Inclusion statistics and particle condensation in 2 dimensionsWe propose a new type of quantum statistics, which we call inclusion
statistics, in which particles tend to coalesce more than ordinary bosons.
Inclusion statistics is defined in analogy with exclusion statistics, in which
statistical exclusion is stronger than in Fermi statistics, but now
extrapolating beyond Bose statistics, resulting in statistical inclusion. A
consequence of inclusion statistics is that the lowest space dimension in which
particles can condense in the absence of potentials is $d=2$, unlike $d=3$ for
the usual Bose-Einstein condensation. This reduction in the dimension happens
for any inclusion stronger than bosons, and the critical temperature increases
with stronger inclusion. Possible physical realizations of inclusion statistics
involving attractive interactions between bosons may be experimentally
achievable.
arxiv.org