An arena for model building in the Cohen—Glashow very special relativity

The Cohen—Glashow Very Special Relativity (VSR) algebra is defined as the part of the Lorentz algebra which upon addition of CP or T invariance enhances to the full Lorentz group, plus the space—time translations. We show that noncommutative space—time, in particular noncommutative Moyal plane, with light- like noncommutativity provides a robust mathematical setting for quantum field theories which are VSR invariant and hence set the stage for building VSR invariant particle physics models. In our setting the VSR invariant theories are specified with a single deformation parameter, the noncommutativity scale ╕_NC. Preliminary analysis with the available data leads to ╕_NC ≳ 1–10 TeV.     

Correlation Inequalities for Interacting Particle Systems with Duality

We prove a comparison inequality between a system of independent random walkers and a system of random walkers which either interact by attracting each other—a process which we call here the symmetric inclusion process (SIP)—or repel each other—a generalized version of the well-known symmetric exclusion process. As an application, new correlation inequalities are obtained for the SIP, as well as for some interacting diffusions which are used as models of heat conduction,—the so-called Brownian momentum process, and the Brownian energy process. These inequalities are counterparts of the inequalities (in the opposite direction) for the symmetric exclusion process, showing that the SIP is a natural bosonic analogue of the symmetric exclusion process, which is fermionic. Finally, we consider a boundary driven version of the SIP for which we prove duality and then obtain correlation inequalities.     

Studies of phase transitions and quantum chaos relationships in extended Casten triangle of IBM-1

A precise solution of the classical energy functional E(N, η, χ; β) minimum problem with respect to deformation parameter β is obtained for the simplified Casten version of the standard interacting boson model (IBM-1) Hamiltonian. The first-order phase transition lines as well as the critical points of X(5), -X(5), and E(5) symmetries are considered. The dynamical criteria of quantum chaos—the basis state fragmentation width and the wave function entropy—are studied for the (η, χ) parameter space of the extended Casten triangle, and the possible relationships between these criteria and phase transition lines are discussed. The text was submitted by the authors in English.     

Nuclear structure investigations in the region of superheavy nuclei

Radioactive decay from the ground state or isomeric states has been investigated for a series of nuclei in the region of Z = 100–106 by means of α–γ—or evaporation residue-(γ, conversion electron)—measurements in prompt and delayed coincidence. Systematic trends in single-particle level energies in N = 145–151 odd-even isotones could be extended up to Z = 104, while an energy systematics of lowlying Nilsson levels in odd-mass einsteinium isotopes was established. Information on nuclear levels at E* > 500 keV was obtained from the decay study of isomeric states in ^251−255No. The text was submitted by the author in English.     

Some top-quark propertie s mea sured in $$p\bar p$$ colli sion s u sing CDF detector at √ s = 1.96 TeV (Review)

This review considers important properties of the top-quark. The top-quark decays before hadronization, and the spin information is directly transferred to the decay products. Therefore the structure of the weak interaction is investigated by measuring the helicity fractions, f, of the W boson—the top-quark decay product. Other investigations: search for the presence of V+A interaction, search for exotic top-quark charge — 4/3 and for t[`(t)]t\bar t — resonances—all of them, so far, were not found in the experiments — testifies against of going out of the Standard Model.     

Superintegrability on N-dimensional spaces of constant curvature from so(N + 1) and its contractions

The Lie—Poisson algebra so(N + 1) and some of its contractions are used to construct a family of superintegrable Hamiltonians on the N-dimensional spherical, Euclidean, hyperbolic, Minkowskian, and (anti-)de Sitter spaces. We firstly present a Hamiltonian which is a superposition of an arbitrary central potential with N arbitrary centrifugal terms. Such a system is quasi-maximally superintegrable since this is endowed with 2N — 3 functionally independent constants of motion (plus the Hamiltonian). Secondly, we identify two maximally superintegrable Hamiltonians by choosing a specific central potential and finding at the same time the remaining integral. The former is the generalization of the Smorodinsky—Winternitz system to the above six spaces, while the latter is a generalization of the Kepler—Coulomb potential, for which the Laplace—Runge—Lenz N vector is also given. All the systems and constants of motion are explicitly expressed in a unified form in terms of ambient and polar coordinates as they are parametrized by two contraction parameters (curvature and signature of the metric). The text was submitted by the authors in English.     

Cold nuclear modifications at RHIC and LHC

We use recent nuclear parton distributions, among them the Hirai — Kumano — Nagai (HKN) and Eskola — Paukkunen — Salgado (EPS08) parameterizations, in our pQCD-improved parton model to calculate the nuclear modification factor, R _AA′ (p _T ), at RHIC and at the LHC. At RHIC, the deuteron-gold nuclear modification factor for pions, measured at p _T ≥ 10 GeV/c in central collisions, appears to deviate more from unity than the model results. The slopes of the calculated R _dAu (p _T ) are similar to the slopes of the PHENIX pion and photon data. At LHC, without final-state effects we see a small enhancement of R _dPb (p _T ) in the transverse momentum range 10 GeV/c ≥ p _T ≥ 100 GeV/c for most parameterizations. The inclusion of final-state energy loss will reduce the R _dPb (p _T ) values.     

Structure of quantum-mechanical relativistic two-body interactions for spinning particles

Relativistic constraint mechanics yields consistent systems of coupled Dirac equations for pairs of spinning particles. We explicitly connect these equations to the Bethe-Salpeter equation of quantum field theory and to the interactions of classical Fokker-Tetrode dynamics (and hence to classical relativistic field theory) to obtain versions of these equations governed by systems of (possibly noncoulombic) relativistic potentials whose detailed structures contain important relativistic effects like correct Darwin interactions. We recast the defining pair of Dirac equations in a number of equivalent but important forms—“external potential,” Sazdjian, hyperbolic, and Breit— and examine their interconnection. Since the potentials in these equations are no more singular than — 1/4r² we are able to solve appropriate versions of them nonperturbatively for the qˉq system to obtain a very good fit to the entire meson spectrum and for the e ⁺ e ⁻ system to calculate the positronium spectrum of QED correct through order α ⁴ .     

Unparticles in gauge theory

A field model for a quark and an antiquark binding is described. Quarks interact via a gauge unparticle (“ungluon”). The model is formulated in terms of Lagrangian which features the source field S(x) which becomes a local pseudo-Goldstone field of conformal symmetry — the pseudodilaton mode and from which the gauge non-primary unparticle field is derived by B _μ(x) ∼ ∂_μ S(x). Because the conformal sector is strongly coupled, the mode S(x) may be one of new states accessible at high energies. We have carried out an analysis of the important quantity that enters in the “ungluon” exchange pattern — the “ungluon” propagator.     

Bi-large neutrino mixings by radiative magnification

Starting with the unification hypothesis of mixings of quarks and leptons and small quark-like mixings at the see-saw scale, we find that two large mixings for ν_e —νx03BC; andv _μ—v _τ at the weak scale are obtained as a result of renormalization group evolution and radiative magnification if the three neutrinos are quasi degenerate in masses and possess the same CP parity. We also find thatU _e3 remains small and well within the CHOOZ-Palo Verde bound since the correspondingV _ub for CKM mixing is very small. Several testable pedictions are pointed out.     

The wideband attenuation of short radio waves on mid-latitude paths during X-ray flares in January 2005

We present the results of the ionosphere oblique chirp sounding on the Cyprus—Nizhny Novgorod, Cyprus—Rostov-on-Don, and Moscow—Rostov-on-Don mid-latitude paths during X-ray flares in January 17, 19, and 20, 2005. It is found that during strong flares the blackout of short radio waves was observed over the entire frequency range of chirp sounding on the Cyprus—Nizhny Novgorod and Cyprus—Rostov-on-Don paths. Modeling of the electron-density profiles in the lower ionosphere based on absorption of short radio waves on the Moscow—Rostov-on-Don path at different stages of the decay of the X-ray radiation intensity is carried out. It is shown that at the instant corresponding to the maximum value of the flare radiation flux, the electron density in the lower ionosphere at altitudes 60–80 km increased by a factor of about 10 and 100 for flares with radiation flux densities 5·10⁻² and 3·10⁻¹ erg/(cm ²·s) in the wavelength range 0.5–4.0 Å which took place in January 19 and 20, respectively. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 50, No. 1, pp. 1–8, January 2007.     

Reflective and photoacoustic infrared spectroscopic techniques in assessment of binding media in paintings

This study proposes a method to estimate the lipid content in binding media in paintings that can be used at any laboratory equipped with an infrared spectrometer. The lipid content estimator, termed greasiness index (GI), is defined as a ratio of lipid ν(C=O) and protein amide I bands at 1743 and 1635 cm⁻¹, respectively. Three Fourier transform infrared (FTIR) sampling techniques were evaluated for GI determination: reflective attenuated total reflection—ATR, specular reflection microscopy—μSR and photoacoustic—PAS. A set of model painting samples containing three tempera binding media (casein, egg, egg + oil), seven pigments and one varnish type were used in the study. Multivariate analysis was used to evaluate the resulting data. A good reproducibility of GI was obtained by ATR and PAS but not with μSR. The discriminative power of the technique is higher for unvarnished samples, but, generally, the GI estimator can be used for the categorisation of binding media in large populations of painting samples analysed with the same FTIR technique (sampling technique, detection, etc.).     

The Number of Nodal Domains on Quantum Graphs as a Stability Index of Graph Partitions

The Courant theorem provides an upper bound for the number of nodal domains of eigenfunctions of a wide class of Laplacian-type operators. In particular, it holds for generic eigenfunctions of a quantum graph. The theorem stipulates that, after ordering the eigenvalues as a non decreasing sequence, the number of nodal domains ν _n of the n ^th eigenfunction satisfies n ≥ ν _n . Here, we provide a new interpretation for the Courant nodal deficiency d _n = n − ν _n in the case of quantum graphs. It equals the Morse index — at a critical point — of an energy functional on a suitably defined space of graph partitions. Thus, the nodal deficiency assumes a previously unknown and profound meaning — it is the number of unstable directions in the vicinity of the critical point corresponding to the n ^th eigenfunction. To demonstrate this connection, the space of graph partitions and the energy functional are defined and the corresponding critical partitions are studied in detail.     

Spin excitons — a new mechanism of superconducting pairing in copper oxides

The Fermi and Bose quasiparticle spectrum in copper oxides is studied in a many-band p-d model taking account of the strong electronic correlations. It is shown that hole-doped systems possess a Bose mode — a spin exciton — which is associated with the singlet-triplet excitation of the two-hole ground-state term of CuO₄ clusters. Intercluster hopping leads to fermion-boson interaction with a spin exciton as the intermediate boson. Such a mechanism does not exist for n-type systems. Pis'ma Zh. éksp. Teor. Fiz. 64, No. 1, 23–28 (10 July 1996)     

Self-localized carrier states in disordered ferroelectrics

A theory of self-localized states of free carriers near polarization fluctuations (fluctuons) in disordered ferroelectrics is developed. Calculations are carried out for the model disordered ferroelectric K_{1− x} Li_xTaO₃ (x≪0.05). The basic characteristics of the fluctuon — the energy and radius of the fluctuon state — are calculated as functions of the impurity dipole concentration and temperature. The theory predicts the appearence of stable fluctuon states in both the mixed ferroelectric-dipole-glass phase (a dipole glass is the electric analog of a spin glass) and the dipole-glass state of disordered ferroelectrics. The possible role of fluctuons in kinetic phenomena such as conductivity in these substances is discussed. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 5, 425–429 (10 March 1997) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Polarization of light: Fourth-order effects and polarization-squeezed states

The polarization properties of a monochromatic beam of light are ordinarily determined by three numbers, for example, the Stokes parameters. However, three numbers are no longer sufficient when intensity fluctuations in the polarized modes (or the correlation between them) are recorded. It is shown that in this case nine parameters, which can be arranged into 3×3 matrices, must be prescribed. The transformation properties of these matrices under polarization converters and the invariants of the matrices are analyzed. Specifically, the fourth-order polarization P ₄ is introduced. Several examples are examined of light with “hidden” polarization—light which is not polarized in the ordinary sense (P ₂=0) but is polarized in fourth order (P ₄≠0)—as well as “polarization-squeezed” light in which the quantum fluctuations of the Stokes parameters are suppressed. Zh. éksp. Teor. Fiz. 111, 1955–1983 (June 1997)     

“Regge-like” relations for stable (non-evaporating) black holes

Within a purely classical formulation of “strong gravity,” we associated hadron constituents (and even hadrons themselves) with suitable stationary, axisymmetric solutions of certain new Einsteintype equations supposed to describe the strong field inside hadrons. Such equations are nothing but Einstein equations—with cosmological term—suitably scaled down. As a consequence, the cosmological constant Λ and the massesM result in our theory to be scaled up, and transformed into a “hadronic constant” and into “strong masses,” respectively. Due to the unusual range of Λ andM values considered, we met a series of solutions of the Kerr-Newman-de Sitter (KNdS) type with rather interesting properties: aim of the present work is putting forth such results, while “translating” them into the more popular language of ordinary gravity. The requirement that those solutions be stable, i.e., that their temperature (or surface gravity) bevanishingly small, implies the coincidence of at least two of their (in general, three) horizons. Imposing the stability condition of a certain horizon does yield (once chosen the values ofJ, q and Λ) mass and radius of the associated black hole. In the case of ordinary Einstein equations and for stable blackholes of the KNdS type, we get in particular Regge-like relations among massM, angular momentumJ, chargeq and cosmological constant Λ; which did not receive enough attention in the previous literature. For instance, with the standard definitionsQ ² = Gq²/(4πε ₀ c ⁴), a ≡ J/(Mc), m ≡GM/c ², in the case Λ=0 in whichm ²=a²+Q² and ifq is negligible, we findm ²=J. When considering, for simplicity, Λ>0 andJ=0 (andq still negligible), then we obtainm ² = 1/(9Λ). In the most general case, the condition, for instance, of “triple coincidence” among the three horizons yields for |Λa ²|<< 1 the couple of independent relationsm ² = 2/(9Λ) andm ² = 8(a ² + Q². Another interesting point is that—with few exceptions—all such relations (amongM, J, q, Λ) lead to solutions that can be regarded as (stable) cosmological models. Work partially supported by INFN, MURST, and CNR and by CNPq, FAPESP, and CAPES.