Quantum tunneling as a classical anomaly

TL;DR

This paper proposes that classical particles with complex energies can exhibit tunneling behavior similar to quantum particles, suggesting quantum tunneling as an anomaly in a generalized classical framework.

Contribution

It introduces a novel approach of complexifying classical mechanics to explain quantum tunneling phenomena as an anomaly, extending the Bohr correspondence principle.

Findings

Complex classical tunneling probabilities approach quantum tunneling probabilities as Re(E) increases.

Complex-energy classical particles can traverse potential barriers, mimicking quantum tunneling.

Quantum tunneling interpreted as a classical anomaly in a generalized framework.

Abstract

Classical mechanics is a singular theory in that real-energy classical particles can never enter classically forbidden regions. However, if one regulates classical mechanics by allowing the energy E of a particle to be complex, the particle exhibits quantum-like behavior: Complex-energy classical particles can travel between classically allowed regions separated by potential barriers. When Im(E) -> 0, the classical tunneling probabilities persist. Hence, one can interpret quantum tunneling as an anomaly. A numerical comparison of complex classical tunneling probabilities with quantum tunneling probabilities leads to the conjecture that as ReE increases, complex classical tunneling probabilities approach the corresponding quantum probabilities. Thus, this work attempts to generalize the Bohr correspondence principle from classically allowed to classically forbidden regions.