What does this equation mean?

Joos and Zeh made this quantitative in 1985 by deriving a genuine, non-phenomenological master equation for the reduced density matrix of an object’s centre-of-mass position under repeated recoil-free scattering [ 7 ] . For the off-diagonal elements of that density matrix — the very quantity whose survival or destruction is the entire question of macroscopic superposition — their result, in the short-time, many-collisions regime, takes the form of a simple exponential decay in the separation between the two positions being superposed: $\rho(x, x', t) = \rho(x, x', 0)\, \exp\!\left[-\Lambda (x - x')^2 t\right]$. Here $\Lambda$ 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 ] . Everything about how fast a given superposition dies is contained in $\Lambda$ , and $\Lambda$ is a number you can actually compute for a real object in a real environment — which is exactly what Joos and Zeh went on to do, in the paper’s Table 2, for three sizes of hypothetical “dust particle”: a large grain of radius 10^{-3} centimetres, a small grain of 10^{-5} centimetres, and a body of 10^{-6} centimetres that the paper itself labels a “large molecule” [ 7 ] :