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[en] It is hard to find a satisfactory answer to the question, ''What is a resonance?'' To get a better feeling for the question and for what is required of an answer, consider the following thought experiment. Suppose that you are given a one-to-one symplectic mapping, F, defined over some four-dimensional phase space and realized in an unspecified system of coordinates. (Think of F, for example, as a tracking program that models the Poincare map of a 2 1/2 degree of freedom Hamiltonian system.) Starting from any number of points in phase space, you can calculate forward or backward iterates of F infinitely quickly. Further, you have unlimited capabilities for displaying these orbits on a four-dimensional graphics terminal. Given even these extraordinary tools, how would you test the simple hypothesis: ''This system exhibits a first order sextupole resonance''? What topological features of the separatrix must be reflected in the ''data'' in order to confirm or deny such a statement? There is not enough space in a short paper like this to present a full analysis of this problem. The authors short-circuit the process and simply assert what is needed to define the separatrix of an integrably resonant dynamical system on a general 2p-dimensional phase space
[en] We investigate up to the fourth order normalized factorial moments of free-propagating and pulsed single photons displaced in phase space in a phase-averaged manner. Due to their loss independence, these moments offer expedient methods for quantum optical state characterization. We examine quantum features of the prepared displaced states, retrieve information on their photon-number content and study the reliability of the state reconstruction method used. (paper)
[en] In this article, we give a simple proof of the fact that the optimal collective attacks against continuous-variable quantum key distribution with a Gaussian modulation are Gaussian attacks. Our proof, which makes use of symmetry properties of the protocol in phase space, is particularly relevant for the finite-key analysis of the protocol and therefore for practical applications.
[en] The notion of dimension as a quantitative characteristic of space geometry is discussed. It is supposed that hadrons created in interactions between particles and nuclei can be considered sets of points possessing fractal properties in the three-dimensional phase space (pT, η, ϕ). The Hausdorff-Besicovich dimension DF is considered the most natural characteristic for determining the fractal dimension. Different methods for determining the fractal dimension are compared: box counting (BC), P-adic coverage (PaC), and system of equations of P-adic coverage (SePaC). A procedure for choosing optimum values of parameters of the considered methods is presented. These parameters are shown to be able to reconstruct the fractal dimension DF, number of levels Nlev, and fractal structure with maximal efficiency. The features of the PaC- and SePaC-methods in the analysis of fractals with independent branching are noted.
[en] We study the effect of friction on the dynamics of a classical point particle in a one-dimensional double-well potential. It turns out that finite uncertainty in the initial conditions of the particle may prevent us from reliably predicting the well in which the particle will come to rest. This difficulty—to make reliable long-term predictions—originates from the layered structure of phase-space regions sending the particle to the left and the right well, respectively. Similar structures are known to arise in models used, for example, to described the tossing of a coin where friction is, however, not the root cause of the phenomenon. (paper)
[en] We study certain bispectral operators that are remain bispectral under the flows of some subhierarchies of Kadomtsev - Petviashvili (KP) hierarchy. We show that the dynamics of the poles of these bispectral operators are governed by Hamiltonian systems on the Calogero-Moser phase spaces. (author)
[en] The problem of the lattice structure of a quantum logic is solved by embedding the logic into the so-called phase geometry of the physical system, being an atomistic complete lattice. The latter is constructed using pure states of the physical system
[en] In this note I shall continue the study of the non-commutative phase space functor, Ph(A), defined for any associative algebra A, and its derived differential co-simplicial algebra, Ph*(A). The main focus will be on its relationship to the classical de Rham complex, to the dynamics of finite dimensional Ph∞(A)-modules, and to the notion of Entropy. These subjects are treated within the set-up of my book [2011 Geometry of Time-Spaces (World Scientific)].