Related papers: Differential Geometry of Quantum States, Observabl…
In this survey the possible approaches to the description of the evolution of states of quantum many-particle systems by means of the possible modifications of the density operator which kernel known as density matrix are considered. In…
The aim of this work is to study the geometry underlying mechanics and its application to describe autonomous and nonautonomous conservative dynamical systems of different types; as well as dissipative dynamical systems. We use different…
We give an explicit expression for the geometric measure of entanglement for three qubit states that are linear combinations of four orthogonal product states. It turns out that the geometric measure for these states has three different…
The mathematical formulation of Quantum Mechanics is derived from purely operational axioms based on a general definition of "experiment" as a set of transformations. The main ingredient of the mathematical construction is the postulated…
We discuss a general quantum theoretical example of quantum cohomology and show that various mathematical aspects of quantum cohomology have quantum mechanical and also observable significance.
We derive an explicit expressions for geometric description of state manifold obtained from evolution governed by a three parameter family of Hamiltonians covering most cases related to real interacting two-qubit systems. We discuss types…
The Hermiticity condition in quantum mechanics required for the characterisation of (a) physical observables and (b) generators of unitary motions can be relaxed into a wider class of operators whose eigenvalues are real and whose…
This paper is a review of our recent work on three notorious problems of non-relativistic quantum mechanics: realist interpretation, quantum theory of classical properties and the problem of quantum measurement. A considerable progress has…
The concept of off-diagonal geometric phases for mixed quantal states in unitary evolution is developed. We show that these phases arise from three basic ideas: (1) fulfillment of quantum parallel transport of a complete basis, (2) a…
The logical structure of Quantum Mechanics (QM) and its relation to other fundamental principles of Nature has been for decades a subject of intensive research. In particular, the question whether the dynamical axiom of QM can be derived…
We study deterministic and quantum dynamics from a constructive "finite" point of view, since the introduction of a continuum, or other actual infinities in physics poses serious conceptual and technical difficulties, without any need for…
We present a description of finite dimensional quantum entanglement, based on a study of the space of all convex decompositions of a given density matrix. On this space we construct a system of real polynomial equations describing separable…
The dynamics of a quantum system, undergoing unitary evolution and continuous monitoring, can be described in term of quantum trajectories. Although the averaged state fully characterises expectation values, the entire ensamble of…
The basic physical problems that necessitated the emergence of quantum physics are summarized, along with the elements of wave mechanics and its traditional statistical interpretation. Alternative interpretations to the statistical one,…
Contemporary scientific perspectivism is re-evaluated and extended to a comprehensive perspectivist methodology and 'mediated' realistic epistemology, especially, with reference to quantum mechanics. In the present study, this is realized…
A geometric construction of the arrival time in conventional quantum mechanics is presented. It is based on a careful mathematical analysis of different quantization procedures for classical observables as functions of positions and…
We present a detailed discussion of some features of quantum mechanical metastability. We analyze the nature of decaying (quasistationary) states and the regime of validity of the exponencial law, as well as decays at finite temperature. We…
This paper presents a new approach to phase space trajectories in quantum mechanics. A Moyal description of quantum theory is used, where observables and states are treated as classical functions on a classical phase space. A quantum…
The main formal structures of Generalized Quantum Theory are summarized. Recent progress has sharpened some of the concepts, in particular the notion of an observable, the action of an observable on states (putting more emphasis on the role…
Quantum algebraic observables representing localization in space-time of a Dirac electron are defined. Inertial motion of the electron is represented in the quantum algebra with electron mass acting as the generator of motion. Since…