What do the World-Wide-Web and an ecological systems have in common with a quantum Bose system?
The answer to this question might seem surprising, but all these systems might show a condensation phase transition.
If you are a physicist you will know everything about the Bose-Einstein condensation of a Bose system. A Bose-Einstein condensation occurs in a ideal Bose system below the critical temperature T
_{c}. For T < T
_{c}, a finite fraction of all the particles is found in the ground state.
Actually it turns out that condensation transitions are common to many out-of equilibrium and disordered systems as spin-glass, zero range processes and wealth distribution models.
In a complex network a condensation occurs when one node acquires a finite fraction of all the links. This is what happens in a competitive complex system described by the
BIANCONI-BARABASI MODEL (See figures below).
In an ecological system, in presence of migration of species one species can become dominant and the biodiversity of the ecosystem is strongly reduced. This transition is relevant for studying the role of invasive species in stable ecologies.
Both these transitions can be mapped to the Bose-Einstein condensation in a Bose gas.
(Curiosity: There are also evolving networks that can be constructed similarly to the
BIANCONI-BARABASI MODEL and can be mapped to a Fermi distributions. These networks are actually trees that evolve through a modified directed percolation process).
These model have been recently put under the same comon framework of network geometry with flavor and Complex Quantum Network Manifolds.