Date/Time
Date(s) - 22/11/2024
11:30 am - 12:30 pm

Location: Hamilton Hall, Room 312

Speaker: Boris Shakarov (University of Toulouse)

Title: NLS on Quantum Graphs and the Shrinking Limit for Fractured Strips

Abstract: Quantum graphs, often modeled as one-dimensional structures, provide simplified yet powerful approximations of higher-dimensional systems. This talk explores the behavior of ground states in a strip domain under the influence of delta potentials within the framework of the nonlinear Schr¨odinger equation. Specifically, we focus on the convergence of ground states from a two-dimensional fractured strip with Neumann boundary conditions to a one-dimensional line as the strip width approaches zero. Through variational methods, we demonstrate the existence and stability of ground states in both attractive and repulsive cases. Additionally, we analyze how minimizers of the energy and action functionals evolve in the shrinking limit, revealing insights into the dimensional reduction process. This study offers a foundation for understanding the connections between higher-dimensional quantum structures and their graph-like approximations, paving the way for future applications in quantum networks.