Manuscript VII-J@1 · VII-J.tex · section · d8c01b04

An explicit finite-volume tail

The Hamiltonian route: tails and a constructive error › An explicit finite-volume tail · lines 1168–1182

Let $G = (X, E)$ be a finite graph and

H (t) = x \in X \sum h_{x} (t) + e \in E \sum h_{e} (t),

where $h_{x}$ acts at one site, $h_{e}$ at the two endpoints of $e$ , and all terms are bounded, self-adjoint, and piecewise continuous. Put

Λ (s, t) = \int_{s}^{t} e \in E \sum ∥ h_{e} (r) ∥ d r .

Let $d_{G} (A, B)$ be the minimum graph distance between the two nonempty disjoint regions.

Displayed formulas in this passage

unlabeled · line 1171
$H (t) = x \in X \sum h_{x} (t) + e \in E \sum h_{e} (t),$
unlabeled · line 1177
$Λ (s, t) = \int_{s}^{t} e \in E \sum ∥ h_{e} (r) ∥ d r .$