Feynman Path Integrals Demonstrate Non-Dispersive Airy Wave Packets and Predict Heavy Meson Mass Gaps

The behaviour of quantum wave packets typically spreads over time, limiting their usefulness in precise measurements, but certain solutions defy this tendency, remaining remarkably stable. Paul Ferrante, Connor Donovan, and Chueng-Ryong Ji from North Carolina State University investigate this phenomenon using the Feynman path integral formulation to model non-dispersive Airy wave packets, revealing their surprising connections to seemingly unrelated areas of physics. Their work demonstrates that these wave packets maintain their shape even when propagating freely, and crucially, the researchers establish a compelling link between the zeros of Airy functions and the mass spectra of heavy mesons, achieving accurate predictions when compared to existing calculations. Furthermore, this research extends to modelling the behaviour of ultra-cold neutrons within Earth’s gravitational field, successfully demonstrating that the measured heights of these neutrons correspond to the zeros of the Airy function, offering a novel approach that complements traditional approximations.

Scientists derived a linear kernel and employed time evolution to prove that Airy function wave packets maintain their shape in free space, experiencing only positional translation over time. This unique property stems from the Airy function acting as a generalization of freely propagating waves, establishing a correspondence with the zeros of the Airy function when modeling the confining contribution to the mass gap of heavy mesons. Predictions of the confining contribution to the mass gap achieved good accuracy when compared to calculations performed using the light front formalism, allowing for novel approaches to understanding the strong force that binds quarks together.

Researchers further applied these Airy function solutions to model the states of a neutron under Earth’s gravitational field, confirming the model’s predictive power as measurements of neutron heights align with the zeros of the Airy function and providing an alternative to calculations using the WKB approximation. The team showed that the linear kernel is a generalization of the free kernel, meaning that the linear potential case reduces to the free particle case when the potential strength is zero, providing a powerful tool for analyzing quantum systems in the presence of linear potentials. This generalization establishes a quantitative proof of non-dispersal, confirming that Airy wave packets undergo only positional translation in a free potential, maintaining their invariant shape over time.

Airy Wave Packets and Linear Potential Solutions

This research demonstrates the non-dispersive behavior of Airy wave packets using the Feynman path integral formulation, revealing a fundamental property of linear potentials and establishing a connection between these Airy functions and physical systems, specifically the energy levels within heavy mesons and the behavior of ultra-cold neutrons in Earth’s gravitational field. By applying this mathematical framework, scientists established that the wave packets maintain their shape as they propagate. The team successfully modeled the mass gaps in heavy mesons, achieving good agreement with calculations performed using alternative methods, and demonstrated that the heights attained by bouncing ultra-cold neutrons can be accurately predicted using the zeros of the Airy function, corroborating experimental data and offering an alternative to the WKB approximation. This work provides a novel theoretical foundation for analyzing diverse physical phenomena, linking mathematical elegance with observable quantum behavior.