Related papers: Topics in quantum statistical mechanics and operat…
This paper examines language modeling based on the theory of quantum mechanics. It focuses on the introduction of quantum mechanics into the symbol-meaning pairs of language in order to build a representation model of natural language. At…
The biological hierarchy and the differences between living and non-living systems are considered from the standpoint of quantum mechanics. The hierarchical organization of biological systems requires hierarchical organization of quantum…
The goal of the presented paper is to provide an introduction to the basic computational models used in quantum information theory. We review various models of quantum Turing machine, quantum circuits and quantum random access machine…
After some historical remarks concerning Schroedinger's discovery of wave mechanics, we present a unified formalism for the mathematical description of classical and quantum-mechanical systems, utilizing elements of the theory of operator…
The conceptual setting of quantum mechanics is subject to an ongoing debate from its beginnings until now. The consequences of the apparent differences between quantum statistics and classical statistics range from the philosophical…
Under some hypotheses (symmetry, confluence), we enumerate all quadratically presented algebras, generated by creation and destruction operators, in which number operators exist. We show that these are algebras of bosons, fermions, their…
The purpose of this work is to discuss recent progress in deriving the fundamental laws of thermodynamics (0th, 1st and 2nd-law) from nonequilibrium quantum statistical mechanics. Basic thermodynamic notions are clarified and different…
As experiments continue to push the quantum-classical boundary using increasingly complex dynamical systems, the interpretation of experimental data becomes more and more challenging: when the observations are noisy, indirect, and limited,…
This is an exposition of some of the aspects of quantum computation and quantum information that have connections with operator theory. After a brief introduction, we discuss quantum algorithms. We outline basic properties of quantum…
In Quantum Physics, a measurement is represented by a projection on some closed subspace of a Hilbert space. We study algebras of operators that abstract from the algebra of projections on closed subspaces of a Hilbert space. The properties…
The operator algebra is introduced based on the framework of logarithmic representation of infinitesimal generators. In conclusion a set of generally-unbounded infinitesimal generators is characterized as a module over the Banach algebra.
Recent advances in the theory of complex symmetric operators are presented and related to current studies in non-hermitian quantum mechanics. The main themes of the survey are: the structure of complex symmetric operators, $C$-selfadjoint…
We review some of the recent developments in two dimensional statistical mechanics in which corner transfer matrices provide the vital link between the physical system and the representation theory of quantum affine algebras. This opens…
Bessel beams are studied within the general framework of quantum optics. The two modes of the electromagnetic field are quantized and the basic dynamical operators are identified. The algebra of these operators is analyzed in detail; it is…
A non-associative algebra of observables cannot be represented as operators on a Hilbert space, but it may appear in certain physical situations. This article employs algebraic methods in order to derive uncertainty relations and…
The concept of number is fundamental to the formulation of any physical theory. We give a heuristic motivation for the reformulation of Quantum Mechanics in terms of non-standard real numbers called Quantum Real Numbers. The standard axioms…
In this dissertation, we analyze equilibrium and out-of-equilibrium quantum phase transitions present in quantum spin-$\frac{1}{2}$ models, using a quantum information approach through quantum correlations and phase space formalism, and a…
We provide a systematic approach to quantum mechanics from an information-theoretic perspective using the language of tensor networks. Our formulation needs only a single kind of object, so-called positive *-tensors. Physical models…
Given are a first principles derivation and formulation of the probabilistic concepts that underly equilibrium quantum statistical mechanics. The transition to non-equilibrium probability is traversed briefly.
We first introduce and discuss density operator interpretations of quantum theory as a special case of a more general class of interpretations, giving special attention to a version that we call the `atomic version'. We then review some…