This research aims to study the behavior of quantum tunneling within the framework of polymer quantization, where spacetime has a discrete structure with a fundamental length $\mu_0$ . From the Hamiltonian difference equation, we obtained analytical wave functions in each region of the potential barrier and numerically calculated the transmission coefficient and Wigner time delay $\tau_w$ for comparison with standard quantum mechanics. The calculation results show that when the particle energy is lower than the potential barrier $E < W_0$ , the tunneling time $\tau_w(n)$ increases rapidly within the narrow barrier and saturates when the width is sufficiently large, confirming that the Hartman effect phenomenon persists even when the spacetime structure is discontinuous. The value of $\mu_0$ affects the saturation time but does not change the qualitative nature of this behavior. In the case of $E > W_0$ , the time increases continuously with width, which is consistent with standard quantum mechanics. This result suggests that the semi-classical properties of potential barrier penetration, particularly the Hartman effect, are stable against modifications to spacetime structure and provide important insights into understanding the behavior of quantum systems within a framework inspired by Loop Quantum Gravity (LQG).This research aims to study the behavior of quantum tunneling within the framework of polymer quantization, where spacetime has a discrete structure with a fundamental length $\mu_0$. From the Hamiltonian difference equation, we obtained analytical wave functions in each region of the potential barrier and numerically calculated the transmission coefficient and Wigner time delay $\tau_w$ for comparison with standard quantum mechanics. The calculation results show that when the particle energy is lower than the potential barrier $E < W_0$, the tunneling time $\tau_w(n)$ increases rapidly within the narrow barrier and saturates when the width is sufficiently large, confirming that the Hartman effect phenomenon persists even when the spacetime structure is discontinuous. The value of $\mu_0$ affects the saturation time but does not change the qualitative nature of this behavior. In the case of $E > W_0$, the time increases continuously with width, which is consistent with standard quantum mechanics. This result suggests that the semi-classical properties of potential barrier penetration, particularly the Hartman effect, are stable against modifications to spacetime structure and provide important insights into understanding the behavior of quantum systems within a framework inspired by Loop Quantum Gravity (LQG).

Dec 2, 20250 citations

Energy, Quantization and Quantum Tunneling

Jean-Louis Basdevant

Graduate texts in physicsJan 1, 20230 citations

The Anyon Zeno Effect

David F. Mross

Two anyons encircling each other acquire a quantized braiding phase that is independent of their spatial separation. We show that detecting this phase in a fractional quantum Hall interference experiment results in a quantum Zeno effect: a localized anyon is trapped by constant observation from a stream of anyons supplied by the measurement current. Interferometers with an embedded antidot are ideal for accessing the Zeno regime, where the bare tunneling rate of localized anyons is much lower than the measurement rate. The Zeno-suppressed tunneling rate of the trapped anyon depends on the braiding phase and the transmission of the quantum point contacts. Our primary prediction is that the autocorrelation time of the conductance through the interferometer increases with the bias current. This effect may be used to experimentally control the anyon dynamics, in particular to increase the lifetime of localized anyons.Two anyons encircling each other acquire a quantized braiding phase that is independent of their spatial separation. We show that detecting this phase in a fractional quantum Hall interference experiment results in a quantum Zeno effect: a localized anyon is trapped by constant observation from a stream of anyons supplied by the measurement current. Interferometers with an embedded antidot are ideal for accessing the Zeno regime, where the bare tunneling rate of localized anyons is much lower than the measurement rate. The Zeno-suppressed tunneling rate of the trapped anyon depends on the braiding phase and the transmission of the quantum point contacts. Our primary prediction is that the autocorrelation time of the conductance through the interferometer increases with the bias current. This effect may be used to experimentally control the anyon dynamics, in particular to increase the lifetime of localized anyons.

arXiv:2602.22322Feb 25, 20260 citations

This research aims to study the behavior of quantum tunneling within the framework of polymer quantization, where spacetime has a discrete structure with a fundamental length

\mu_0

. From the Hamiltonian difference equation, we obtained analytical wave functions in each region of the potential barrier and numerically calculated the transmission coefficient and Wigner time delay

\tau_w

for comparison with standard quantum mechanics. The calculation results show that when the particle energy is lower than the potential barrier

E < W_0

, the tunneling time

\tau_w(n)

increases rapidly within the narrow barrier and saturates when the width is sufficiently large, confirming that the Hartman effect phenomenon persists even when the spacetime structure is discontinuous. The value of

\mu_0

affects the saturation time but does not change the qualitative nature of this behavior. In the case of

E > W_0

, the time increases continuously with width, which is consistent with standard quantum mechanics. This result suggests that the semi-classical properties of potential barrier penetration, particularly the Hartman effect, are stable against modifications to spacetime structure and provide important insights into understanding the behavior of quantum systems within a framework inspired by Loop Quantum Gravity (LQG).