Related papers: Many-body States and Operator Algebra for Exclusio…
The thermodynamic distribution function for exclusion statistics is derived. Creation and annihilation operators for particles obeying such statistics are discussed. A connection with anyons is pointed out.
We propose 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,…
The language of operator algebras is of great help for the formulation of questions and answers in quantum statistical mechanics. In Chapter 1 we present a minimal mathematical introduction to operator algebras, with physical applications…
A procedure to derive the partition function of non-interacting particles with exotic or intermediate statistics is presented. The partition function is directly related to the associated creation and annihilation operators that obey some…
A new kind of quantum statistics which interpolates between Bose and Fermi statistics is proposed beginning with the assumption that the quantum state of a many-particle system is a functional on the internal space of the particles. The…
We construct the number operator for particles obeying infinite statistics, defined by a generalized q-deformation of the Heisenberg algebra, and prove the positivity of the norm of linearly independent state vectors.
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…
Multi-agent complex systems comprising populations of decision-making particles, have wide application across the biological, informational and social sciences. We uncover a formal analogy between these systems' time-averaged dynamics and…
We formulate and study the microscopic statistical mechanics of systems of particles with exclusion statistics in a discrete one-body spectrum. The statistical mechanics of these systems can be expressed in terms of effective single-level…
Statistical mechanics and thermodynamics for ideal fractional exclusion statistics with mutual statistical interactions is studied systematically. We discuss properties of the single-state partition functions and derive the general form of…
We define a class of deformed multimode oscillator algebras which possess number operators and can be mapped to multimode Bose algebra.We construct and discuss the states in the Fock space and the corresponding number operators.
In this pedagogical note I present the operator form of Wick's theorem, i.e. a procedure to bring a product of 1-particle creation and destruction operators to normal order, with respect to some reference many-body state. Both the static…
Remarks are given to the structure of physical states in 2D gravity coupled to $C\leq 1$ matter. The operator algebra of the discrete state operators is calculated for the theory with non-vanishing cosmological constant.
New algebraic structure on electronic Fock space is studied in detail. This structure is defined in terms of a certain multiplication of many electron wave functions and has close interrelation with coupled cluster and similar approaches.…
The many-body Hamiltonians and other fermionic physical observables are expressed in terms of fermionic creation and annihilation operators, which form the algebra of canonical anti-commutation relations (CAR). In this work we use a…
A new distribution for systems of particles obeying statistical exclusion of correlated states is presented following the Haldane's state counting. It relies upon a conjecture to deal with the multiple exclusion that takes place when the…
The restricted solid-on-solid models in the anti-ferromagnetic regime is studied in the framework of quantum affine algebras. Following the line developed recently for vertex models, a representation theoretical picture is presented for the…
A new distribution for systems of particles in equilibrium obeying exclusion of correlated states is presented following the Haldane's state counting. It relies upon an ansatz to deal with the multiple exclusion that takes place when the…
The cosmological many-body problem is effectively an infinite system of gravitationally interacting masses in an expanding universe. Despite the interactions' long-range nature, an analytical theory of statistical mechanics describes the…
We summarize and deepen recent results on systems of orthogonal pure states on operator algebras. Especially, we focus on noncommutative generalizations of some principles of topology of locally compact spaces such as exposining points by…