Related papers: Canonical structures of $A$ and $B$ forms
Different approaches are compared to formulation of quantum mechanics of a particle on the curved spaces. At first, the canonical, quasi-classical and path integration formalisms are considered for quantization of geodesic motion on the…
Understanding whether the features of open quantum dynamics are genuinely quantum remains a central challenge in quantum dynamics. Even though the non-Markovian behavior of quantum dynamics has been widely investigated across different…
This paper studies the nature of fractional linear transformations in a general relativity context as well as in a quantum theoretical framework. Two features are found to deserve special attention: the first is the possibility of…
In this paper, we discuss the quantum dynamics of a nonlinear system that admits temporally localized solutions at the classical level. We consider a general ordered position-dependent mass Hamiltonian in which the ordering parameters of…
We present a heuristic derivation of Born's rule and unitary transforms in Quantum Mechanics, from a simple set of axioms built upon a physical phenomenology of quantization. This approach naturally leads to the usual quantum formalism,…
An explicit expression in terms of canonical variables is obtained for the Hamiltonian functional determining the fully nonlinear dynamics of two-dimensional potential flows of an ideal fluid with a free surface over an arbitrary nonuniform…
We provide a general and consistent formulation for linear subsystem quantum dynamical maps, developed from a minimal set of postulates, primary among which is a relaxation of the usual, restrictive assumption of uncorrelated initial…
Assuming that quantum states, including pure states, represent subjective degrees of belief rather than objective properties of systems, the question of what other elements of the quantum formalism must also be taken as subjective is…
Using the example of the harmonic oscillator, we illustrate the use of hybrid dynamical brackets in analyzing quantum-classical interaction. We only assume that a hybrid dynamical bracket exists, is bilinear, and reduces to the pure…
In the study of bi-Hamiltonian systems (both classical and quantum) one starts with a given dynamics and looks for all alternative Hamiltonian descriptions it admits.In this paper we start with two compatible Hermitian structures (the…
The main purpose of this paper is to define dynamical degrees for rational maps over an algebraic closed field of characteristic zero and prove some basic properties (such as log-concavity) and give some applications. We also define…
It is considered, in the framework of constrained systems, the quantum dynamics of non-relativistic particles moving on a d-dimensional Riemannian manifold M isometrically embedded in $R^{d+n}$. This generalizes recent investigations where…
Classical and quantum physics represent two distinct theories; however, quantum physics is regarded as the more fundamental of the two. It is posited that classical mechanics should arise from quantum mechanics under certain limiting…
We investigate the possibility of dividing quantum channels into concatenations of other channels, thereby studying the semigroup structure of the set of completely-positive trace-preserving maps. We show the existence of 'indivisible'…
We present the quantum and classical mechanics formalisms for a particle with position-dependent mass in the context of a deformed algebraic structure (named $\kappa$-algebra), motivated by the Kappa-statistics. From this structure we…
The main purpose of thispaper is to show that composite quantum-like (QL) systems can closely mimic the separable states of quantum systems, and that suitable physical systems exhibiting these states exist. It is shown that QL graphs can…
Experiments violating Bell's inequality appear to indicate deterministic models do not correspond to a realistic theory of quantum mechanics. The theory of pilot waves seemingly overcomes this hurdle via nonlocality and statistical…
This paper develops a gravitational-thermodynamic interpretation of two ensemble structures with singular behavior, denoted as canonical ensemble A and grand canonical ensemble B. Ensemble A is modeled as a stellar-type system in which…
We study the dynamics of a two-level quantum system interacting with an external electromagnetic field periodic and quasiperiodic in time. The quantum evolution is described exactly by the classical equations of motion of a gyromagnet in a…
Classical block designs are important combinatorial structures with a wide range of applications in Computer Science and Statistics. Here we give a new abstract description of block designs based on the arrow category construction. We show…