Related papers: Topics in quantum statistical mechanics and operat…
After an historical introduction on the standard algebraic approach to quantum mechanics of large systems we review the basic mathematical aspects of the algebras of unbounded operators. After that we discuss in some details their relevance…
These notes are intended as an introduction to a study of applications of noncommutative calculus to quantum statistical Physics. Centered on noncommutative calculus we describe the physical concepts and mathematical structures appearing in…
In this master thesis, I discuss how the theory of operator algebras, also called operator theory, can be applied in quantum computer science.
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 attempt to contribute some novel points of view to the "foundations of quantum mechanics", using mathematical tools from "quantum probability theory" (such as the theory of operator algebras). We first introduce an abstract algebraic…
Several quantum systems have been used in the last few years to extend supersymmetry. In this paper we show all this systems fit into the picture of what we call "Number Operator Algebras".
In this second paper in a series, we show that the the general statistical approach to nonrelativistic quantum mechanics developed in the first paper yields a representation of quantum spin and magnetic moments based on classical…
The random matrix ensembles are applied to the quantum statistical two-dimensional systems of electrons. The quantum systems are studied using the finite dimensional real, complex and quaternion Hilbert spaces of the eigenfunctions. The…
A very elementary introduction to quantum algebras is presented and a few examples of their physical applications are mentioned.
It is proposed the scheme of quantum mechanics, in which a Hilbert space and the linear operators are not primary elements of the theory. Instead of it certain variant of the algebraic approach is considered. The elements of noncommutative…
In this paper we discuss and analyse the idea of trying to see (non-relativistic) quantum mechanics as a ``space-time statistical mechanics'', by using the classical statistical mechanical method on objective microscopic space-time…
The role of operational quantum mechanics, quantum axiomatics and quantum structures in general is presented as a contribution to a compendium on quantum physics, its history and philosophy.
This article is a short introduction to the general topic of quantum spin systems. After a brief sketch of the history of the subject, the standard mathematical framework for formulating problems and results in quantum spin systems is…
The determination of a quantum observable from the first and second moments of its measurement outcome statistics is investigated. Operational conditions for the moments of a probability measure are given which suffice to determine the…
The random matrix ensembles are applied to the quantum statistical systems. The quantum systems are studied using the finite dimensional real, complex and quaternion Hilbert spaces of the eigenfunctions. The linear operators describing the…
Recently a sufficient and necessary condition for Pauli's spin- statistics connection in nonrelativistic quantum mechanics has been established [quant-ph/0208151]. The two-dimensional part of this result is extended to n-particle systems…
A formulation of quantum mechanics, which begins by postulating assertions for individual physical systems, is given. The statistical predictions of quantum mechanics for infinite ensembles are then derived from its assertions for…
We study the statistical mechanics of classical and quantum systems in non-equilibrium steady states. Emphasis is placed on systems in strong thermal gradients. Various measures and functional forms of observables are presented. The quantum…
It is shown that the statistical conception of quantum mechanics is dynamical but not probabilistic, i.e. the statistical description in quantum mechanics is founded on dynamics. A use of the probability theory, when it takes place, is…
Quantum estimation of the operators of a system is investigated by analyzing its Liouville space of operators. In this way it is possible to easily derive some general characterization for the sets of observables (i.e. the possible quorums)…