Simulation of tunneling in the quantum tomography approach

Abstract

A method for the simulation of nonstationary quantum processes is proposed. The method is based on the tomography representation of quantum mechanics, i.e., the state of the system is described by a nonnegative function (quantum tomogram). In the framework of the method one uses the ensemble of trajectories in the tomographic space to represent evolution of the system (therefore direct calculation of the quantum tomogram is avoided). To illustrate the method we consider the problem of nonstationary tunneling of a wave packet. A number of characteristics of tunneling, such as tunneling time, evolution of spatial and momentum distributions, and tunneling probability are calculated within the quantum tomography approach. Tunneling of a wave packet of a composite particle, an exciton, is also considered; exciton ionization due to the scattering on the barrier is analyzed.