Related papers: Many-body States and Operator Algebra for Exclusio…
Motivated by the sharp contrast between classical and quantum physics as probability theories, in these lecture notes I introduce the basic notions of operator algebras that are relevant for the algebraic approach to quantum physics.…
We construct the energy operator for particles obeying infinite statistics defined by a q-deformation of the Heisenberg algebra. (This paper appeared published in CMP in 1992, but was not archived at the time.)
The treatment of the number-theoretical problem of integer partitions within the approach of statistical mechanics is discussed. Historical overview is given and known asymptotic results for linear and plane partitions are reproduced. From…
We study various forms of amalgamation for Boolean algebras with operations. We will also have the occasion to weaken the Boolean structure dealing with MV and BL algebras with operators.
A many-body theory approach to the calculation of gamma spectra of positron annihilation on many-electron atoms is developed. We evaluate the first-order correlation correction to the annihilation vertex and perform numerical calculations…
The states of the physical algebra, namely the algebra generated by the operators involved in encoding and processing qubits, are considered instead of those of the whole system-algebra. If the physical algebra commutes with the interaction…
A categorical axiomatic theory of creation/annihilation operators on bosonic Fock space is introduced and the combinatorial model that motivated it is presented. Commutation relations and coherent states are considered in both frameworks.
In this master thesis, I discuss how the theory of operator algebras, also called operator theory, can be applied in quantum computer science.
The atomic third-order open-shell many-body perturbation theory is developed. Special attention is paid to the generation and algebraic analysis of terms of the wave operator and the effective Hamiltonian as well. Making use of…
We give a formulation of the single particle occupation probabilities for a system of identical particles obeying fractional exclusion statistics of Haldane. We first derive a set of constraints using an exactly solvable model which…
We unify parastatistics, defined as triple operator algebras represented on Fock space, in a simple way using the transition number operators. We express them as a normal ordered expansion of creation and annihilation operators. We discuss…
An interpretation of the multiple Meixner polynomials of the first kind is provided through an infinite Lie algebra realized in terms of the creation and annihilation operators of a set of independent oscillators. The model is used to…
Many-body entanglement is studied within the algebraic approach to quantum physics in systems made of Majorana fermions. In this framework, the notion of separability stems from partitions of the algebra of observables and properties of the…
A many-body theory approach developed by the authors [Phys. Rev. A 70, 032720 (2004)] is applied to positron bound states and annihilation rates in atomic systems. Within the formalism, full account of virtual positronium (Ps) formation is…
We construct a general state which is an eigenvector of the annihilation operator of the Generalized Heisenberg Algebra. We show for several systems, which are characterized by different energy spectra, that this general state satisfies the…
The study of quantum mechanical few-body systems is a century old pursuit relevant to countless subfields of physics. While the two-body problem is generally considered to be well-understood theoretically and numerically, venturing to three…
Second quantization is revisited and creation and annihilation operators areshown to be related, on the same footing both to the algebra h(1), and to the superalgebra osp(1|2) that are shown to be both compatible with Bose and Fermi…
We define creation and annihilation operators for any 2D non-abelian anyon theory by studying the algebraic structure from the anyon diagrammatic formalism. We construct the creation operators for Fibonacci anyons explicitly. We obtain that…
We derive an exact equation of motion for the reduced density matrices of individual subsystems of quantum many-body systems of any lattice dimension and arbitrary system size. Our projection operator based theory yields a highly efficient…
Orthofermi statistics is characterized by an exclusion principle which is more ``exclusive'' than Pauli's exclusion principle: an orbital state shall not contain more than one particle, no matter what the spin direction is. The wavefunction…