Published equation contexts

$(k/\Lambda_{\mathrm{curv}})^2$

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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k

Symbol k

k is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

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\Lambda_{\mathrm{curv}}

Symbol Lambda_curv

Lambd $a_c$ urv is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

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Published contexts (1)

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(k/\Lambda_{\mathrm{curv}})^2

Equation 37 · Crossed Fields

Every Crystal Has Its Own Speed of Light

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

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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(k/Λcurv)2(k/\Lambda_{\mathrm{curv}})^2(k/Λcurv​)2