Tunneling in the Energy Domain

Neepa T. Maitra, Eric J. Heller

The issue of quantum barrier crossing and reflection in the time domain is addressed. We find that (1) classically forbidden barrier tunneling and above-barrier reflection are well-defined and important processes in the time domain, (2) classically forbidden processes can overshadow allowed ones when both are present, and (3) classically allowed trajectories in the time domain are not, in general, sufficient to explain tunneling amplitudes in the energy domain. We also make clear the essential distinction of barriers which flatten out at large distance and those which do not.

Ángel S. Sanz, Salvador Miret-Artés

Eugene M. Chudnovsky, Javier Tejada

Jaka Vodeb, Michele Diego, Yevhenii Vaskivskyi +3 more

Domains are homogeneous areas of discrete symmetry, created in nonequilibrium phase transitions. They are separated by domain walls, topological objects which prevent them from fusing together. Domains may reconfigure by thermally-driven microscopic processes, and in quantum systems, by macroscopic quantum tunnelling. The underlying microscopic physics that defines the system's energy landscape for tunnelling is of interest in many different systems, from cosmology and other quantum domain systems, and more generally to nuclear physics, matter waves, magnetism, and biology. A unique opportunity to investigate the dynamics of microscopic correlations leading to emergent behaviour, such as quantum domain dynamics is offered by quantum materials. Here, as a direct realization of Feynman's idea of using a quantum computer to simulate a quantum system, we report an investigation of quantum electron reconfiguration dynamics and domain melting in two matching embodiments: a prototypical two-dimensionally electronically ordered solid-state quantum material and a simulation on a latest-generation quantum simulator. We use scanning tunnelling microscopy to measure the time-evolution of electronic domain reconfiguration dynamics and compare this with the time evolution of domains in an ensemble of entangled correlated electrons in simulated quantum domain melting. The domain reconfiguration is found to proceed by tunnelling in an emergent, self-configuring energy landscape, with characteristic step-like time evolution and temperature-dependences observed macroscopically. The remarkable correspondence in the dynamics of a quantum material and a quantum simulation opens the way to an understanding of emergent behaviour in diverse interacting many-body quantum systems at the microscopic level.

J. M. Combes, Pierre Duclos, Ruedi Seiler

Eric Needham

This paper presents a finite, physical resolution of quantum tunneling within the Dual Regulator Framework, interpreting barrier penetration as a temporary excursion into the virtual domain rather than a paradoxical traversal of classically forbidden space. In this framework, particles encountering a potential barrier transition from the real domain (on-shell, position space, RG-regulated) into a virtual domain (off-shell, momentum space, Λφ-regulated), where position-space potentials are undefined. After traversing the barrier off-shell, particles re-emerge into the real domain on the opposite side. Energy conservation is preserved through finite energy–time uncertainty, without invoking nonphysical violations. The formalism yields a modified tunneling length scale and probability law, introducing a universal Λφ correction to standard WKB results. This leads to quantitative, testable predictions across multiple systems, including: alpha decay half-lives with sub-percent accuracy across the periodic table, scanning tunneling microscope current–distance relations with φ-harmonic structure, ammonia inversion frequency corrected by a (1 + Λφ/π) factor matching experiment, tunneling time saturation consistent with the Hartman effect and attosecond measurements. All results derive solely from the Trinity constants {π, φ, e} with zero adjustable parameters. The paper resolves the tunneling mystery by identifying tunneling as a finite, domain-limited physical process rather than a purely mathematical artifact. This work constitutes Paper IV in a planned sequence addressing foundational inconsistencies in quantum field theory, following finite resolutions of measurement, wave–particle duality, and entanglement. Licenses Creative Commons Attribution Non Commercial No Derivatives 4.0 Internationa