Related papers: Exploring complete positivity in hierarchy equatio…
We consider matrices whose elements enumerate weights of walks in planar directed weighted graphs (not necessarily acyclic). These matrices are totally nonnegative; more precisely, all their minors are formal power series in edge weights…
The relevance that the property of complete positivity has had in the determination of quantum structures is briefly reviewed, together with recent applications to neutron optics and quantum Brownian motion. A possible useful application…
We consider complete positivity of dynamics regarding subsystems of an open composite quantum system, which is subject of a completely positive dynamics. By "completely positive dynamics", we assume the dynamical maps called the completely…
Positivity or the stronger notion of complete positivity, and contextuality are central properties of quantum dynamics. In this work, we demonstrate that a physical unitary-universe dilation model could be employed to characterize the…
In this paper, we derive equations of motion for the normal-order, the symmetric-order and the antinormal-order quantum characteristic functions, applicable for general Hamiltonian systems. We do this by utilizing the `characteristic form'…
A new approach for arbitrary dimension to the Friedmann cosmological models is presented. Taking suitable changes of the parameters of the spacetime the harmonic motion equations appear, where the curvature determines the angular frequency.…
We define a hierarchy of systems with topological completely positive entropy in the context of continuous countable amenable group actions on compact metric spaces. For each countable ordinal we construct a dynamical system on the…
We obtain new types of exponential decay laws for solutions of density-matrix master equations in the weak-coupling limit: after comparing with results already present in the literature and developing the necessary techniques, we study the…
Two recent arguments for linear dynamics in quantum theory are critically re-examined. Neither argument is found to be satisfactory as it stands, although an improved version of one of the arguments can in fact be given. This improved…
We develop a general approach for monitoring and controlling evolution of open quantum systems. In contrast to the master equations describing time evolution of density operators, here, we formulate a dynamical equation for the evolution of…
It is shown that if the decoherence matrix corresponding to a qubit master equation has a block-diagonal real part, then the evolution is determined by a one-dimensional oscillator equation. Further, when the full decoherence matrix is…
Basing on a new approach to the fundamental conception of the momentum of a variable-mass point, the paper deals with the hyperreactive model of motion. The equations of motion are different in this model from the known…
We show that complete positivity is not only sufficient but also necessary for the validity of the quantum data-processing inequality. As a consequence, the reduced dynamics of a quantum system are completely positive, even in the presence…
Complete positivity is a ubiquitous assumption in the study of quantum systems interacting with the environment, despite repeated efforts to point out that the assumption is not empirically justified. It will be shown that Hamiltonian…
A concise and self-contained derivation of hybrid quantum-classical dynamics is given in terms of Markovian master equations. Many previously known results are re-derived, revised, some of them completed or corrected. Using as simple method…
We present a detailed analysis of random motions moving in higher spaces with a natural number of velocities. In the case of the so-called minimal random dynamics, under some wide assumptions, we show the joint distribution of the position…
A new framework for deriving equations of motion for constrained quantum systems is introduced, and a procedure for its implementation is outlined. In special cases the framework reduces to a quantum analogue of the Dirac theory of…
The goal of this contribution is to introduce the Hamiltonian formalism of theoretical mechanics for analysing motion in generic linear and non-linear dynamical systems, including particle accelerators. This framework allows the derivation…
We develop the canonical formalism for a system of $N$ bodies in lineal gravity and obtain exact solutions to the equations of motion for N=2. The determining equation of the Hamiltonian is derived in the form of a transcendental equation,…
Universality of quantum mechanics -- its applicability to physical systems of quite different nature and scales -- indicates that quantum behavior can be a manifestation of general mathematical properties of systems containing…