Tunneling through a time-dependent barrier — a numerical study

Fumika Suzuki, William George Unruh

We numerically study two methods of measuring tunneling times using a quantum clock. In the conventional method using the Larmor clock, we show that the Larmor tunneling time can be shorter for higher tunneling barriers. In the second method, we study the probability of a spin-flip of a particle when it is transmitted through a potential barrier including a spatially rotating field interacting with its spin. According to the adiabatic theorem, the probability depends on the velocity of the particle inside the barrier. It is numerically observed that the probability increases for higher barriers, which is consistent with the result obtained by the Larmor clock. By comparing outcomes for different initial spin states, we suggest that one of the main causes of the apparent decrease in the tunneling time can be the filtering effect occurring at the end of the barrier.

Fernando J. Pineda, D. H. E. Gross

Jiu-Yuan Ge, John Z. H. Zhang

We present a numerical investigation of quantum mechanical tunneling process in a time-dependent (fluctuating) barrier using a one dimensional model of Eckart barrier. The tunneling probability is calculated for two cases in which (1) the height of the barrier is undergoing harmonic oscillation with frequency ω and (2) the location of the barrier is undergoing harmonic oscillation with frequency ω. It is observed in both cases that the quantum mechanical tunneling probability exhibits a maximum as a function of the oscillating frequency ω between the low and high frequency limits. The physical origin and process underlying this resonantlike phenomenon are proposed in this paper based on the current model study.

Juan Pedro Palomares-Báez, Boris I. Ivlev, José Luis Rodríguez‐López

Quantum tunneling through a nonstationary barrier is studied analytically and by a direct numerical solution of Schr\"odinger equation. Both methods are in agreement and say that the main features of the phenomenon can be described in terms of classical trajectories which are solutions of Newton's equation in complex time. The probability of tunneling is governed by analytical properties of a time-dependent perturbation and the classical trajectory in the plane of complex time. Some preliminary numerical calculations of Euclidean resonance (an easy penetration through a classical nonstationary barrier due to an underbarrier interference) are presented.