Related papers: Quantum mechanics in a metric sheaf: a model theor…
Until recently, a quantum instrument was defined to be a completely positive operation-valued measure from the set of states on a Hilbert space to itself. In the last few years, this definition has been generalized to such measures between…
Consider a statistical model with an epistemic restriction such that, unlike in classical mechanics, the allowed distribution of positions is fundamentally restricted by the form of an underlying momentum field. Assume an agent (observer)…
Quantum gauge theory in the connection representation uses functions of holonomies as configuration observables. Physical observables (gauge and diffeomorphism invariant) are represented in the Hilbert space of physical states; physical…
We develop the idea of employing localization systems of Boolean coverings, associated with measurement situations, in order to comprehend structures of Quantum Observables. In this manner, Boolean domain observables constitute structure…
In this paper we provide a general account of the causal models which attempt to provide a solution to the famous measurement problem of Quantum Mechanics (QM). We will argue that --leaving aside instrumentalism which restricts the physical…
The theory of Lie systems has recently been applied to Quantum Mechanics and additionally some integrability conditions for Lie systems of differential equations have also recently been analysed from a geometric perspective. In this paper…
Quantum-mechanical wave equation for a particle with spin 1 is investigated in presence of external magnetic field in spaces with non-Euclidean geometry with constant positive curvature. Separation of the variable is performed; differential…
This manuscript gathers and subsumes a long series of works on using QW to simulate transport phenomena. Quantum Walks (QWs) consist of single and isolated quantum systems, evolving in discrete or continuous time steps according to a…
This paper is a programmatic article presenting an outline of a new view of the foundations of quantum mechanics and quantum field theory. In short, the proposed foundations are given by the following statements: * Coherent quantum physics…
Aspects of quantum mechanics on a ring are studied. Either one or two impenetrable barriers are inserted at nodal and non-nodal points to turn the ring into either one or two infinite square wells. In the process, the wave function of a…
Using the frame formalism we determine some possible metrics and metric-compatible connections on the noncommutative differential geometry of the real quantum plane. By definition a metric maps the tensor product of two 1-forms into a…
Quantum Mechanics (QM) is a very special probabilistic theory, yet we don't know which operational principles make it so. All axiomatization attempts suffer at least one postulate of a mathematical nature. Here I will analyze the…
The paper studies a general scheme for constructing metrics on a product of metric spaces by means of a family of continuous convex functions. This construction includes the conventional $p$-metrics and generates metrics that are…
We constructed a Hilbert space representation of a contextual Kolmogorov model. This representation is based on two fundamental observables -- in the standard quantum model these are position and momentum observables. This representation…
We construct a space of quantum states and an algebra of quantum observables, over the set of all metrics of arbitrary but fixed signature, defined on a manifold. The construction is diffeomorphism invariant, and unique up to natural…
If one takes seriously the postulate of quantum mechanics in which physical states are rays in the standard Hilbert space of the theory, one is naturally lead to a geometric formulation of the theory. Within this formulation of quantum…
Based on general and minimal properties of the {\it discrete} circuit complexity, we define the complexity in {\it continuous} systems in a geometrical way. We first show that the Finsler metric naturally emerges in the geometry of the…
The pure state space of Quantum Mechanics is investigated as Hermitian Symmetric Kaehler manifold. The classical principles of Quantum Mechanics (Quantum Superposition Principle, Heisenberg Uncertainty Principle, Quantum Probability…
We show that the key problems of quantum measurement theory, namely the reduction of the wave packet of a microsystem and the specification of its quantum state by a macroscopic measuring instrument, may be rigorously resolved within the…
We define a formal framework for reasoning about linear-time properties of quantum systems in which quantum automata are employed in the modeling of systems and certain closed subspaces of state (Hilbert) spaces are used as the atomic…