Statistics in a dissipative medium

We consider a gas of bosons or fermions where the particles are coupled dissipatively to an external medium. The effect of dissipation is to reduce the weight in the partition function of paths which permute particle positions, an effect which can ultimately destroy the distinctions between fermions and bosons. The crossover temperature kT, is given by the solutions of 4γ[ψ(1+γ/kT) -ψ(1)+ln2]=${\mathit{kT}}_0$-kT. $gamma = hbar eta /2 pi M—, η is the fraction coefficient, M is the particle mass, ${\mathit{T}}_0$ is the degeneracy temperature in the absence of dissipation, and k is Boltzmann’s constant. Thus for overdamped particles γ≫${\mathit{kT}}_0$ Bose and Fermi statistics are indistinguishable. We suggest that the results may provide a model for charge carriers in the normal state of high-temperature superconductors.