2. Exclusion, inclusion, and quantum statistics

Stéphane Ouvry, Alexios P. Polychronakos

We propose a 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.

Yuri A. Rylov

Two equivalent modes of statistical description of stochastic particle production are considered, exclusive and inclusive. Information about particle production processes are distributed inside exclusive and inclusive descriptions in different ways. The exclusive description realizes an ‘‘all or nothing’’ investigation strategy, whereas the inclusive description realizes the ‘‘step by step’’ investigation strategy. Conventional quantum field theory is shown to use essentially an exclusive description. The possibility of a transition to a more reasonable investigation strategy (inclusive description) of particle production description is discussed.

Keith S. Stowe

William Band, Gordon Frank Newell

G. Kaniadakis

By using an appropriate dynamic stochastic quantization method, we quantize a Marcoffian process obeying a generalized Pauli exclusion-inclusion principle. The dynamics of the so obtained quantum system is governed by a nonlinear Schr\"odinger equation. If the exclusion-inclusion principle holds in the momentum space, the ground states of the system are described by statistical distributions interpolating between boson and fermion ones.