Gentile statistics with a large maximum occupation number

Abstract

In Gentile statistics the maximum occupation number can take on unrestricted integers: $1<n<\infty$. It is usually believed that Gentile statistics will reduce to Bose-Einstein statistics when n equals the total number of particles in the system N. In this paper, we will show that this statement is valid only when the fugacity z<1; nevertheless, if z>1 the Bose-Einstein case is not recovered from Gentile statistics as n goes to % N . Attention is also concentrated on the contribution of the ground state which was ignored in related literature. The thermodynamic behavior of a -dimensional Gentile ideal gas of particle of dispersion $E=\frac{p^{s}%}{2m}$, where $\nu$ and s are arbitrary, is analyzed in detail. Moreover, we provide an alternative derivation of the partition function for Gentile statistics.

9 pages. v2: minor changes. v3: a minor mistake in eq. (28) is corrected

Cited by in corpus (17)

• The difference of boundary effects between Bose and Fermi systems
• Intermediate-statistics quantum bracket, coherent state, oscillator, and representation of angular momentum (su(2)) algebra
• Calculating statistical distributions from operator relations: the statistical distributions of various intermediate statistics
• Topological Exchange Statistics in One Dimension
• Canonical partition functions: ideal quantum gases, interacting classical gases, and interacting quantum gases
• Intermediate-statistics spin waves
• An intermediate distribution between Gaussian and Cauchy distributions
• Calculating eigenvalues of many-body systems from partition functions
• An exactly solvable phase transition model: generalized statistics and generalized Bose-Einstein condensation
• The explicit expression of the fugacity for weakly interacting Bose and Fermi gases
• A statistical mechanical approach to restricted integer partition functions
• Do bosons obey Bose-Einstein distribution: two iterated limits of Gentile distribution
• Finite temperature analytical results for a harmonically confined gas obeying exclusion statistics in $d$-dimensions
• Bose-like few-fermion systems
• A New Method for Derivation of Statistical Weight of the Gentile Statistics
• Engineering a multi-level bath for transmons with three-wave mixing and parametric drives
• Unified framework for generalized quantum statistics: canonical partition function, maximum occupation number, and permutation phase of wave function