The Quantum Phase Problem: Steps Toward a Resolution

Robert Lynch

J. Felber, R. Gähler, C. Rausch +1 more

We investigate the time-dependent Schr\"odinger equation for the case of a plane matter wave incident on an oscillating potential step. Approximate solutions are given for different regimes of the problem. The resulting energy spectra are quantized. This may either be interpreted as a phase modulation of the wave or as a coherent multiphonon exchange. A comparison to the results that apply for a beam of classical particles is made. In particular, the transition from the quantum-mechanical to the classical case is examined. We have performed an experiment with very cold neutrons that clearly revealed the discussed effects. Energy splittings of 2.8 to 9.1 neV of the reflected waves were analyzed with an energy resolution of \ensuremath{\sim}1 neV, thus demonstrating the feasibility of such high-resolution experiments with neutron reflectometry. \textcopyright{} 1996 The American Physical Society.

Ettabiy Abderrahmane

The fundamental equation of the model titled “mathematical formulation of nuclear collision mechanisms” [1] was solved. The solution is compounded of two steps, the first step consists in calculating the values of the parameters of the mechanism-operator underlying a given nuclear collision and the second step, consists in deducing the open channels for this collision. Knowing that the equation is not classic, its resolution has required the development of an innovative mathematical method that sets on the use of physical constraints of the problem.

L. Mandeļ

Wei-Ting Wang, Pei-Ming Ho, Ching-Ray Chang

Dirac Cellular Automata (DCA) provide a framework for simulating Dirac dynamics, yet the rigid coupling between spatial and temporal resolutions can introduce artificial phase-matching symmetries on finite grids that suppress interference phenomena such as Zitterbewegung. In this work, we propose a Split-Step Dirac Cellular Automaton (SDCA) that enables continuous-time Dirac evolution at fixed spatial discretization. By employing a Trotterized fractional-step scheme in the momentum representation, SDCA breaks the phase-matching cancellation present in the standard DCA and recovers the interference dynamics of the continuous-time limit. We benchmark the SDCA through analytical and numerical studies and demonstrate its implementation on IBM Quantum processors. Despite the increased circuit depth required for finer temporal resolution, the NISQ implementation reproduces the characteristic velocity oscillations and entanglement-entropy dynamics of the continuous-time model. We further investigate hardware-topology trade-offs and dynamic circuit implementations of the Quantum Fourier Transform (QFT), highlighting the competing effects of gate errors, measurement, and feed-forward latency. These results demonstrate that SDCA provides a practical framework for improving temporal resolution while maintaining a fixed spatial quantum register, enabling the exploration of relativistic quantum dynamics on near-term quantum devices.

Jan Sładkowski