Tunneling in polymer quantization and the Quantum Zeno Effect

• Quantum mechanical tunneling in the context of Polymer Quantization is presented.
• Tunneling rates have been calculated.
• Changes in the tunneling times are investigated as a function of polymer length scale.
• Quantum Zeno Effect is observed as a result of changes in the polymerization scale.
• Bounds on the polymerization scale is placed by comparison to experiments.

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.