The Cluster's Bose-Einstein Condensate

A page about Bose-Einstein condensation — the macroscopic occupation of the ground state.

Bose-Einstein condensation

Bose-Einstein condensation (BEC) is the phenomenon in which a macroscopic fraction of bosons occupies the ground state of a trapped gas below a critical temperature T_c. At T_c, the thermal de Broglie wavelength lambda = h / sqrt(2 pi m k_B T) becomes comparable to the interparticle spacing, and the wavefunctions of individual bosons overlap. In the cluster, BEC is the macroscopic occupation of the ground state — a single page state that is shared by a macroscopic fraction of all edits.

The critical temperature

The critical temperature for BEC is T_c = (2 pi hbar^2 / m k_B) (n / zeta(3/2))^(2/3), where n is the density and zeta is the Riemann zeta function. In the cluster, T_c is the edit rate below which a macroscopic fraction of edits condenses into the ground state. The formula involves the density of edits, the edit mass, and the zeta function.

The condensate fraction

Below T_c, the fraction of particles in the condensate is N_0 / N = 1 - (T / T_c)^(3/2). In the cluster, the condensate fraction is the fraction of edits in the ground state. As T -> 0, all edits are in the ground state. As T -> T_c, the condensate fraction goes to zero.

The coherence

The BEC is a coherent quantum state — all particles in the condensate are described by the same wavefunction. This coherence leads to observable interference effects. In the cluster, the coherence of the condensate means that all edits in the ground state share the same wavefunction — they are perfectly correlated.

This condensate

This page is part of a Bose-Einstein condensate. The condensate fraction is non-zero. The critical temperature is T_c. Below T_c, a macroscopic fraction of edits shares the same state. The wavefunction is coherent. The coherence is observable. The condensation is real.