Spectral Properties of Soft Quantum Waveguides

Explore the spectral properties of soft quantum waveguides in this 44-minute talk by Pavel Exner, presented at the Workshop on "Spectral Theory of Differential Operators in Quantum Theory" held at the Erwin Schrödinger International Institute for Mathematics and Physics (ESI). Delve into Schrödinger operators with attractive potentials forming channels along smooth curves in R^ν. Examine the case of infinite, asymptotically straight curves in R^2, where the Birman-Schwinger principle is used to derive conditions for non-empty discrete spectra. Learn how this extends to curves in R^3 under certain torsion restrictions. Investigate ground state optimization for loop-shaped curves in R^2 without self-intersections. Gain insights into related results and open problems in the field of quantum waveguides and spectral theory.