TY - JOUR
T1 - The Fundamental Gap for a Class of SchrÃ¶dinger Operators on Path and Hypercube Graphs
JF - Journal of Mathematical Physics
Y1 - 2014
A1 - Michael Jarret
A1 - Stephen P. Jordan
AB - We consider the difference between the two lowest eigenvalues (the fundamental gap) of a Schr\"{o}dinger operator acting on a class of graphs. In particular, we derive tight bounds for the gap of Schr\"{o}dinger operators with convex potentials acting on the path graph. Additionally, for the hypercube graph, we derive a tight bound for the gap of Schr\"{o}dinger operators with convex potentials dependent only upon vertex Hamming weight. Our proof makes use of tools from the literature of the fundamental gap theorem as proved in the continuum combined with techniques unique to the discrete case. We prove the tight bound for the hypercube graph as a corollary to our path graph results.
VL - 55
U4 - 052104
UR - http://arxiv.org/abs/1403.1473v1
CP - 5
J1 - J. Math. Phys.
U5 - 10.1063/1.4878120
ER -