Quasi-modular Symmetry and Quasi-hypergeometric Functions in Quantum Statistical Mechanics of Fractional Exclusion Statistics
چکیده
We investigate a novel symmetry in dualities of Wu’s equation: wg(1+w)1−g = eβ( −μ) for a degenerate g-on gas with fractional exclusion statistics of g, where β = 1/kBT , the energy, and μ the chemical potential of the system. We find that the particle–hole duality between g and 1/g and the supersymmetric duality between g and 1 − g form a novel quasi-modular group of order six for Wu’s equation. And we show that many physical quantities in quantum systems with the fractional exclusion statistics can be represented in terms of quasi-hypergeometric functions and that the quasi-modular symmetry acts on these functions.