The relation between fractional statistics and finite bosonic systems in the one-dimensional case

The equivalence is established between a one-dimensional (1D) Bose system with a finite number of particles and a system obeying fractional (intermediate) Gentile statistics, in which the maximum occupation of single-particle energy levels is limited. A system of 1D harmonic oscillators, providing a model for a harmonically trapped Bose gas, is considered. The results are generalized for a system with a power-law energy spectrum.