Tunneling of Polymer Particles

TL;DR

This paper investigates polymer quantization effects on quantum tunneling, showing convergence to standard quantum results at low energies and notable deviations near maximum energies, including anomalous tunneling time peaks.

Contribution

It introduces a background independent polymer quantization approach to tunneling, comparing it with standard quantum mechanics and revealing unique high-energy behaviors.

Findings

Polymer transmission coefficients match quantum results at low energies.

Polymer tunneling time shows anomalous peaks compared to standard theory.

Transmission behavior remains qualitatively similar between polymer and quantum models.

Abstract

In this paper we study the tunneling using a background independent (polymer) quantization scheme. We show that at low energies, for the tunneling through a single potential barrier, the polymer transmission coefficient and the polymer tunneling time converge to its quantum-mechanical counterparts in a clear fashion. As the energy approaches the maximum these polymer quantities abruptly decrease to zero. We use the transfer matrix method to study the tunneling through a series of identical potential barriers. We obtain that the transmission coefficients (polymer and quantum-mechanical) behave qualitatively in a similar manner, as expected. Finally we show that the polymer tunneling time exhibits anomalous peaks compared with the standard result. Numerical results are also presented.