Exponential estimates for quantum graphs

Abstract

The article studies the exponential localization of eigenfunctions associated with isolated eigenvalues of Schrodinger operators on infinite metric graphs. We strengthen the result obtained in [3] providing a bound for the rate of exponential localization in terms of the distance between the eigenvalue and the essential spectrum. In particular, if the spectrum is purely discrete, then the eigenfunctions decay super-exponentially.

Keywords

• Infinite metric graph
• Schrodinger operator
• eigenfunction
• exponential decay