Complexity, Tunneling and Geometrical Symmetry

TL;DR

This paper explores how geometrical symmetry and near-degeneracy of energy levels influence the complex behavior of quantum wave functions during tunneling in a simple one-dimensional system.

Contribution

It demonstrates the link between spectral degeneracy caused by symmetry and the complexity of wave function evolution during tunneling.

Findings

Complex behavior correlates with near-degenerate energy levels.

Symmetry influences the number of almost degenerate levels.

Shifting the barrier position affects degeneracy and complexity.

Abstract

It is demonstrated in the context of the simple one-dimensional example of a barrier in an infinite well, that highly complex behavior of the time evolution of a wave function is associated with the almost degeneracy of levels in the process of tunneling. Degenerate conditions are obtained by shifting the position of the barrier. The complexity strength depends on the number of almost degenerate levels which depend on geometrical symmetry. The presence of complex behavior is studied to establish correlation with spectral degeneracy.