Microscopic and macroscopic properties of A-superstatistics

Abstract

The microscopic and the macroscopic properties of A-superstatistics, related to the class A(0,n-1)\equiv sl(1|n) of simple Lie superalgebras are investigated. The algebra sl(1|n) is described in terms of generators f_1^\pm, >..., f_n^\pm, which satisfy certain triple relations and are called Jacobson generators. The Fock spaces of A-superstatistics are investigated and the Pauli principle of the corresponding statistics is formulated. Some thermal properties of A-superstatistics are constructed under the assumption that the particles interact only via statistical interaction imposed by the Pauli principle. The grand partition function and the average number of particles are written down explicitly in the general case and in two particular examples: 1) the particles have one and the same energy and chemical potential; 2) the energy spectrum of the orbitals is equidistant.

26 pages, 3 figures

References in corpus (8)

• Superstatistics
• Many-Body Wigner Quantum Systems
• Partition functions and symmetric polynomials
• The non-commutative and discrete spatial structure of a 3D Wigner quantum oscillator
• Jacobson generators, Fock representations and statistics of sl(n+1)
• Supersymmetric Hubbard Operators
• Macroscopic properties of A-statistics
• An Analogue of Holstein-Primakoff and Dyson Realizations for Lie Superalgebras. The Lie superalgebra sl(1/n)

Cited by in corpus (7)

• The non-commutative and discrete spatial structure of a 3D Wigner quantum oscillator
• A non-commutative n-particle 3D Wigner quantum oscillator
• Orthosymplectic $Z_2\times Z_2$-graded Lie superalgebras and parastatistics
• A classification of generalized quantum statistics associated with the exceptional Lie (super)algebras
• Solutions of the compatibility conditions for a Wigner quantum oscillator
• A classification of generalized quantum statistics associated with basic classical Lie superalgebras
• All fundamental fermions fit inside one su(1|5) irreducible representation