Compressible effect algebras

We define a special type of additive map J on an effect algebra E called a compression. We call J(1) the focus of J and if p is the focus of a compression then p is called a projection. The set of projections in E is denoted by P(E). A compression J is direct if J(a) ≤ a for all a ε E. We show that direct compressions are equivalent to projections onto components of cartesian products. An effect algebra E is said to be compressible if every compression on E is uniquely determined by its focus and every compression on E has a supplement. We define and characterize the commutant C(p) of a projection p and show that a compression with focus p is direct if and only if C(p) = E. We show that P(E) is an orthomodular poset. It is proved that the cartesian product of effect algebras is compressible if and only if each component is compressible. We then consider compressible sequential effect algebras, Lüders maps and conditional probabilities.     

Interacting generalized ghost dark energy in a non-flat universe

We investigate the generalized Quantum Chromodynamics (QCD) ghost model of dark energy in the framework of Einstein gravity. First, we study the non-interacting generalized ghost dark energy in a flat Friedmann-Robertson-Walker (FRW) background. We obtain the equation of state parameter, w _D = p/ρ, the deceleration parameter, and the evolution equation of the generalized ghost dark energy. We find that, in this case, w _D cannot cross the phantom line (w _D > ?1) and eventually the universe approaches a de-Sitter phase of expansion (w _D → ?1). Then, we extend the study to the interacting ghost dark energy in both a flat and non-flat FRW universe. We find that the equation of state parameter of the interacting generalized ghost dark energy can cross the phantom line (w _D < ?1) provided the parameters of the model are chosen suitably. Finally, we constrain the model parameters by using the Markov Chain Monte Carlo (MCMC) method and a combined dataset of SNIa, CMB, BAO and X-ray gas mass fraction.     

QCD estimates for associated charm production by weak neutral currents

We give quantitative estimates for associated charm production in neutrino and antineutrino induced neutral current interactions, based on (a) quantum chromodynamics (QCD) and (b) the quark parton model (QPM) and a phenomenological generalization thereof. We emphasize the need for a precise measurement of the ratio σ(v_μN→v_μe⁺X)/σ(v_μN→μ^?X) and the corresponding ratio for antineutrinos, as these can provide clean tests of certain characteristic features of QCD. Bounds are obtained for single charm production by charm-changing neutral currents.     

Representation theory of osp(1,2) q

We investigate the representations of the osp(1, 2) _q algebra. We derive all the finite-dimensional irreducible representations, whenq is not a root of unity. We also discuss the connection between those of osp(1, 2) _q and sl(2) _q .     

An Infinite Family of Adsorption Models and Restricted Lukasiewicz Paths

We define (k,?)-restricted Lukasiewicz paths, k??????₀, and use these paths as models of polymer adsorption. We write down a polynomial expression satisfied by the generating function for arbitrary values of (k,?). The resulting polynomial is of degree ?+1 and hence cannot be solved explicitly for sufficiently large ?. We provide two different approaches to obtain the phase diagram. In addition to a more conventional analysis, we also develop a new mathematical characterisation of the phase diagram in terms of the discriminant of the polynomial and a zero of its highest degree coefficient. We then give a bijection between (k,?)-restricted Lukasiewicz paths and ??rise??-restricted Dyck paths, identifying another family of path models which share the same critical behaviour. For (k,?)=(1,??) we provide a new bijection to Motzkin paths. We also consider the area-weighted generating function and show that it is a q-deformed algebraic function. We determine the generating function explicitly in particular cases of (k,?)-restricted Lukasiewicz paths, and for (k,?)=(0,??) we provide a bijection to Dyck paths.     

Quantum magneto-transport in two-dimensional GaAs electron gases and SiGe hole gases

We have measured the low-temperature transport properties of two-dimensional (2D) GaAs electron gases and 2D SiGe hole gases. Our experimental results fall into three categories. (i) Collapse of spin-splitting and an enhanced Landé g-factor at Landau level filling factors both ν=3 and ν=1 in a 2D GaAs electron gas are observed. Our experimental results show direct evidence that the effective disorder is stronger at ν=1 than that at ν=3 over approximately the same perpendicular magnetic field range. (ii) We present evidence for spin-polarisation of a dilute 2D GaAs electron gas. The Lande g-factor of the system is estimated to be 1.66. This enhanced g value is ascribed to electron–electron interactions at ultra low carrier density limit. (iii) In a high-quality SiGe hole gas, there is a temperature-independent point in the magnetoresistivity ρ_xx and ρ_xy which is ascribed to experimental evidence for a quantum phase transition between ν=3 and ν=5. We also present a study on the temperature(T)-driven flow lines in our system.     

Fulop-Tsutsui interactions on quantum graphs

We examine scale invariant Fulop-Tsutsui couplings in a quantum vertex of a general degree n. We demonstrate that essentially same scattering amplitudes as for the free coupling can be achieved for two (n−1)-parameter Fulop-Tsutsui subfamilies if n is odd, and for three (n−1)-parameter Fulop-Tsutsui subfamilies if n is even. We also work up an approximation scheme for a general Fulop-Tsutsui vertex, using only n δ function potentials.     

Self-avoiding and planar random surfaces on the lattice

We study models of self-avoiding (SARS) and of planar (PRS) random surfaces on a (hyper-) cubic lattice. If N_γ(A) is the number of such surfaces with given boundary γ and area A, then N_γ(A) = exp(β₀A + o(A)), where β₀ is independent of γ. We prove that, for β > β₀, the string tension is finite for the SARS model and strictly positive for the PRS model and that in both models the correlation length (inverse mass) is positive and finite. We discuss the possibility of the existence of a critical point and of a roughening transition. Estimates on intersection probabilities for random surfaces and connections with lattice gauge theories are sketched.     

Modified Lee-Friedberg soliton-bag model with absolute confinement

We systematically investigate solutions of a modified Lee-Friedberg model for fermions bound in a non-linearly self-interacting scalar fieldσ. In this model a runningσ-fermion coupling strengthg(σ) is introduced such as to interpolate between a perturbative vacuum withσ=0 and a non-trivial vacuum (σ=σ _v ) with strong coupling. We find soliton-bag-like solutions in which the fermions experience absolute confinement. These solutions are almost independent of the detailed form ofg(σ).     

Comparison of the π and Δ operator approximations for the two-dimensional t–J model

We compare the spectra of the new π operator of the SO(5) theory and the conventional Δ operator for the two-dimensional t–J model. We also calculate the weight transferred to the two-hole ground state from half-filling by these operators. We find that the spectra of these operators are quite similar and the weight for the π operator is smaller than the weight for the Δ operator. We argue that the two-dimensional t–J model does not have a good approximate SO(5) symmetry claimed in Ref. [1].     

The electromagnetic interaction in chiral perturbation theory

We investigate electromagnetic effects in the framework of chiral perturbation theory. Using a completely independent method, we confirm Urech’s results for the divergences of the one-loop functional in the electromagnetic sector. We perform a one-loop analysis of allP _t2 (P=π, K, η) and theK _t3 form factors $f_ + ^{K^ + \pi ^o } (0),f_ + ^{K^o \pi ^ - } (0)$ , including a systematic treatment of theO(e ² p ²) contributions in the mesonic part. We illustrate our results by several numerical estimates.     

OnD→ππ andK\bar K decays

We have analysed the recent data onD→ππ and \(K\bar K\) decays from ARGUS, CLEO and E691. (i) We find that Bauer, Stech and Wirbel (BSW) model does fairly well in explaining all data if we assume that final state interactions simply rotate the amplitudes in the complex plane. However, to get a good fit one needs to raiseD→K transition amplitudes by (5–10)% over the BSW values and lowerD→π amplitudes by a similar amount. (ii) We show that all the data can also be understood in a coupled channel inelastic model. (iii) We also find that the Isgur, Scora, Grinstein and Wise (ISGW) model-form factors, if extrapolated to small momentum transfers (t) by a single pole formula, yield branching ratios too small in comparison to data. We propose an alternate scheme to interpolate between BSW form factors att=0 and ISGW form factors att=t _max.     

Inflationary models with exponential potentials

In this paper we consider cosmological models containing a self-interacting scalar field possessing a potential of the form V(φ) = Λ exp(−λφ). We investigate the inflationary nature of the model in an (N + 1)-dimensional Friedman space-time as well as in some (3 + 1)-dimensional anisotropic cosmological models. We determine the conditions under which power-law inflation occurs by a detailed stability analysis which determines all possible asymptotic behaviour. We also present some new exact solutions which exhibit the transition to power-law inflation. We determine the range of evolutionary behaviours in each case for all λ ⩾ 0 and find the range of λ values for which power-law inflation occurs. We also discuss how potentials of the exponential type may arise in realistic models of the early universe.     

Dynamical aspects of photonuclear reactions below pion threshold

We study the reactions (γ,p), (γ,n), (γ,pp) and (γ,nn) below pion threshold in view of a systematic treatment of electromagnetic meson exchange currents. As a numerical example we calculate the integrated and differential cross sections for (γ,p) and (γ,n) on ⁴He.     

Diffusion anomaly in a three-dimensional lattice gas

We investigate the relationship between thermodynamic and dynamic properties of an associating lattice-gas (ALG) model. The ALG combines a three-dimensional lattice gas with particles interacting through a soft core potential and orientational degrees of freedom. The competition between the directional attractive forces and the soft core potential results in two liquid phases, double criticality and density anomaly. We study the mobility of the molecules in this model by calculating the diffusion constant at a constant temperature, D. We show that D has a maximum at a density ρ_max and a minimum at a density ρ_min<ρ_max. Between these densities the diffusivity differs from the one expected for normal liquids. We also show that in the pressure-temperature phase-diagram the line of extrema in diffusivity is close to the liquid-liquid critical point and it is partially inside the temperature of maximum density (TMD) line.     

Approach to saturation of the magnetization of dilute AuFe alloys

We present a reinterpretation of our recent measurements of the magnetic properties of some dilute AuFe alloys. We find that the observed approach to saturation of the magnetization for these AuFe alloys can be understood if both single-impurity (Kondo) effects and effects due to interactions between impurities via the Rudeman-Kittel-Kasuya-Yosida (RKKY) interaction, V(r) = (V₀ cos 2k_Fr)/r³, are properly included in the analysis. The analysis yields for the strength of the RKKY interaction V₀ = (1.1 ± 0.3) × 10^-36ergcm³, for the s-d exchange parameter |J| = (1.9 ± 0.3) eV, and for the Kondo temperature T_K = (0.8 ± 0.1) K. We conclude that mean free path effects do not significantly influence the observed approach to saturation of the magnetization for the AuFe alloys studied.     

Hopf -deformation of any Lie group

We use the Neroslavsky-Vlassov (1981) method to find a star product _h on a class of exact Poisson-Lie groups such that (C^∞(G)[[h]], _h, Δ) is a Hopf algebra. We show that we can find such a nontrivial star product on every Lie group.     

Cavitation in holographic sQGP

We study the possibility of cavitation in the non-conformal N=^2?SU(N) theory which is a mass deformation of N=4SU(N) Yang-Mills theory. The second order transport coefficients are known from the numerical work using AdS/CFT by Buchel and collaborators. Using these and the approach of Rajagopal and Tripuraneni, we investigate the flow equations in a (1+1)-dimensional boost invariant set up. We find that the string theory model does not exhibit cavitation before phase transition is reached. We give a semi-analytic explanation of this finding.     

Statistical independence in nonlinear maps coupled to non-invertible transformations

We investigate the connections between functions of type xn=p(θTzn) and nonlinear maps coupled to non-invertible transformations. These systems can produce unpredictable dynamics. We study the higher-order correlations in the generated sequences. We show that (theoretically) it is possible to construct systems that can generate sequences that constitute a set of statistically independent random variables. We apply the results in the improvement of a two-dimensional coupled map system that has been used in practical applications as e.g. cryptosystems and data compression.