Related Experiment Video
Updated: Nov 27, 2025

In Situ Monitoring of Diffusion of Guest Molecules in Porous Media Using Electron Paramagnetic Resonance Imaging
Published on: September 2, 2016
A Note on the Spectral Gap of the Fredrickson-Andersen One Spin Facilitated Model
1Universita degli Studi Roma Tre, Rome, Italy.
Abstract:
This note discusses the spectral gap of the Fredrickson-Andersen one spin facilitated model in two different settings. The model describes an interacting particle system on a graph, where each site is either occupied or empty; and a site may change its occupation when at least one of its neighbors is empty. We will first consider the model on the infinite lattice , with density close to 1. The second result is on finite graphs, with density that grows with the size of the graph in a way that guarantees O(1) empty sites. In both models lower and upper bounds on the spectral gap were known, but in general did not match. The purpose of this paper is to present new upper bounds that have the same asymptotics as the known lower bounds.
Related Concept Videos
Spin–Spin Coupling Constant: Overview
Qualitatively, any spin plus-half nucleus polarizes the spins of its electrons to the minus-half state. Consequently, the paired electron in the hydrogen–carbon bond must...
Spin–Spin Coupling: One-Bond Coupling
¹H NMR: Interpreting Distorted and Overlapping Signals
As Δν decreases and the signals move closer, the doublets appear increasingly distorted. The intensities of the inner lines increase at the cost of those of the outer lines as the signals are...
¹H NMR Signal Multiplicity: Splitting Patterns
NMR Spectroscopy: Spin–Spin Coupling
Spin–Spin Coupling: Two-Bond Coupling (Geminal Coupling)
The central atom need not be NMR-active because its electrons are affected by the electron polarization of the spin-active atoms. However, spin information is transmitted less effectively than in one-bond coupling, and 2J values are usually weaker than 1J values. The energy of...

