Tunneling in Polymer Quantization and the Quantum Zeno Effect

TL;DR

This paper explores quantum tunneling within polymer quantization, deriving transmission/reflection coefficients and tunneling times, and suggests the emergence of the Quantum Zeno Effect in this discrete quantum framework.

Contribution

It introduces a novel analysis of tunneling times and the Quantum Zeno Effect using polymer quantization, extending the understanding of quantum phenomena in discrete space models.

Findings

Polymer quantization affects tunneling behavior.

Tunneling times are analytically derived in the polymer framework.

Evidence suggests the Quantum Zeno Effect appears in polymer quantization.

Abstract

As an application of the polymer quantization scheme, in this work we investigate the one dimensional quantum mechanical tunneling phenomenon from the perspective of polymer representation of a non-relativistic point particle and derive the transmission and reflection coefficients. Since any tunneling phenomenon inevitably evokes a tunneling time we attempt an analytical calculation of tunneling times by defining an operator well suited in discrete spatial geometry. The results that we come up with hint at appearance of the Quantum Zeno Effect in polymer framework.