On the spectral gap of one-dimensional Schrödinger operators on large intervals

Abstract

We study the effect of non-negative potentials on the spectral gap of one-dimensional Schrödinger operators in the limit of large intervals. In particular, we derive upper and lower bounds on the gap for different classes of potentials which characterize its asymptotic behaviour.

References in corpus (4)

• On a condition for type-I Bose-Einstein condensation in random potentials in $d$ dimensions
• On the spectral gap in the Kac-Luttinger model and Bose-Einstein condensation
• A lower bound on the spectral gap of one-dimensional Schrödinger operators
• A lower bound on the spectral gap of Schrödinger operators with weak potentials of compact support

Cited by in corpus (1)

• On the spectral gap of the path graph in the limit of large volume