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Equation 15 · Part 3 · Decoherence: The Quiet Selection That Makes the World Look Solid

Symbol Lambda

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

What this part means

what Joos and Zeh call the localization rate: a single number.

Its job in the formula

Lambda is one of the signed contributions combined to compute the quantity on the left.

Where the article explains it

[−Λ(x−x′)2t]\left[-\Lambda (x - x')^2 t\right] Here Λ\Lambda is what Joos and Zeh call the localization rate: a single number, with units of inverse length squared per unit time, built from the scattering cross-section of the object, the flux and momentum of whatever is doing the scattering, and nothing else [ 7 ] .

The passage around this formula

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…

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Sources cited in the surrounding passage

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