Ergodical time evolution of a Gaussian wave packet in quantum dots

The time evolution of a Gaussian wave packet (GWP) confined in a quantum dot is numerically studied. The quantum dots are modelled by a two-dimensional square box and by the potential x⁴ + y⁴. For the case of an incommensurate energy spectrum the time evolution of observables has no global period. As a result this leads to ergodic phase portraits with a finite phase volume. For the spatially wide GWP the distribution function of quantum observables may be approximated as a Gaussian one. For the case of commensurate transition frequencies in the quantum well the time evolution of observables is periodical and the phase portraits have a zero phase volume.     

Clusterisation and isospin effects in heavy-ion collisions at intermediate energies

We study the multifragmentation phenomenon in heavy-ion collisions by varying the spatial constraint criterion in minimum spanning tree (MST) clusterisation procedure. Within the framework of isospin-dependent quantum molecular dynamics (IQMD) model, the role of isospin-dependent spatial constraint, i.e. iso-MST version, is investigated on different fragment observables in various isobaric pair of reaction systems varying in the entrance channel isospin (N / Z) content. The fragment observables such as persistence, gain, average yield of free nucleons, light and intermediate mass fragments are slightly sensitive to the isospin-dependent spatial constraint criterion particularly in heavier reaction systems. For a given isobaric pair of reaction systems, the fragment production, however, remains indifferent to isospin content of the colliding nuclei.     

Observables and quark confinement in the covariant canonical formalism of Yang-Mills theory

A concise criterion for observables in Yang-Mills theory is presented in the framework of covariant canonical field theory. As an example, the symmetric energy-momentum tensor θ_øν is proved to be an observable and its physically meaningful form is clarified. The validity of the “Maxwell-type” equation of motion is established in the physical subspace $\text{V}$_phys defined by the subsidiary condition $\text{Q}{}_{\mathrm{<mtext>B</mtext>}}\text{?}\text{phys}\text{〉 = 0}$ (Q_B: BRS charge). Its meaning and consequences are discussed in connection with the notion of observables: especially, all (quasi-) local observables in QCD are shown to be colour singlets and this fact paves the way to quark confinement.     

Positive pion production from polarized protons by linearly polarized photons in the energy range 280–420 MeV

The method is described of measuring the polarization observables Σ, P and T for the reaction γp → nπ⁺ in a double polarization experiment (polarized target + polarized beam). The measured angular distribution of these observables are presented for the photon energy range 280–420 MeV at c.m. pion emission angles between 30° and 150°. The obtained experimental data are included in the energy-independent multipole analysis of the reactions γp → Nπ.     

Quantum logics and chemical kinetics

A statistical theory of chemical kinetics is presented based on the quantum logical concept of chemical observables. The apparatus of Boolean algebra $\text{B}$ is applied for the construction of appropriate composition polynomials referring to any stipulated arrangement of the atomic constituents. A physically motivated probability measure μ(F) is introduced on the field $\text{B}$ of chemical observables, which considers the occurrence of the yes response of a given F ? $\text{B}$. The equations for the time evolution of the species density operators and the master equations for the corresponding number densities are derived. The general treatment is applied to a superposition of elementary substitution reactions (AB)_α + C ? (AC)_β + B. The expressions for the reaction rate coefficients are established.     

Recent developments in ab-initio few-body scattering calculations including the Coulomb interaction

Recent progress on the solution of ab-initio three- and four-nucleon scattering equations in momentum space that include the correct treatment of the Coulomb interaction is reviewed; results for specific observables in reactions initiated by p + d, p + ³He and n + ³He are shown. In addition three-body calculations of d + ¹²C reactions are compared with equivalent CDCC calculations.     

Probabilistic scission of a fissile nucleus into fragments

A probabilistic criterion is proposed for the scission of a fissile nucleus into fragments. The probability of the rupture of the neck between would-be fragments is estimated by considering scission as a fluctuation. The energy of the prescission configuration and the energy of the separated-fragment configuration are computed on the basis of a macroscopic model that takes into account a finite range of nuclear forces and the diffuseness of the nuclear surface. The effect of the probabilistic criterion of nuclear scission on fission-process observables, such as the moments of the mass-energy distribution of fission fragments, the mean multiplicity of prescission neutrons, and mean fission times, is demonstrated. It is shown that the Strutinsky criterion, according to which nuclear scission occurs at a finite neck radius of 0.3R₀, is a rather good approximation to the probabilistic scission criterion in Langevin dynamical calculations employing the one-body nuclear-viscosity mechanism modified in such a way that the wall-formula contribution is reduced, the reduction factor satisfying the condition k _s <05.     

Complete Sets of Polarization Observables in Electromagnetic Deuteron Breakup

 For deuteron photo- and electrodisintegration the selection of complete sets of polarization observables is discussed in detail by applying a recently developed new criterion for the check of completeness of a chosen set of observables. The question of ambiguities and their resolution by considering additional observables is discussed for a numerical example, for which the role of experimental uncertainties is also investigated. Furthermore, by inversion of the expressions of the observables as Hermitean forms in the t-matrix elements a bilinear term of the form can be given as a complex linear form in the observables from which an explicit solution for in terms of observables can be obtained. These can also be used to select sets of observables for the explicit representation of the t-matrix. Received May 15, 1999; accepted for publication August 30, 1999     

Effects of (V+A)-, S-, T-interaction admixtures and of a time reversal invariance violation on the first-forbidden beta-decay of RaE

The shape factor and the electron longitudinal polarization of RaE have been calculated under the assumption of (V+A)-,S-,T-interaction admixtures. In addition the influence of a time reversal invariance violation has been considered. It is shown that the effect of (V+A) admixtures on the electron longitudinal polarization is enhanced by two orders of magnitude compared to the case of allowed transitions. Such an effect is also observed for the shape factor. It is also demonstrated that a time reversal invariance violation also affects the observables mentioned above.     

Effect of meson exchange corrections on allowed muon capture

Corrections to the impulse approximation calculation of the γ?ν angular correlation coefficient and recoil nuclear polarization in allowed muon capture transitions, arising from meson exchange effects, are studied and the value for the induced pseudoscalar coupling consistent with both observables is found to be (13.3 + 3)_gA, to a large extent free from nuclear wave function uncertainties.     

Polarization phenomena in NN ↔ Dπ reactions

On the basis of a relativistic approach, NN ? Dπ reactions are analyzed in detail. The coherent sum of one-nucleon-exchange and pion-rescattering diagrams is calculated. It is shown that polarization observables are highly sensitive to off-mass-shell effects within the deuteron and that some of these observables can change sign upon taking these effects into account. The effect of the deuteron P wave is also investigated. The results obtained by calculating a full set of observables are compared with experimental data on the reaction pp → Dπ ⁺.     

A frame bundle generalization of multisymplectic momentum mappings

We construct momentum mappings for covariant Hamiltonian field theories using a generalization of symplectic geometry to the bundle L_VY of vertically adapted linear frames over the bundle of field configurations Y. Field momentum observables are vector-valued momentum mappings generated from automorphisms of Y, using the (n + k)-symplectic geometry of L_VY. These momentum observables on L_VY generalize those in covariant multisymplectic geometry and produce conserved field quantities along flows. Three examples illustrate the utility of these momentum mappings: orthogonal symmetry of a Kaluza-Klein theory generates the conservation of field angular momentum, affine reparametrization symmetry in time-evolution mechanics produces a version of the parallel axis theorem of rotational dynamics, and time reparametrization symmetry in time-evolution mechanics gives us an improvement upon a parallel transport law.     

Polarization phenomena in hadronic reactions

Predictions are made in the framework of the effective color field (ECF) model for polarization observables in $p + A \to \bar \Lambda X$ , A + A → ΛX and p + Pb → pX reactions. The predictions can be checked in the polarization experiments at IHEP (SPASCHARM), JINR (NICA) and BNL (RHIC). Estimates of quark masses and anamolous chromomagnetic quark moments are given.     

An abstract derivation of the inequality related to heisenberg's uncertainty principle

It is shown that Heisenberg's uncertainty principle can be derived from algebraic properties of observables, without involving Hilbert space formalism of quantum mechanics. Namely, if m(A,? ) denotes the statisctical second moment of an observable A measured in the state ? and we define $\text{m([A,B]),?)=}\text{1}\text{2}\text{(m(A+B,?)?m(A,?) ?(B,?))}$, then the property of oddness with respect to observables m([A,?B],?) =?m([A,B),?) implies an abstract from of Heisenberg's inequality. If, in addition, there is a canonical pair of observables A,B such that m([A,B],[?,?ψ]) =?m([A,B],[?,ψ]), then the classical uncertainty principle of Heisenberg follows. These results allow us to formulate and derive Heisenberg's principle in the framework of axiomatic quantum mechanics from an equational assumption about the profitability function of the system.     

Evaporation and fission decay of 132Ce compound nuclei at Ex=122 MeV: some limitations of the statistical model

Light charged particle (LCP) emission in the evaporation residue (ER) and fusion fission (FF) channels have been studied for the 200 MeV ³²S + ¹⁰⁰Mo reaction, leading to ¹³²Ce composite nuclei at E _x =122 MeV. The main goal was to study the decay of ¹³² Ce on the basis of an extended set of observables, to get insights on the fission dynamics. The proton and alpha particle energy spectra, their multiplicities, ER-LCP angular correlations, ER and FF angular distributions, and ER and FF cross-sections were measured. The measured observables were compared with the Statistical Model (SM). Using standard parameters, the model was able to reproduce only the pre-scission multiplicities and the FF and ER cross-sections. The calculation was observed to strongly overestimate the proton and alpha particle multiplicities in the ER channel. Disagreements were also observed for the ER-LCP correlations, the LCP energy spectra and the ER angular distribution. By varying the SM input parameters over a wide range of values, it is shown that it is not possible to reproduce all the observables simultaneously with a unique set of parameters. The inadequacy of the model in reproducing the ER particle multiplicities is also observed analysing data from the literature for other systems in the A ≈ 150 and E _x ≈ 100?200 MeV region. These results indicate serious limitations about the use of the SM in extracting information on fission dynamics.     

Microscopic description of the reactions d + d → p + 3H and d + d → n + 3He at low energies

A collective adiabatic approach is used to explore the total and differential cross sections for the reactions d + d → p + ³H and d + d → n + ³He at incident-deuteron energies of up to 6 MeV. All substantially contributing partial waves of order not higher than that of G waves are taken into account. The experimental value of the difference of the cross sections for the above mirror reactions is reproduced theoretically under the assumption that nuclear forces obey the condition of isotopic invariance. The positions and amplitudes of the maxima in the calculated total cross sections virtually coincide with those of the corresponding experimental values. It is shown that, around the maxima of the cross sections under study, dominant contributions to them come from the P wave. The sensitivity of observables to the parameters of nucleon-nucleon interaction is analyzed.     

Searches for electroweak γ-Z-Z’ interference at the LEP2 e + e − collider

Indirect effects of the Z’ boson in the process e ⁺ e ^? → μ⁺μ^? as implemented at the LEP2 electron-positron collider are investigated in terms of new integrated observables σ^±. It is demonstrated that these observables furnish more definitive information about Z’-boson effects than the canonical observables σ_± and A _FB. It is established that the deviations Δσ^± induced by Z’ bosons show a specific energy dependence, which is determined primarily by the parameters of the Standard Model. This permits making unambiguous model-independent predictions. In particular, two points, $\sqrt {s_ + } \approx 78GeV$ and $\sqrt {s_ - } \approx 113GeV$ , are determined at which, respectively, σ₊ and σ_? vanish both in the Standard Model and in presence of the extra Z’ boson. These energy values can be of use in searches for phenomenological manifestations of alternative sources of new physics that are different from Z’.     

Quark models and polarized electroproduction of the Roper resonance

We calculate the recoil polarization observables for neutral pion electroproduction on the proton. In particular, for theN(938)→N ^*(1440) transition, we study these observables for several quark models of the resonant amplitudes. We find that the polarization response functions, unlike the unpolarized cross section, have encouragingly large sensitivity to the presence of the Roper. Furthermore, these observables can clearly reveal the presence of a longitudinal coupling.