Quantum Mechanics: Tunneling

James R F SUTTON

GQR 7: Tunnelling Rates, Speeds, and Flux Dynamics The Gated Quantum Resonator (GQR) framework is introduced to formalize deviations from textbook quantum-mechanical (QM) tunnelling relations. GQR maps the classical exponential decay law to a dynamic band of rates by incorporating aperture control, field coupling, and coherence feedback. Numerical sweeps (Amp = 0–3) for electrons and protons demonstrate that this coherent gating mechanism can yield order-of-magnitude rate increases in the enzymatic tunnelling window (0.8–1.2 Å). This shows that GQR can provide both suppression and enhancement to tunnelling rates.

N. Riga, Rebecca Seviour, Kevin L. Jensen +2 more

We present a theoretical study of the correspondence between quantum mechanics (QM) and electromagnetism (EM) using the transfer matrix approach (TMA). This analogy has been studied previously [1] , [2] , [3] ; here we adapt it to electromagnetic wave propagation through an isotropic metamaterial for comparison with quantum tunneling through a one-dimensional barrier. Wigner trajectory calculations for quantum mechanical tunneling have been developed previously [4] , [5] to present a method for modeling electron emission at an atomistic level and to allow for coupling to larger-scale particle-based simulations. To provide a means for computational verification and macroscopic experimental validation of these microscale simulations, we use the TMA to calculate both the QM and EM transmission and reflection coefficients, which enables direct comparison of the respective outputs.

Ossama Kullie

Attosecond science is of a fundamental interest in physics. The measurement of the tunneling time in attosecond experiments, offers a fruitful opportunity to understand the role of time in quantum mechanics (QM). We discuss in this paper our tunneling time model in relation to two time operator definitions introduced by Bauer and Aharonov–Bohm. We found that both definitions can be generalized to the same type of time operator. Moreover, we found that the introduction of a phenomenological parameter by Bauer to fit the experimental data is unnecessary. The issue is resolved with our tunneling model by considering the correct barrier width, which avoids a misleading interpretation of the experimental data. Our analysis shows that the use of the so-called classical barrier width, to be precise, is incorrect.