Effective Schroedinger dynamics on $\epsilon$-thin Dirichlet waveguides via Quantum Graphs I: star-shaped graphs

Abstract

We describe the boundary conditions at the vertex that one must choose to obtain a dynamical system that best describes the low-energy part of the evolution of a quantum system confined to a very small neighbourhood of a star-shaped metric graph.

in memory of Pierre Duclos

References in corpus (3)

• Scattering solutions in a network of thin fibers: small diameter asymptotics
• Spectra of graph neighborhoods and scattering
• Coupling in the singular limit of thin quantum waveguides

Cited by in corpus (7)

• Nonlinear Schrödinger equation on graphs: recent results and open problems
• Eigenvalue inequalities and absence of threshold resonances for waveguide junctions
• Soliton transport in tubular networks: transmission at vertices in the shrinking limit
• Standing waves on quantum graphs
• A general approximation of quantum graph vertex couplings by scaled Schroedinger operators on thin branched manifolds
• Diffusion processes in thin tubes and their limits on graphs
• Spectral properties of size-invariant shape transformation