arXiv subjects

Gunwoo Cho

Publications and source records attributed to Gunwoo Cho.

2 recordsLinked to original sources

arXiv2023

Talbot effect for the third order Lugiato-Lefever equation

We discuss the Lugiato-Lefever equation and its variant with third-order dispersion, which are mathematical models used to describe how a light beam forms patterns within an optical cavity. It is mathematically demonstrated that the solutions of these equations follow the Talbot effect, which is a phenomenon of periodic self-imaging of an object under certain conditions of diffraction. The Talbot effect is regarded as the underlying cause of pattern formation in optical cavities.

math.AP↗

arXiv2021

Quantum revivals and fractality for the Schr\"odinger equation

We investigate the behavior of the Schr\"odinger equation under the influence of potentials, focusing on its relationship to quantum revivals and fractality. Our findings reveal that the solution displays fractal behavior at irrational times, while exhibiting regularity similar to the initial data at rational times. These extend the results of Oskolkov \cite{O} and Rodnianski \cite{R2} on the free Schr\"odinger evolution to the general case regarding potentials.

math.AP↗