Numerical study of barrier tunneling in 2-d systems

Pranab Sarkar

Ekaterina A. Volkova, A. M. Popov, Olga V. Tikhonova

The tunneling of a quantum system with an internal degree of freedom through a potential barrier is considered. Based on the exact numerical solution to the nonstationary Schrödinger equation, the tunneling of a model two-particle system through a potential barrier is studied and the dependences of the tunneling transparency of the barrier on the parameters of the wave packet that describes the system at the initial moment are obtained. A sharp increase in the tunneling probability related to the formation of a long-lived quasibound state of the system in the barrier region is demonstrated. A simple analytical model of the tunneling of a system with an internal degree of freedom that allows for a qualitative interpretation of the main features of the tunneling is constructed.

Xingrong Zheng, Yujie Li, Kaiqiang Xie

Yoshitaka Tanimura, Peter Guy Wolynes

We discuss the interplay of various quantum effects on barrier crossing for a one-dimensional system with dissipation. This is based on a numerical study using a hierarchy of kinetic equations introduced by Tanimura and Kubo. The numerical work uses a grid in phase space for the Wigner distribution and deals with both the classical limit and the tunneling regimes.

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.