Lower bounds on the lowest spectral gap of singular potential Hamiltonians

Details Lower bounds on the lowest spectral gap of singular potential Hamiltonians Lower bounds on the lowest spectral gap of singular potential Hamiltonians

2006-05-31

arxiv.org/abs/math-ph/0605080v1

Physics

Mathematical Physics

24 pages. To appear in slightly different form in Annales Henri Poincare

Scientific paper

10.1007/s00023-006-0302-8

We analyze Schr\"odinger operators whose potential is given by a singular interaction supported on a sub-manifold of the ambient space. Under the assumption that the operator has at least two eigenvalues below its essential spectrum we derive estimates on the lowest spectral gap. In the case where the sub-manifold is a finite curve in two dimensional Euclidean space the size of the gap depends only on the following parameters: the length, diameter and maximal curvature of the curve, a certain parameter measuring the injectivity of the curve embedding, and a compact sub-interval of the open, negative energy half-axis which contains the two lowest eigenvalues.

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