aqora

Operator algebras and statistical mechanics

Huzihiro Araki

Springer eBooksApr 6, 200829 citations

Quantum Statistics and the Many-Body Problem

Trickey, Samuel, Kirk, Wiley, Dufty, James

Springer eBooksJan 1, 1975133 citations

A GENERALIZATION OF QUANTUM STATISTICS

WEI CHEN, Yee Jack Ng, H. van Dam

We examine a new fractional statistics for arbitrary dimensions, based on an extension of Pauli’s exclusion principle, to allow for finite multi-occupancies of a single quantum state. By explicitly constructing the many-body Hilbert space, we obtain a new algebra of operators and a new thermodynamics. The new statistics is different from fractional exclusion statistics. For a single species of particles it is equivalent to parafermi statistics; but their algebras are very different for the case of multiple species.We examine a new fractional statistics for arbitrary dimensions, based on an extension of Pauli’s exclusion principle, to allow for finite multi-occupancies of a single quantum state. By explicitly constructing the many-body Hilbert space, we obtain a new algebra of operators and a new thermodynamics. The new statistics is different from fractional exclusion statistics. For a single species of particles it is equivalent to parafermi statistics; but their algebras are very different for the case of multiple species.

arXiv:hep-th/9503236Modern Physics Letters AMar 28, 19967 citations

Exclusion statistics, operator algebras and Fock space representations

Stjepan Meljanac, Marijan Milekovic, Marko Stojic

We study exclusion statistics within the second quantized approach. We consider operator algebras with positive definite Fock space and restrict them in a such a way that certain state vectors in Fock space are forbidden ab initio.We describe three characteristic examples of such exclusion, namely exclusion on the base space which is characterized by states with specific constraint on quantum numbers belonging to base space M (e.g. Calogero-Sutherland type of exclusion statistics), exclusion in the single-oscillator Fock space, where some states in single oscillator Fock space are forbidden (e.g. the Gentile realization of exclusion statistics) and a combination of these two exclusions (e.g. Green's realization of para-Fermi statistics). For these types of exclusions we discuss extended Haldane statistics parameters g, recently introduced by two of us in Mod.Phys.Lett.A 11, 3081 (1996), and associated counting rules. Within these three types of exclusions in Fock space the original Haldane exclusion statistics cannot be realized.We study exclusion statistics within the second quantized approach. We consider operator algebras with positive definite Fock space and restrict them in a such a way that certain state vectors in Fock space are forbidden ab initio.We describe three characteristic examples of such exclusion, namely exclusion on the base space which is characterized by states with specific constraint on quantum numbers belonging to base space M (e.g. Calogero-Sutherland type of exclusion statistics), exclusion in the single-oscillator Fock space, where some states in single oscillator Fock space are forbidden (e.g. the Gentile realization of exclusion statistics) and a combination of these two exclusions (e.g. Green's realization of para-Fermi statistics). For these types of exclusions we discuss extended Haldane statistics parameters g, recently introduced by two of us in Mod.Phys.Lett.A 11, 3081 (1996), and associated counting rules. Within these three types of exclusions in Fock space the original Haldane exclusion statistics cannot be realized.

arXiv:math-ph/9812003Journal of Physics A Mathematical and GeneralJan 1, 19999 citations

Many-particle quantum statistics and co-algebra

E. Celeghini, Mario Rasetti

Jan 1, 19960 citations

Braid Structure and Raising-Lowering Operator Formalism in Sutherland Model

Akira Takamura

We algebraically construct the Fock space of the Sutherland model in terms of the eigenstates of the pseudomomenta as basis vectors. We introduce the following characteristic operators and systematically produce all the eigenstates starting from the ground state by multiplying the operators. The braid-exclusion operators exchange eigenvalues of pseudomomenta; they follow the algebra of a braid group and also include effects of the exclusion statistics. The raising and lowering operators increase and decrease eigenvalues of pseudomomenta. The Sutherland model is a solvable quantum many-body system with inversesquare interaction on a circumference [1]. The ground-state wave function is of the Jastrow type and excited states are represented as polynomials multiplied by the ground state. Among the polynomials symmetric ones are the Jack polynomials [2, 3, 4], while the others are called nonsymmetric Jack polynomials. These states can be taken as eigenstates of the pseudomomenta or DunkelWe algebraically construct the Fock space of the Sutherland model in terms of the eigenstates of the pseudomomenta as basis vectors. We introduce the following characteristic operators and systematically produce all the eigenstates starting from the ground state by multiplying the operators. The braid-exclusion operators exchange eigenvalues of pseudomomenta; they follow the algebra of a braid group and also include effects of the exclusion statistics. The raising and lowering operators increase and decrease eigenvalues of pseudomomenta. The Sutherland model is a solvable quantum many-body system with inversesquare interaction on a circumference [1]. The ground-state wave function is of the Jastrow type and excited states are represented as polynomials multiplied by the ground state. Among the polynomials symmetric ones are the Jack polynomials [2, 3, 4], while the others are called nonsymmetric Jack polynomials. These states can be taken as eigenstates of the pseudomomenta or Dunkel

Jan 1, 19983 citations

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