Cophonicity

A vibrational-overlap metric measuring how strongly two atomic species contribute together within a selected frequency range.

Version

v2 · 2026-09-19 · History

Domain-specific #

3910

Domain group

Natural Sciences

Origin domain

Physics

Subdomain

Condensed Matter Physics → Physics

Core Idea

The score is derived from species-resolved phonon participation or density-of-states information and depends on frequency window, mode normalization and structural model. Mode eigenvectors are projected onto the two atomic species, their spectral contributions are compared across the target band and normalized overlap quantifies whether the pair moves in the same vibrational region. The abstraction is therefore identified by a declared carrier, a transformation or constraint over that carrier, and an invariant that tells an analyst whether the named structure is genuinely present.

How would you explain it like I'm…

Wiggle-Match Score

The tiny atoms inside a solid are always jiggling, some with fast wiggles and some with slow ones. If a material has two kinds of atoms, cophonicity is a score that tells whether both kinds do their jiggling in the same range of fast or slow — like checking whether two singers sing in the same range of notes.

Shared Vibration Range

Everything solid is made of atoms that shake back and forth all the time, like tiny springs. Some shakes are quick and some are slow, and each kind of atom tends to do most of its shaking in certain speed ranges. Cophonicity is a number scientists compute to see whether two kinds of atoms in a material shake in the same range. They take a computer calculation or measurement of the vibrations, see how much each kind of atom takes part at each speed, and measure how much those overlap. The answer depends on which speed range you look at and how you do the math, so those choices must be stated.

Phonon Spectral Overlap Score

In a crystal, atoms vibrate together in collective patterns called phonons, each with its own frequency. For a given pair of atomic species, you can ask how much each species participates in the vibrations at each frequency. Cophonicity is a score that compares those two species-resolved contributions across a chosen frequency band and measures their normalized overlap — in other words, whether the two kinds of atoms vibrate in the same frequency region. The inputs come from phonon calculations or measurements, using the mode eigenvectors projected onto each species or a projected density of states. The value depends on the frequency window, how modes are normalized, the overlap formula, and the structural model, so it isn't meaningful unless those are specified. It is interpreted alongside other bonding descriptors rather than on its own.

 

Cophonicity is a descriptor in condensed matter physics that quantifies whether two atomic species in a material vibrate in the same spectral region. It is computed from species-resolved phonon information: phonon mode eigenvectors are projected onto each of the two species (or a species-projected phonon density of states is used), their spectral contributions across a target frequency band are compared, and a normalized overlap measures how much the pair participates in the same vibrational region. The value depends on the material and structural model, the species pair, whether phonons are calculated or measured, the frequency window, the eigenvector or projected-density convention, the normalization, and the overlap formula and its range or sign. Computational uncertainty should be reported, and the score is interpreted together with bonding descriptors rather than standing alone. Without those conventions stated, two cophonicity values are not comparable.

Scope of Application

Cophonicity belongs to condensed matter physics and is useful where the analyst can specify the typed condensed matter physics carrier, including objects, relations, parameters, conventions, evidence, boundaries, and comparison targets, then evaluate the material and structure, atomic species pair, phonon calculation or measurement, frequency window, eigenvector or projected-density convention, normalization, overlap formula, sign or range, computational uncertainty and interpretation alongside bonding descriptors are explicit. The scope is broad within that domain but bounded by the need for the material and structure, atomic species pair, phonon calculation or measurement, frequency window, eigenvector or projected-density convention, normalization, overlap formula, sign or range, computational uncertainty and interpretation alongside bonding descriptors are explicit. Descriptive computational-materials metric only; no synthesis or laboratory procedure is provided.

Clarity

The abstraction clarifies a crowded vocabulary by making the material and structure, atomic species pair, phonon calculation or measurement, frequency window, eigenvector or projected-density convention, normalization, overlap formula, sign or range, computational uncertainty and interpretation alongside bonding descriptors are explicit the center of the account. A claim should name the carrier, the governing operation or relation, the applicable assumptions, and the recognition test.

Manages Complexity

Without the abstraction, an analyst must reason directly over many local details: the carrier roles, admissibility assumptions, competing conventions, derived invariants, boundary cases, and proof or validation obligations specific to Cophonicity. Cophonicity compresses them into the roles in the structural signature. That compression permits comparison across instances without erasing the variables that determine validity. It also exposes which details may be varied safely and which are constitutive.

Abstract Reasoning

1. Identify the carrier. State what the elements, states, objects, or observations are: the typed condensed matter physics carrier, including objects, relations, parameters, conventions, evidence, boundaries, and comparison targets. Reject examples whose alleged carrier belongs to a different problem.
2. Lock the constitutive rule. Express the material and structure, atomic species pair, phonon calculation or measurement, frequency window, eigenvector or projected-density convention, normalization, overlap formula, sign or range, computational uncertainty and interpretation alongside bonding descriptors are explicit independently of one notation or implementation.

Knowledge Transfer

Knowledge transfers strongly among subfields of condensed matter physics because they reuse the typed condensed matter physics carrier, including objects, relations, parameters, conventions, evidence, boundaries, and comparison targets, Mode eigenvectors are projected onto the two atomic species, their spectral contributions are compared across the target band and normalized overlap quantifies whether the pair moves in the same vibrational region., and type the carrier, state every parameter and convention in the definition, test that the material and structure, atomic species pair, phonon calculation or measurement, frequency window, eigenvector or projected-density convention, normalization, overlap formula, sign or range, computational uncertainty and interpretation alongside bonding descriptors are explicit, compare the nearest accepted identity, and report counterexamples, uncertainty, and limiting cases.

Relationships to Other Abstractions

Current abstraction Cophonicity Domain-specific

Parents (1) — outgoing typed relations

• Cophonicity is a kind of Correlation Prime

  It remains its own entry because its identity is fixed by the material and structure, atomic species pair, phonon calculation or measurement, frequency window, eigenvector or projected-density convention, normalization, overlap formula, sign or range, computational uncertainty and interpretation alongside bonding descriptors.

Hierarchy path (1) — routes to 1 parentless root

• Cophonicity → is a kind of Correlation

Neighborhood in Abstraction Space

Cophonicity sits in a crowded region of the domain-specific corpus (16^th percentile for distinctiveness): several abstractions share nearly its structure, so a description that fits it tends to fit its neighbors too.

Family — Condensed Matter & Many-Body Physics (16 abstractions)

Nearest neighbors

• Phase space crystal — 0.93
• Frenkel–Kontorova model — 0.91
• Glass formation — 0.91
• Particle in a one-dimensional lattice — 0.91
• Second sound — 0.90

Computed from structural-signature embeddings · 2026-10-25