Related Experiment Video
Updated: Jul 2, 2025

Generation and Coherent Control of Pulsed Quantum Frequency Combs
Published on: June 8, 2018
Properties of stable ensembles of Euclidean random matrices
Philipp Baumgärtel1, Florian Vogel1, Matthias Fuchs1
1Fachbereich Physik, Universität Konstanz, 78457 Konstanz, Germany.
Abstract:
We study the spectrum of a system of coupled disordered harmonic oscillators in the thermodynamic limit. This Euclidean random matrix ensemble has been suggested as a model for the low temperature vibrational properties of glass. Exact numerical diagonalization is performed in three and two spatial dimensions, which is accompanied by a detailed finite size analysis. It reveals a low-frequency regime of sound waves that are damped by Rayleigh scattering. At large frequencies localized modes exist. In between, the central peak in the vibrational density of states is well described by Wigner's semicircle law for not too large disorder, as is expected for simple random matrix systems. We compare our results with predictions from two recent self-consistent field theories.
Related Concept Videos
Stability of structures
Stability of Equilibrium Configuration
A stable equilibrium occurs when a system tends to return to its original position when given a small displacement, and the potential energy is at its minimum. An example of a stable equilibrium is when a cantilever beam is fixed at one end and a weight is attached to the other end. If the weight...
Stereoisomerism
Isomers are different chemical species that have the same chemical formula.
Transition metal complexes often exist as geometric isomers, in which the same atoms are connected through the same types of bonds but with differences in their orientation in space. Coordination complexes with two different ligands in the cis and trans positions from a ligand of interest form isomers. For example, the octahedral [Co(NH3)4Cl2]+ ion has two isomers (Figure 1) In the cis...
First Law: Particles in Two-dimensional Equilibrium
Newton's first law tells us about...
Types of Enols and Enolates
Stability of Conjugated Dienes
A comparison of the enthalpies of hydrogenation of dienes reveals that conjugated dienes release less heat on hydrogenation, rendering them more stable than their nonconjugated analogs.

