Partition functions for general multi-level systems

Abstract

We describe a unified approach to calculating the partition functions of a general multi-level system with a free Hamiltonian. Particularly, we present new results for parastatistical systems of any order in the second quantized approach. Anyonic-like systems are briefly discussed.

Partition functions and thermodynamic properties of paraboson and parafermion systems

“…Surprisingly, proper forms of Z pB (n, p) as a generating function were not known so far, apart from the trivial case p = 1 and p ≥ n [15][16][17][18][19][20], even though the cases 1 < p < n are the most interesting for investigating thermodynamic properties of the system. GPF's of the form (3.3) consist of a sum over all possible states of the system (including multiplicities).…”

Permutation invariant statistics, duality and simple interpolations

“…( 6),(33), are hermitian and if p is a positive integer their eigenvalues are non-negative [3]. Using the results of [12], we find that the eigenvalues (Λ p,ǫ ) µ , corresponding only to one of equivalent IRREP's µ of S N , are…”

Parastatistics as Examples of the Extended Haldane Statistics

“…where, for parabosons, n(µ) pB = 1 if l(µ) ≤ M and l(µ) ≤ p (otherwise n(µ) pB = 0); for parafermions, n(µ) pF = 1 if l(µ) ≤ M and l(µ T ) ≤ p (otherwise n(µ) pF = 0).The l(µ) and l(µ T ) are the number of rows of the Young tableaux µ and µ T , respectively, and µ T denotes the transposed tableau to µ. Kostka's number K µ,λ is the filling number of an IRREP µ with independent states arranged according to the partition λ, |µ| = |λ|. Hence, from all allowed equivalent IRREP's µ, only one appears in the decomposition (13). It is proved 13 that the pattern for the multiplicities n(µ) is valid for any M,N,λ ,p .…”