Published equation contexts

$v = 0.5\,c_{\mathrm{eff}}$

Why this formula appears here

A fourth fact transfers, but only with a correction the paper computes rather than sets aside. A quasiparticle wavepacket moving at speed v inside the linear window carries an internal clock — a spinor phase, a zitterbewegung oscillation — that runs slow by the familiar factor $\gamma$ = (1 - $v^2$ / $c_{\mathrm{eff}}^2$ )^{-1/2} : 1.15 at v = 0.5\, $c_{\mathrm{eff}}$ , 2.29 at 0.9\, $c_{\mathrm{eff}}$ . That dilation is real and, in principle, measurable, but only inside a window whose edge the band’s own curvature sets. Writing the correction as a term proportional to (k/ $\Lambda_{\mathrm{curv}}$ )^2 , the fractional error in $\gamma$ stays under one percent as long as the wavepacket’s momentum sits below…

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v

Symbol v

v is part of the quantity the equation computes from the expression on the right.

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c_{\mathrm{eff}}

Symbol c_eff

the including.

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Published contexts (1)

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v = 0.5\,c_{\mathrm{eff}}

Equation 35 · Crossed Fields

Every Crystal Has Its Own Speed of Light

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

A fourth fact transfers, but only with a correction the paper computes rather than sets aside. A quasiparticle wavepacket moving at speed v inside the linear window carries an internal clock — a spinor phase, a zitterbewegung oscillation — that runs slow by the familiar factor $\gamma$ = (1 - $v^2$ / $c_{\mathrm{eff}}^2$ )^{-1/2} : 1.15 at v = 0.5\, $c_{\mathrm{eff}}$ , 2.29 at 0.9\, $c_{\mathrm{eff}}$ . That dilation is real and, in principle, measurable, but only inside a window whose edge the band’s own curvature sets. Writing the correction as a term proportional to (k/ $\Lambda_{\mathrm{curv}}$ )^2 , the fractional error in $\gamma$ stays under one percent as long as the wavepacket’s momentum sits below…

Meanings in this article

$c_{\mathrm{eff}}$ : the including.

Equation guide → · Article →

v=0.5 ceffv = 0.5\,c_{\mathrm{eff}}v=0.5ceff​