Seminars And Colloquia Next Week

TBA

Undergraduates should be more exposed to an exactly solvable problem of nonrelativistic quantum mechanics: the motional spectrum of a hard elastic ball in the presence of a uniform gravitational field and a flat reflecting surface of infinite extent.

That has indeed been the subject of a series of remarkable experiments using ultracold neutrons bouncing along the floor in Earth’s gravity. [1,2]

The nonrelativistic Schrödinger equation for stationary states of that system can be solved in terms of Airy functions, first introduced by George Biddell Airy in his study of the rainbow. [3]

A delightful American Journal of Physics paper by Michael V. Berry and Nándor Balázs [4] showed that Airy functions provide a framework for non-trivial exact solutions of the time-dependent Schrödinger equation for a free particle.  These demonstrate self-acceleration and healing.

Such solutions promoted interest [5] in laboratory realization, which has been attained in light, [6] electrons, [7] and most recently by our neutron physics collaboration. [8]   I will discuss the background and possible applications of this work.

[1] “Realization of a gravity-resonance-spectroscopy technique,” T. Jenke, P. Geltenbort, H. Lemmel, and H. Abele, Nature Phys. 7, 468 (2011)

[2] “Quantum bouncing ball resonates,” G. L. Greene, Nature Phys. 7, 447 (2011)

[3] “On the intensity of light in the neighborhood of a caustic,” G. B. Airy, Trans. Camb. Phil. Soc. 6, 379 (1838)

[4] “Nonspreading wave packets,” M. V. Berry and N. L. Balazs, Am. J. Phys. 47, 264 (1979)

[5] “Airy beam.” Wikipedia, Wikimedia Foundation, 21 Apr. 2025, en.wikipedia.org/wiki/Airy_beam

[6] “Observation of accelerating Airy beams,” G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 213901 (2007)

[7]  “Generation of electron Airy beams,” N. Voloch-Bloch, Y. Lereah, Y. Lilach, A. Gover, A. Arie, Nature 494, 331 (2013)

[8]  “Generation of neutron Airy beams,” D. Sarenac, et al., Phys. Rev. Lett. 134, 153401 (2025)

Generalized parton distributions (GPDs) are a key construct for understanding the spatial distribution of quarks and gluons inside nucleons. These distributions are accessed through deeply virtual exclusive processes, such as deeply virtual Compton scattering (DVCS) and deeply virtual meson production (DVMP). We present a spectator model-based parameterization of twist 2, chiral-even, GPDs in the quark, anti-quark, and the gluon sectors. Our model parameters are constrained using high precision electron-nucleon elastic scattering data, deep inelastic scattering data, and recent lattice QCD moment data. The parametrization is used to calculate Compton form factors (CFFs) which allow us to make predictions for DVCS experiments in the kinematic regions currently accessed at Jefferson Lab. Predictions for kinematic regions that will be accessible by the electron ion collider (EIC) are also presented. We also discuss preliminary results on an approach to learn GPDs with a neural network.