← Mathematical compendium

Published equation contexts

l(t)=(8Λt)−1/2l(t) = (8\Lambda t)^{-1/2}

Why this formula appears here

The same paper also tracks what happens to the coherence length itself, not just the decay rate: solving the full master equation for a free particle gives a coherence width l(t) = (8Λ\Lambda t)^{-1/2} , meaning it shrinks as the inverse square root of time for as long as scattering dominates, and does so from whatever width the particle’s wave packet started with [ 7 ] . Joos and Zeh flag the counterintuitive consequence themselves: the everyday expectation that a free wave packet spreads out over time is not what this equation describes at all. “The much-discussed dispersion hardly ever shows up even for small dust particles or large molecules,” they write; instead “the coherence length…

Read the full article-specific guide →

Read the representative guide

How to interpret it

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

Research cited beside this formula

Published contexts (1)

A symbol can carry a different meaning in another article. Each occurrence keeps its own guide and term definitions.

l(t)=(8Λt)−1/2l(t) = (8\Lambda t)^{-1/2}

Equation 15 · Evolutionary Physics

Decoherence: The Quiet Selection That Makes the World Look Solid

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

The same paper also tracks what happens to the coherence length itself, not just the decay rate: solving the full master equation for a free particle gives a coherence width l(t) = (8Λ\Lambda t)^{-1/2} , meaning it shrinks as the inverse square root of time for as long as scattering dominates, and does so from whatever width the particle’s wave packet started with [ 7 ] . Joos and Zeh flag the counterintuitive consequence themselves: the everyday expectation that a free wave packet spreads out over time is not what this equation describes at all. “The much-discussed dispersion hardly ever shows up even for small dust particles or large molecules,” they write; instead “the coherence length…

Meanings in this article

  • Λ\Lambda: what Joos and Zeh call the localization rate: a single number.
Equation guide → · Article →