one dimensional barriers is treated analytically. The tunneling rate is calculated exactly for a potential mimicking a constant electric field with arbitrary time dependence. The pole…
The tunneling of Gaussian wave packets has been investigated by numerically solving the one-dimensional Schr\"odinger equation. The shape of wave packets interacting with a square barrier has been monitored for various values of the barrier…
The tunneling time of particle through given barrier is commonly defined in terms of "internal clocks" which effectively measure the interaction time with internal degrees of freedom of the barrier. It is known that this definition of the…
By using an exact solution to the time-dependent Schr\"{o}dinger equation with a point source initial condition, we investigate both the time and spatial dependence of quantum waves in a step potential barrier. We find that for a source…
Time dependence for barrier penetration is considered in the phase space. An asymptotic phase-space propagator for nonrelativistic scattering on a one - dimensional barrier is constructed. The propagator has a form universal for various…
The stationary phase method is often employed for computing tunneling {\em phase} times of analytically-continuous {\em gaussian} or infinite-bandwidth step pulses which collide with a potential barrier. The indiscriminate utilization of…
After reexamining the above barrier diffusion problem where we notice that the wave packet collision implies the existence of {\em multiple} reflected and transmitted wave packets, we analyze the way of obtaining phase times for…
A known limitation of time-dependent mean-field approaches is a lack of quantum tunneling for collective motions such as in sub-barrier fusion reactions. As a first step toward a solution, a time-dependent model is considered using a…
The phase time in quantum tunneling can be disentangled into a dwell time plus a term arising due to the interference of the reflected and incident waves in front of the barrier. The interference term dominates at low energies and as E -->…
We theoretically study the tunneling time by investigating a wave packet of Bose-condensed atoms passing through a square barrier. We find that the tunneling time exhibits different scaling laws in different energy regimes. For negative…
Tunneling delay times of wavepackets in quantum mechanical penetration of rectangular barriers have long been known to show a perplexing independence with respect to the width of the barrier. This also has relevence to the transmission of…
The transitional regime of plane channel flow is investigated {above} the transitional point below which turbulence is not sustained, using direct numerical simulation in large domains. Statistics of laminar-turbulent spatio-temporal…
This paper revisited quantum tunneling dynamics through a square double-barrier potential. We emphasized the similarity of tunneling dynamics through double-barrier and that of optical Fabry--P$\acute{e}$rot (FP) interferometer. Based on…
An explicit expression is obtained for the phase-time corresponding to tunneling of a (non-relativistic) particle through two rectangular barriers, both in the case of resonant and in the case of non-resonant tunneling. It is shown that the…
Quantum mechanical tunneling across smooth double barrier potentials modeled using Gaussian functions, is analyzed numerically and by using the WKB approximation. The transmission probability, resonances as a function of incident particle…
Tunneling, though a physical reality, is shrouded in mystery. Wave packets cannot be constructed under the barrier and group velocity cannot be defined. The tunneling particle can be observed on either sides of the barrier but its…
We use an one dimensional model of a square barrier embedded in an infinite potential well to demonstrate that tunneling leads to a complex behavior of the wave function and that the degree of complexity may be quantified by use of the…