Solvable <Emphasis Type="Italic">PT</Emphasis>-symmetric Hamiltonians

Within the so-called PT-symmetric version of quantum mechanics, a brief review of exactly solvable models is given. The distinction is made between curved and straight coordinate lines, between their unbounded (aperiodic) and bounded (periodic) choices, and between completely and partially solvable cases.     

<Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>) Cosmology from <Emphasis Type="Italic">q</Emphasis>-theory

From a macroscopic theory of the quantum vacuum in terms of conserved relativistic charges (generically denoted by q ^(a) with label a), we have obtained, in the low-energy limit, a particular type of f(R) model relevant to cosmology. The macroscopic quantum-vacuum theory allows us to distinguish between different phenomenological f(R) models on physical grounds. The text was submitted by the authors in English.     

Non-vacuum Bianchi types <Emphasis Type="Italic">I</Emphasis> and <Emphasis Type="Italic">V</Emphasis> in <Emphasis Type="Italic">f</Emphasis> (<Emphasis Type="Italic">R</Emphasis>) gravity

In a recent paper (Sharif and Shamir in Class. Quantum Grav. 26:235020, 2009), we have studied the vacuum solutions of Bianchi types I and V spacetimes in the framework of metric f (R) gravity. Here we extend this work to perfect fluid solutions. For this purpose, we take stiff matter to find energy density and pressure of the universe. In particular, we find two exact solutions in each case which correspond to two models of the universe. The first solution gives a singular model while the second solution provides a non-singular model. The physical behavior of these models has been discussed using some physical quantities. Also, the function of the Ricci scalar is evaluated.     

Ferromagnetism and ferroelectricity in Eu<Emphasis Type="Italic">X</Emphasis> (<Emphasis Type="Italic">X</Emphasis> = <Emphasis Type="Italic">O</Emphasis>, <Emphasis Type="Italic">S</Emphasis>): pressure effects

Ferromagnetism and ferroelectricity in Eu monochalcogenides have been investigated by ab initio density functional theory in the DFT+U approach. Exchange interaction parameters and Curie temperatures under pressure are studied and discussed using Heisenberg Hamiltonian with first and second-nearest-neighbor interactions. The calculations showed that the hydrostatic pressure perfectly improves the Curie temperature (EuO: T _C = 175 K; EuS: T _C = 33.8 K) and in the other hand it cannot induce the spontaneous polarization (P _s ). The effect of uniaxial and biaxial pressure is also studied. Although the uniaxial strains slightly increases the Curie temperature, it ensures the ferrolectricity in these systems by producing a spontaneous polarization of the order of P _s (EuO) = 57.50 μC/cm² and P _s (EuS) = 42.86 μC/cm² with pressures of 5% and 4%, respectively. The search for new model systems is a necessity to better understand the physics related to multiferroïc materials and to consider possible applications.     

Photonic Scattering on a Trimer with <Emphasis Type="Italic">PT</Emphasis>-Symmetry

We analyze photonic scattering on a trimer with PT symmetry, where the photon propagates in an array of cavities. In the system, a passive and an active cavity couple to another cavity without loss and gain simultaneously, which is in the middle of the cavity array. Such three cavities can be regarded as the scattering target coupling to the unlimited number of cavities from two directions respectively. Our approach is to use the Schrödinger equation to calculate the reflection coefficient and transmission coefficient, and then let photonic transmission spreads from gain or loss cavity. It shows that the scattering of the photon is closely associated with the PT symmetric characteristic of the dynamics of the system. The atom’s modulation on the photonic transmission is also investigated. We found that the scattering center can behave as a photonic switch, which could be used potentially to control the photonic transmission.     

Energy dependence of Cronin momentum in saturation model for <Emphasis Type="Italic">p</Emphasis> + <Emphasis Type="Italic">A</Emphasis> and <Emphasis Type="Italic">A</Emphasis> + <Emphasis Type="Italic">A</Emphasis> collisions

The energy dependence of the Cronin momentum for p + A and A + A collisions in the saturation model are calculated. This dependence is consistent with simple dimensional considerations and can be used to test the validity of the saturation model. It gives the possibility to distinguish the different variants of the saturation model with precise experimental data and to measure the x dependence of the saturation momentum.     

<Emphasis Type="Italic">V</Emphasis>-<Emphasis Type="Italic">A</Emphasis> sum rules with <Emphasis Type="Italic">D</Emphasis> = 10 operators

The difference of vector and axial-vector charged current correlators is analyzed by means of QCD sum rules. The contribution of 10-dimensional 4-quark condensates is calculated and its value is estimated within the framework of the factorization hypothesis. It is compared to the result obtained from an operator fit of Borel sum rules in the complex q ²-plane, calculated from experimental data on hadronic -decays. This fit gives accurate values of the light quark condensate and the quark-gluon mixed condensate. The size of the high-order operators and the convergence of the operator series are discussed.Received: 10 May 2004, Revised: 7 September 2004, Published online: 18 November 2004     

Reconstruction of some cosmological models in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>,<Emphasis Type="Italic">T</Emphasis>) cosmology

In this paper, we reconstruct cosmological models in the framework of f(R,T) gravity, where R is the Ricci scalar and T is the trace of the stress-energy tensor. We show that the dust fluid reproduces ΛCDM, phantom–non-phantom era and phantom cosmology. Further, we reconstruct different cosmological models, including the Chaplygin gas, and scalar field with some specific forms of f(R,T). Our numerical simulation for the Hubble parameter shows good agreement with the BAO observational data for low redshifts, z<2.     

Spherical Symmetric Perfect Fluid Collapse in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>, <Emphasis Type="Italic">T</Emphasis>) Gravity

This paper contains the study of spherically symmetric perfect fluid collapse in the frame work of f(R, T) modified theory of gravity. We proceed our work by considering the non-static spherically symmetric background in the interior and static spherically symmetric background in the exterior regions of the star. The junction conditions between exterior and interior regions are presented by matching the exterior and interior regions. The field equations are solved by taking the assumptions that the Ricci scalar as well as the trace of energy-momentum tensor are to be constant, for a particular f(R, T) model. By inserting the solution of the field equations in junction conditions, we evaluate the gravitational mass of the collapsing system. Also, we discuss the apparent horizons and their time formation for different possible cases. It is concluded that the term f(R ₀, T ₀) behaves as a source of repulsive force and that’s why it slowdowns the collapse of the matter.     

<Emphasis Type="Italic">f</Emphasis> (<Emphasis Type="Italic">R</Emphasis>) black holes

We study the f (R)-Maxwell black hole imposed by constant curvature and its all thermodynamic quantities, which may lead to the Reissner-Nordström-AdS black hole by redefining Newtonian constant and charge. Further, we obtain the f (R)-Yang-Mills black hole imposed by constant curvature, which is related to the Einstein-Yang-Mills black hole in AdS space. Since there is no analytic black hole solution in the presence of Yang-Mills field, we obtain asymptotic solutions. Then, we confirm the presence of these solutions in a numerical way.     

Multiple two-variable <Emphasis Type="Italic">p</Emphasis>-adic <Emphasis Type="Italic">q-L</Emphasis>-function and its behavior at <Emphasis Type="Italic">s</Emphasis> = 0

The objective of this paper is to construct a multiple p-adic q-L-function of two variables which interpolates multiple generalized q-Bernoulli polynomials. By using this function, we solve a question of Kim and Cho. We also define a multiple partial q-zeta function which is related to the multiple q-L-function of two variables. Finally, we give a finite-sum representation of the multiple p-adic q-L-function of two variables and prove a multiple q-extension of the generalized formula of Diamond and Ferrero-Greenberg.     

<Emphasis Type="Italic">O</Emphasis>(1) eV sterile neutrino in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>) gravity

We refer [1] to the role of an additional O(1) eV sterile neutrino in modified gravity models. We find parameter constraints in particular f(R) gravity model using following up-to-dated cosmological data: measurements of the cosmic microwave background (CMB) anisotropy, the CMB lensing potential, the baryon acoustic oscillations (BAO), the cluster mass function and the Hubble constant. It was obtained for the sterile neutrino mass 0.47 eV < m _ν,sterile < 1 eV (2σ) assuming that the sterile neutrinos are thermalized and the active neutrinos are massless, not significantly larger than in the standard cosmology model within the same data set: 0.45 eV < m _ν,sterile < 0.92 eV (2σ). But, if the mass of sterile neutrino is fixed and equals ≈ 1.5 eV according to various anomalies in neutrino oscillation experiments, f(R) gravity is much more consistent with observation data than the CDM model.     

<Emphasis Type="Italic">EPJdirect</Emphasis>

Quark mass effects are analyzed at high Q² in the current fragmentation region of DIS. It is found that the linear combination F ₂ -2.75F ^c ₂ scales at large Q² and small x. We obtained a lower bound for the ratio F ^c ₂/F ₂ which lies very close to the data from HERA. Received: 14 January 2002 / Revised version: 9 October 2002 Published online: 9 December 2002 RID="a" ID="a" e-mail: ryutin@th1.ihep.su     

Conformal behavior of a single chain <Emphasis Type="Italic">AB</Emphasis> block copolymer with mobile <Emphasis Type="Italic">B</Emphasis>-blocks

Monte-Carlo computer modeling was used to investigate the conformal behavior of a single chain AB block copolymer with mobile hydrophobic B-blocks and hydrophilic A-links. The formation of a “tailed globule” was observed with an increase of the energy of attraction between hydrophobic links. A comparison between the collapsing of a chain with mobile blocks and the behavior of regular and random block copolymers of the same structure was conducted.     

Analysis of the spectrum of the Zn-like Kr VII ion: Highly excited 4<Emphasis Type="Italic">p</Emphasis>4<Emphasis Type="Italic">d</Emphasis> and 4<Emphasis Type="Italic">p</Emphasis>5<Emphasis Type="Italic">s</Emphasis> configurations

The spectrum of the Zn-like Kr VII ion, excited in a capillary discharge and recorded with a high resolution in the wavelength range of 300–1000 Å, was studied. Previously performed identification of the transitions from the levels of the 4s4f, 4s5s, 4s5p, and 4s5d configurations is confirmed and extended, and the energies of these levels are specified. The (4p ²+4s4d)?4p4d and (4p ²+4s5s)?4p5s transitions are identified for the first time, and the energies of all the levels of the 4p4d and 4p5s configurations are determined. The results of the analysis performed are confirmed by semiempirical calculations in terms of the Hartree-Fock method. These results are also shown to conform to the experimental data obtained for lighter ions of the Zn I isoelectronic sequence.     

Ionization of <Emphasis Type="Italic">nS</Emphasis>, <Emphasis Type="Italic">nP</Emphasis>, and <Emphasis Type="Italic">nD</Emphasis> lithium,potassium, and cesium Rydberg atoms by blackbody radiation

The results of theoretical calculations of the blackbody ionization rates of lithium, potassium, and cesium atoms residing in Rydberg states are presented. The calculations are performed for nS, nP, and nD states in a wide range of principal quantum numbers, n = 8?65, for blackbody radiation temperatures T = 77, 300, and 600 K. The calculations are performed using the known quasi-classical formulas for the photoionization cross sections and for the radial matrix elements of transitions in the discrete spectrum. The effect of the blackbody-radiation-induced population redistribution between Rydberg states on the blackbody ionization rates measured under laboratory conditions is quantitatively analyzed. Simple analytical formulas that approximate the numerical results and that can be used to estimate the blackbody ionization rates of Rydberg atoms are presented. For the S series of lithium, the rate of population of high-lying Rydberg levels by blackbody radiation is found to anomalously behave as a function of n. This anomaly is similar to the occurrence of the Cooper minimum in the discrete spectrum.     

The <Emphasis Type="Italic">q</Emphasis>-boson-fermion realizations of the quantum superalgebra <Emphasis Type="Italic">U</Emphasis><Subscript><Emphasis Type="Italic">q</Emphasis></Subscript>(<Emphasis Type="Italic">osp</Emphasis>(1/2))

We show that our construction of realizations for algebras and quantum algebras can be generalized to quantum superalgebras too. We studyan example of quantum superalgebra U _q (osp(1/2)) and give the boson-fermion realization with respect to one pair of q-boson operators and one pair of fermions.     

Quantum Fisher Information for <Emphasis Type="Italic">s</Emphasis><Emphasis Type="Italic">u</Emphasis>(2) Atomic Coherent States and <Emphasis Type="Italic">s</Emphasis><Emphasis Type="Italic">u</Emphasis>(1, 1) Coherent States

We investigate quantum Fisher information (QFI) for s u(2) atomic coherent states and s u(1, 1) coherent states. In this work, we find that for s u(2) atomic coherent states, the QFI with respect to \(\vartheta ~(\mathcal {F}_{\vartheta })\) is independent of φ, the QFI with respect to \(\varphi (\mathcal {F}_{\varphi })\) is governed by ??. Analogously, for s u(1,1) coherent states, \(\mathcal {F}_{\tau }\) is independent of φ, and \(\mathcal {F}_{\varphi }\) is determined by τ. Particularly, our results show that \(\mathcal {F}_{\varphi }\) is symmetric with respect to ?? = π/2 for s u(2) atomic coherent states. And for s u(1,1) coherent states, \(\mathcal {F}_{\varphi }\) also possesses symmetry with respect to τ = 0.     

Fermion Localization on the <Emphasis Type="Italic">orbifold</Emphasis><Emphasis Type="Italic">S</Emphasis><Subscript>1</Subscript>/<Emphasis Type="Italic">Z</Emphasis><Subscript>2</Subscript>

The hierarchical structure of fermion masses of the Standard Model is explained in split fermion models by localizing the fermions at different points in an extra dimension. We consider split fermion models with two bulk scalars compactified on an orbifold. In the static case we find analytical expression for the localizer. We also address the issue of stability of the localizer. We also find exact solutions for the fermion zero modes. We explore the parameter space of the model. We find ample opportunity for construction of phenomenologically viable theories exist.