1109.4109 (Michael Bishop et al.)

Ground State Energy of the One-Dimensional Discrete Random
Schrödinger Operator with Bernoulli Potential    [PDF]

Michael Bishop, Jan Wehr

In this paper, we show the that the ground state energy of the one
dimensional Discrete Random Schroedinger Operator with Bernoulli Potential is
controlled asymptotically as the system size N goes to infinity by the random
variable \ell_N, the length the longest consecutive sequence of sites on the
lattice with potential equal to zero. Specifically, we will show that for
almost every realization of the potential the ground state energy behaves
asymptotically as $\frac{\pi^2}{\ell_N+1)^2}$ in the sense that the ratio of
the quantities goes to one.

View original: http://arxiv.org/abs/1109.4109