← Back to article

Equation 18 · Every Crystal Has Its Own Speed of Light

What does this equation mean?

3×1063\times10^{6}

Read the formula alongside the article passage below. Each part has a deeper page with its role in the equation, the supporting passage and nearby citations.

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.

Read it piece by piece

superscript

superscript

A raised number can be a power. When it is a label or bound, it selects a case or the upper limit of a sum; the formula’s structure distinguishes these uses.

Understand this part →

See an illustrated explanation →

How to interpret it

Read this expression with the definitions, units, and assumptions supplied by the article.

What the article says around this equation

Line up every platform where this cone speed has actually been measured, under one fixed convention — the cone-front group velocity at the relevant filling or interaction strength — and the span comes out to nine and a half orders of magnitude, not the round eleven a first pass at the argument reached for. The bottom of the range is Cheneau’s Bose-Hubbard cone, at 1.1 millimetres per second; the top is graphene’s Dirac cone, whose Fermi velocity runs from about 1×\times10^{6} metres per second at ordinary carrier density up to roughly 3×\times10^{6} metres per second near the point where the conduction and valence bands touch, boosted there by weakly screened electron-electron interactions [ 7…
Read the full surrounding passage
Line up every platform where this cone speed has actually been measured, under one fixed convention — the cone-front group velocity at the relevant filling or interaction strength — and the span comes out to nine and a half orders of magnitude, not the round eleven a first pass at the argument reached for. The bottom of the range is Cheneau’s Bose-Hubbard cone, at 1.1 millimetres per second; the top is graphene’s Dirac cone, whose Fermi velocity runs from about 1×\times10^{6} metres per second at ordinary carrier density up to roughly 3×\times10^{6} metres per second near the point where the conduction and valence bands touch, boosted there by weakly screened electron-electron interactions [ 7 , 8 ] . Divide the two and the ratio is 10^{9.44} , not 10^{11} : still a span of nearly ten orders of magnitude, but an honest one rather than the rounder number a tidier story would have preferred.

Read the equation in its article →

Sources cited in the article section

These citations give research context. Read each source to check which claims it supports.

Return to Every Crystal Has Its Own Speed of Light

See this formula across 1 published context →

Browse the mathematical compendium →