On Observables

We propose a simple set-theoretic model of a generalized probability spaceadmitting intrinsic incompatible events and incompatible observables. It is acoproduct in the category D of D-posets and D-homomorphisms each factor ofwhich is a classical Kolmogorovian probability space. Since classical events,random functions, and probability measures can be treated within D in a canonicalway, the Kolmogorovian model becomes a special case. We show that -additivityand other -notions can be replaced in a natural way by sequential continuity.     

States as Morphisms

Using elementary categorical methods, we survey recent results concerning D-posets (equivalently effect algebras) of fuzzy sets and the corresponding category ID in which states are morphisms. First, we analyze the canonical structures carried by the unit interval I = [0,1] as the range of states and the impact of “states as morphisms” on the probability domains. Second, we analyze categories of various quantum and fuzzy structures and their relationships. Third, we describe some basic properties of ID and show that traditional probability domains such as fields of sets and bold algebras can be viewed as full subcategories of ID and probability measures on fields of sets and states on bold algebras become morphisms. Fourth, we discuss the categorical aspects of the transition from classical to fuzzy probability theory. We conclude with some remarks about generalized probability theory based on ID.     

Asymptotic symmetry for the charmed and upsilon vector mesons

New duality is used to predict the leptonic width of the upsilon meson and derive a generalization of Yennie's relation assuming that is a Q$\text{Q}$ state of a new quark. Large symmetry breakings are found for processes D¹ → Dπ, D¹ → Dγ, F¹ → Fγ. The leptonic widths of some excited vector states are also calculated.     

On Probability Domains

Motivated by IF-probability theory (intuitionistic fuzzy), we study n-component probability domains in which each event represents a body of competing components and the range of a state represents a simplex S _n of n-tuples of possible rewards–the sum of the rewards is a number from [0,1]. For n=1 we get fuzzy events, for example a bold algebra, and the corresponding fuzzy probability theory can be developed within the category ID of D-posets (equivalently effect algebras) of fuzzy sets and sequentially continuous D-homomorphisms. For n=2 we get IF-events, i.e., pairs (μ,ν) of fuzzy sets μ,ν∈[0,1] ^X such that μ(x)+ν(x)≤1 for all x∈X, but we order our pairs (events) coordinatewise. Hence the structure of IF-events (where (μ ₁,ν ₁)≤(μ ₂,ν ₂) whenever μ ₁≤μ ₂ and ν ₂≤ν ₁) is different and, consequently, the resulting IF-probability theory models a different principle. The category ID is cogenerated by I=[0,1] (objects of ID are subobjects of powers I ^X ), has nice properties and basic probabilistic notions and constructions are categorical. For example, states are morphisms. We introduce the category S _n D cogenerated by \(S_{n}=\{(x_{1},x_{2},\ldots ,x_{n})\in I^{n};\:\sum_{i=1}^{n}x_{i}\leq 1\}\) carrying the coordinatewise partial order, difference, and sequential convergence and we show how basic probability notions can be defined within S _n D.     

World-volume and target-space anomalies in the D = 10 super-fivebrane sigma model

The fields of the conjectured “heterotic” super-fivebrane sigma model in ten dimensions are made out of a well-known gravitational sector, the X and the ϑ, and of a still unknown heterotic sector which should be coupled to the Yang-Mills fields. We compute the one-loop d = 6 world-volume and D = 10 target-space Lorentz anomalies which arise from the gravitational sector of the heterotic super-fivebrane sigma model, using a method which we developed previously for the Green-Schwarz heterotic superstring. These anomalies turn out to carry an overall coefficient which is half of that required by the string-fivebrane duality conjecture. As a consequence, the world-volume anomaly vanishes if the heterotic fields consist of 16 (rather than 32) complex Weyl fermions on the world-volume. This implies that the string-fivebrane duality conjecture can not be based on a “heterotic” super-fivebrane sigma model with only fermions in the heterotic sector. Possible implications of this result are discussed.     

Characterization of chaotic maps using the permutation Bandt-Pompe probability distribution

By appealing to a long list of different nonlinear maps we review the characterization of time series arising from chaotic maps. The main tool for this characterization is the permutation Bandt-Pompe probability distribution function. We focus attention on both local and global characteristics of the components of this probability distribution function. We show that forbidden ordinal patterns (local quantifiers) exhibit an exponential growth for pattern-length range 3 ≤ D ≤ 8, in the case of finite time series data. Indeed, there is a minimum D _min-value such that forbidden patterns cannot appear for D < D _min. The system’s localization in an entropy-complexity plane (global quantifier) displays typical specific features associated with its dynamics’ nature. We conclude that a more “robust” distinction between deterministic and stochastic dynamics is achieved via the present time series’ treatment based on the global characteristics of the permutation Bandt-Pompe probability distribution function.     

Examples,problems, and results in effect algebras

This article discusses various unsolved problems and conjectures that have arisen in the study of effect algebras (orD-posets) during the last few years. We also include some examples, counterexamples, and results that motivate or partially solve these problems. The problems mainly concern sharp and principal elements, the existence of infima in Hilbert space effect algebras, tensor products, and interval algebras.     

Exchange magnetic moment form factor of the three-nucleon system

The exchange magnetic moment form factor of ³H and ³He is derived from experiment, regarding the D state probability P_D as free parameter. The isoscalar part is roughly constant. The rms radius corresponding to the isovector part increases as P_D increases.     

Computing parallel/coincident phase D-brane superpotentials and Type-Ⅱ/F-theory duality

In this paper we study the parallel phase and the coincident phase of D-brane systems with the compactification of one closed modulus. D-brane systems with two phases are described by different 4-folds in terms of Type-Ⅱ/F-theory duality, and the phase transitions are related by the blow-up from a 4-fold with singularities to a 4-fold without. In terms of gauge theory, the phase transition corresponds to the enhancement of gauge group U(1)×U(1)→U(2) connecting the Coulomb branch and the Higgs branch. For the sextic and octic with two D-branes,using mirror symmetry and Type-Ⅱ/F theory duality, A-model superpotentials are obtained from the B-model side for the two phases, and the U(1) Ooguri-Vafa invariants for the parallel phase and U(2) Ooguri-Vafa invariants for the coincident phase are extracted from the A-model superpotential. The difference between the invariants of the two phases is evidence of the phase transition between the Coulomb branch and the Higgs branch.     

Negative-ion formation from surface scattering and the Anderson correlation energy U

A theoretical investigation of negative-ion formation from positive-ion-surface scattering is presented from a unified point of view. Based on the time-dependent Anderson-Newns model, the correlation energy U is seen to play an important role in the two-electron transfer process. Calculations of the probability of negative-ion formation are in good agreement with experiments on the conversion of H⁺(D⁺) to H^?(D^?) by scattering from a cesiated W(100) surface.     

Uniqueness of methyl fluoride force field

The uniqueness of the general harmonic force field of methyl fluoride is analyzed. The analysis is applicable to other methyl halides as well. Through the compliance scheme, it is seen that by supplementing the data employed by Aldous and Mills (i.e., vibrational frequencies ω_i, Coriolis coupling constants ζ_i and the centrifugal stretching constants D_J, D_JK of CH₃F and CD₃F molecules), with the frequencies of A′ or A″ species of either CH₂DF or CD₂HF, the force field is uniquely determined. The addition of any other extra data including the ¹²CH₃F¹³CH₃F isotopic shifts only makes the determination of the force field parameters more precise.     

The effect of an external electric field on the optical properties of a quantum-dot molecule with a resonant state of the D 2 − center

The effect of an external electric field on the probability of the electron radiative transition from a resonant u-state to the localized g-state of the D ₂ ^? center in the presence of dissipative tunneling has been investigated in the model of zero-radius potential. It is shown that the probability of radiative transition increases by about two orders of magnitude in the case of the external electric field intensity for which the initially asymmetric double-well oscillator potential simulating a quantum-dot molecule becomes symmetrical.     

Numerical calculations of emission probabilities of primarily excited molecules in dye solutions

The “active sphere” concentration depolarization theory of Jabloński involves the probability, W_Dk, that a photon is emitted by the donor. Up till now, the mean value of W_Dk, has been exactly calculated only for k = 2 (1 donor and 1 acceptor in the active sphere). For k > 2 the approximate method of Knox was employed. In this paper the use of the Monte Carlo integration method to find <W_Dk > for k up to ten is described. The more accurate values thus obtained coincide closely with the ones found using the simplified method. This finding validates the use of the latter method without reservation up to high dye concentration.     

Interaction of a laser with a qubit in thermal motion and its application to robust and efficient readout

We present a detailed theoretical and experimental study on the optical control of a trapped-ion qubit subject to thermally induced fluctuations of the Rabi frequency. The coupling fluctuations are caused by thermal excitation on three harmonic oscillator modes. We develop an effective Maxwell–Boltzmann theory which leads to a replacement of several quantized oscillator modes by an effective continuous probability distribution function for the Rabi frequency. The model is experimentally verified for driving the quadrupole transition with resonant square pulses. This allows for the determination of the ion temperature with an accuracy of better than 2% of the temperature pertaining to the Doppler cooling limit T _D over a range from 0.5T _D to 5T _D . The theory is then applied successfully to model experimental data for rapid adiabatic passage (RAP) pulses. We apply the model and the obtained experimental parameters to elucidate the robustness and efficiency of the RAP process by means of numerical simulations.     

Chemisorption of H2 on W(100): Absolute sticking probability,coverage, and electron stimulated desorption

Measurements of both the absolute sticking probability near normal incidence and the coverage of H₂ adsorbed on W(100) at ~ 300K have been made using a precision gas dosing system; a known fraction of the molecules entering the vacuum chamber struck the sample crystal before reaching a mass spectrometer detector. The initial sticking probability S₀ for H₂/W(100) is 0.51 ± 0.03; the hydrogen coverage extrapolated to S = 0 is 2.0 × 10¹⁵ atoms cm^?2. The initial sticking probability S₀ for D₂/W(100) is 0.57 ± 0.03; the isotope effect for sticking probability is smaller than previously reported. Electron stimulated desorption (ESD) studies reveal that the low coverage β₂ hydrogen state on W(100) yields H⁺ ions upon bombardment by 100 eV electrons; the ion desorption cross section is ~ 1.8 × 10^?23 cm². The H⁺ ion cross section at saturation hydrogen coverage when the β₁ state is fully populated is ? 10^?25 cm². An isotope effect in electron stimulated desorption of H⁺ and D⁺ has been found. The H⁺ ion yield is ? 100 × greater than the D⁺ ion yield, in agreement with theory.     

Geometrical string and dual spin systems

We are able to perform the duality transformation of the spin system which was found before as a lattice realization of the string with linear action. In four and higher dimensions this spin system can be described in terms of a two-plaquette gauge hamiltonian. The duality transformation is constructed in geometrical and algebraic language. The dual hamiltonian represents a new type of spin system with local gauge invariance. At each vertex ξ there are d (d − 1) /2 Ising spins ∧_{μ, η} = ∧_{η,μ N}. ≠ P = 1, … , d and one Ising spin Γ on every linkξ ξ + e,). For the frozen spin Γ  1 the dual hamiltonian factorizes into d (d − 1) /2 two-dimensional Ising ferromagnets and into antiferromagnets in the case Γ  −1. For fluctuating F it is a sort of spin-glass system with local gauge invariance. The generalization to p-membranes is given.     

The deuteron D-state probability

A method of direct determination of the deuteron D-state probability from the experiment, based on the d ↑ p → ppn reaction analyzis is suggested. Using the known results on the vector analyzing power in elastic NN-scattering, the values of the overall nucleon polarization and the deuteron vector polarization have been obtained. The probability of the deuteron D-state is estimated to be w _D = 0.078 ± 0.046.     

Spectroscopic constants of the known electronic states of lead monofluoride

Based on measurements made by mass-resolved 1 + 1′ + 1″ resonance-enhanced multiphoton ionization spectroscopy, we have determined new molecular constants describing the rotational and fine structure levels of the B, D, E, and F states of the most abundant isotopic variant ²⁰⁸Pb¹⁹F, and we summarize the spectroscopic constants for all the know electronic states of the radical. Many spectroscopic constants for the isotopologues ²⁰⁶Pb¹⁹F and ²⁰⁷Pb¹⁹F have also been determined. The symmetry of the D-state is found to be ²Π_1/2, and the F-state is found to be an Ω = 3/2 state.     

The deuteron D-state probability

A method of direct determination of the deuteron D-state probability from the experiment, based on thed ↑p →ppn reaction analyzis is suggested. Using the known results on the vector analyzing power in elasticN N-scattering, the values of the overall nucleon polarization and the deuteron vector polarization have been obtained. The probability of the deuteron D-state is estimated to beW _D =0.078±0.046.