Tunneling as a Source for Quantum Chaos

TL;DR

This paper investigates how quantum tunneling in a one-dimensional potential well influences wave function complexity, using entropy measures to distinguish quantum effects from classical behavior.

Contribution

It introduces a quantitative approach to analyze quantum chaos via entropy in a tunneling model, highlighting the quantum nature of entropy growth.

Findings

Tunneling causes complex wave function behavior.

Increasing barrier height/width reduces tunneling and slows entropy growth.

Entropy growth is identified as a quantum-specific phenomenon.

Abstract

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 spatial entropy function defined by S = -\int |\Psi(x,t)|^2 ln |\Psi(x,t)|^2 dx. There is no classical counterpart to tunneling, but a decrease in the tunneling in a short time interval may be interpreted as an approach of a quantum system to a classical system. We show that changing the square barrier by increasing the height/width do not only decrease the tunneling but also slows down the rapid rise of the entropy function, indicating that the entropy growth is an essentially quantum effect.