Optimization of the Electromagnetic (EM) Perturbative Effects Produced by High-Frequency Gravitational Waves

For the relic gravitational waves in high frequency band, we survey the electromagnetic resonance effect generated from the high frequency gravitational waves, which can be described in the transverse perturbative photon fluxes. Under the fixed tensor-scalar ratio r = 0.2, spectral index n _t = 0 and running index α _t = 0.01, we discuss several properties and quantity changes of the transverse perturbative photon fluxes, which can be improved significantly through setting the longitudinal magnetic component of background EM field in the standard gaussian form, and wave impedance analysis on the transverse direction. Through the theoretical calculation, the transverse perturbative photon fluxes can reach up to 10³ s ^?1 with some optimal parameters such as waist of EM field W ₀ = 0.05m, initial stochastic phase of gravitational waves δ = (0.21 + n)π(n = 0,1,2...). Furthermore the interference of the background transverse photon fluxes can be removed completely through establishing a suitable wave impedance function.     

<Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>) gravity constraints from gravitational waves

The recent LIGO observation sparked interest in the field of gravitational wave signals. Besides the gravitational wave observation the LIGO collaboration used the inspiraling black hole pair to constrain the graviton mass. Unlike general relativity, f(R) theories have a characteristic non-zero mass graviton. We apply this constraint on the graviton mass to viable f(R) models in order to find the effects on model parameters. We find it possible to constrain the parameter space with these gravity wave based observations. We consider the popular Hu–Sawicki model as a case study and find an appropriate parameter bracket. The result generalizes to other f(R) theories and can be used to constrain the parameter space.     

Superconducting properties of superlattices containing ferromagnetic layers

Using the microscopic theory formulated by de Gennes and extended by Takahashi and Tachiki, we calculate the transition temperatureT _c and the pair functionF for the superlattices consisting of superconducting and ferromagnetic layers. Superconducting layers. (s) and ferromagnetic layers (f) are modeled byV _s ≠0 andI _m,s =0 andV _f =0 andI _m,f ≠0, whereV _s .(V _f ) is the BCS coupling constant andI _m,s (I _m,f ) is the molecular field fors (f) layers.     

Doppler three-level (V-scheme) laser without population inversion

The theory of amplification and lasing without population inversion in a three-level medium with inhomogeneous broadening via the formation of an open V configuration is elaborated. The conditions for energy transfer from the infrared into the visible spectral range, i.e., the conditions of up-conversion n _b >n _c >n _a , and the external field required for saturation of the b?a transition are established. Two-photon resonant Raman transitions in ensemble of mobile atoms of a gas-discharge plasma are analyzed. The frequency shift of the probe field spectrum as a whole is shown to be governed by the frequency shift of the pump field multiplied by the ratio of the wave numbers of the probe amplification field and the pump field. The interaction of atoms through Ne transitions with the pump field (λ=1.15 εm, 2p ₄-2s ₂ transition) and the lasing field (λ=0.6328 εm, 3s ₂-2p ₂ transition) with an increase in the lasing frequency by a factor of 1.82 with respect to the absorbed radiation is calculated.     

Many-electron character of Rydberg series converging to the ionization thresholds of the 4<Emphasis Type="Italic">p</Emphasis><Superscript>4</Superscript>5<Emphasis Type="Italic">s</Emphasis> states of KrII

The photoionization cross sections of the 4p shell and the 4s main level and 4p ⁴(³ P) 5s ⁴ P _{5/2, 3/2} satellite subvalence levels of KrII have been calculated in the 4s-near-threshold range of excitation energies from 28.48 to 28.70 eV. The calculation takes into account the core relaxation by the methods of the theory of non-orthogonal orbitals, the interaction between resonant states through autoionization channels by solving the complex secular equation, and the interaction between the channels of the continuous spectrum in all orders of the perturbation theory by the K-matrix method. Good quantitative agreement between the energy-integrated theoretical and experimental photoionization cross sections for the satellite levels has been obtained for the first time. It is shown that only simultaneous consideration of the above-mentioned effects leads to such agreement. The resonant structure of the photoionization cross sections in this excitation energy range is related to the autoionization decay of the 4p ⁴5s(⁴ P _1/2)np and 4p ⁴5s(² P _3/2)np Rydberg series. The specificity of this process is that both series manifest themselves not independently but owing to their strong electrostatic interaction with the prominent 4p ⁴(¹ D)5s ² D _5/2 6p _3/2 resonance, which lies in this excitation energy range.     

Analyse von Hyperfeinstrukturen des Eu151, Am241 und einiger 3 d-Elemente mittels „Exchange Polarization“

It is shown how several discrepancies in the optical hfs of the Eu can be understood as consequences of the exchange polarization of the inner and outers-electrons by the spin of the half filled (4f ⁷)-subshell, an effect which should produce additional magnetic fields at the nucleus. Thus from the two different values of the electronic splitting constanta _6s in the two Eu-II ground states the polarization field from the 6s-shell (Δ H _6s ) is determined to be ca. +260 KG, and the formal splitting constantσ (??3 mK) of the (4f ⁷)-subshell yields ca. ?350 KG for the fieldΔ H _(1?5) from the five innern s-shells (n=1?5) in good agreement with the strength of the inner field obtained from recent Mössbauer effect studies.Δ H _(1?5) is deduced to be approximately equal in all sufficiently analysed ground and excited configurations of the neutral and ionised Eu atom ((4f ⁷) 6s, 6p, 5d, 6s ² and 6s 6p). Other elements with half filled subshells (Am, Mn) show similar features in their optical hfs. For Am⁺ ((5f ⁷) 7s) ca. ?2200 KG are found for the inner field (Δ H _(1?6)). For several 3d-elements it was found that the agreement between the calculated polarization fields and those following from experimental results is better than assumed so far.     

Statefinder—A new geometrical diagnostic of dark energy

We introduce a new cosmological diagnostic pair {r, s} called the Statefinder. The Statefinder is a geometrical diagnostic and allows us to characterize the properties of dark energy in a model-independent manner. The Statefinder is dimensionless and is constructed from the scale factor of the Universe and its time derivatives only. The parameter r forms the next step in the hierarchy of geometrical cosmological parameters after the Hubble parameter H and the deceleration parameter q, while a is a linear combination of q and r chosen in such a way that it does not depend upon the dark energy density. The Statefinder pair {r, s} is algebraically related to the equation of state of dark energy and its first time derivative. The Statefinder pair is calculated for a number of existing models of dark energy having both constant and variable w. For the case of a cosmological constant, the Statefinder acquires a particularly simple form. We demonstrate that the Statefinder diagnostic can effectively differentiate between different forms of dark energy. We also show that the mean Statefinder pair can be determined to very high accuracy from a SNAP-type experiment.     

Quantenstatistik eines Gases mit verschiedener Bahn- und Spintemperatur

A system of particles with spin in a magnetic field may possess an orbital temperatureT _o different from the spin temperatureT _s (?0), if it is possible to neglect the energetic interaction between the orbital and the spin system. The calculation of the quantum statistical most probable distribution of identical independent particles on the orbital and spin energy levels yields the introduction of three Lagrange multipliers—according to the fact that the orbital and the spin energy and the number of particles are fixed—representing the orbital and spin temperature and a generalizedPlanck's “characteristic function”. Apart from the Boltzmann-approximation being valid in the case of small spin values forT _o ?T _e (T _e =customary degeneration temperature) and arbitraryT _s ?0, the distributions and the orbital and the spin energy depend onboth the temperaturesT _o andT _s coming from the principle of exclusion forFermi resp.Bose particles. The equations of state are discussed. There are four heat capacities, which possess characteristic peaks. In stead of the well-known temperature independence of the paramagnetism of degenerated conducting electrons one obtains χ～T _o /T _s . The behaviour of the Einstein-condensation of aBose gas is considered.     

Universal temperature corrections to the free energy for the gravitational field

The temperature correction to the free energy of the gravitational field is considered which does not depend on the Planck energy physics. The leading correction may be interpreted in terms of the temperature-dependent effective gravitational constant G_eff. The temperature correction to appears to be valid for all temperatures T?E_Planck. It is universal since it is determined only by the number of fermionic and bosonic fields with masses m?T, does not contain the Planck energy scale E_Planck which determines the gravitational constant at T=0, and does not depend on whether or not the gravitational field obeys the Einstein equations. That is why this universal modification of the free energy for gravitational field can be used to study thermodynamics of quantum systems in condensed matter (such as quantum liquids superfluid ³He and ⁴He), where the effective gravity emerging for fermionic and/or bosonic quasiparticles in the low-energy corner is quite different from the Einstein gravity.     

Ground-State hyperfine structure and nuclear magnetic moment of Thulium-169

The hyperfine structure of the 4f ¹³ 6s ^{2 2} F _7/2 ground state of Tm¹⁶⁹ has been studied with the atomic beam magnetic resonance method. By measuring strongly field-dependent transitions in external magnetic fields between 2200 and 3000 Gauss the interaction between the nuclear magnetic dipole momentμ _I and the external field was determined. These measurements yielded a direct value forμ _I independent of the electronic properties of the Tm-atom. The results are:μ _I=? 0.2310 (15)μ _n (diamagnetically corrected), magnetic dipole interaction constanta=? 374.137661(3) Mc/sec andg _J(4f ¹³ 6s ^{2 2} F _7/2)=1.141189 (3).     

Phase Diagram of a Generalized ABC Model on the Interval

We study the equilibrium phase diagram of a generalized ABC model on an interval of the one-dimensional lattice: each site i=1,…,N is occupied by a particle of type α=A,B,C, with the average density of each particle species N _α /N=r _α fixed. These particles interact via a mean field nonreflection-symmetric pair interaction. The interaction need not be invariant under cyclic permutation of the particle species as in the standard ABC model studied earlier. We prove in some cases and conjecture in others that the scaled infinite system N→∞, i/N→x∈[0,1] has a unique density profile ρ _α (x) except for some special values of the r _α for which the system undergoes a second order phase transition from a uniform to a nonuniform periodic profile at a critical temperature \(T_{c}=3\sqrt{r_{A} r_{B} r_{C}}/2\pi\).     

Studying the possibility of deep laser cooling of <Superscript>24</Superscript>Mg atoms in an optical lattice: Two-level quantum model

The possible deep laser cooling of ²⁴Mg atoms in a deep optical lattice in the presence of an additional pumping field resonant to the narrow 3s3s¹S₀ → 3s3p³P₁ (λ = 457 nm) optical transition is studied. Two quantum models of the laser cooling of atoms in the optical trap are compared. One is based on the direct numerical solution to the kinetic quantum equation for an atomic density matrix; it considers both optical pumping and quantum recoil effects during interaction between the atoms and field photons. The second, simplified model is based on decomposing the states of the atoms over the levels of vibration in the optical trap and analyzing the evolution of these states. The comparison allows derivation of optical field parameters (pumping field intensity and detuning) that ensure cooling of the atoms to minimal energies. The conditions for fast laser cooling in an optical trap are found.     

A benign property of the ghost mode in massive theory of gravitation

It was shown in the frameworks of massive gravitational theories having in linear approximation mass term \({m^2}\left( {{\varphi ^{\alpha \beta }}{\varphi _{\alpha \beta }} - \frac{1}{2}{\varphi ^2}} \right)\) in the lagrangian, that created some time ago spherically-symmetric static sources should possess inside their light cone not only Yukawa potential, but also nonstationary component. It leads to the long (~ 1/m) period of gravitational evaporation of such sources with the mass loss ? ~ m²M² The magnitude of the flux is c⁴/v⁴ times (с—speed of light, v—velocity of the source particles) bigger then negative gravitational radiation flux corresponding to the ghost scalar mode in the spectrum of such gravitational field, with stabilizing the source.     

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.     

High precision determination of the low-energy constants for the two-dimensional quantum Heisenberg model on the honeycomb lattice

The low-energy constants, namely the staggered magnetization density M? _s per spin, the spin stiffness ρ _s , and the spinwave velocity c of the two-dimensional (2-d) spin-1/2 Heisenberg model on the honeycomb lattice are calculated using first principles Monte Carlo method. The spinwave velocity c is determined first through the winding numbers squared. M? _s and ρ _s are then obtained by employing the relevant volume- and temperature-dependence predictions from magnon chiral perturbation theory. The periodic boundary conditions (PBCs) implemented in our simulations lead to a honeycomb lattice covering both a rectangular and a parallelogram-shaped region. Remarkably, by appropriately utilizing the predictions of magnon chiral perturbation theory, the numerical values of M? _s , ρ _s , and c we obtain for both the considered periodic honeycomb lattice of different geometries are consistent with each other quantitatively. The numerical accuracy reached here is greatly improved. Specifically, by simulating the 2-d quantum Heisenberg model on the periodic honeycomb lattice overlaying a rectangular area, we arrive at M? _s = 0.26882(3), ρ _s  = 0.1012(2)J, and c = 1.2905(8)Ja. The results we obtain provide a useful lesson for some studies such as simulating fermion actions on hyperdiamond lattice and investigating second order phase transitions with twisted boundary conditions.     

Nilpotent Symmetries in Jackiw-Pi Model: Augmented Superfield Approach

We derive the complete set of off-shell nilpotent \(\left (s^{2}_{(a)b} = 0\right )\) and absolutely anticommuting (s_bs_ab+s_abs_b=0) Becchi-Rouet-Stora-Tyutin (BRST) (s_b) as well as anti-BRST symmetry transformations (s_ab) corresponding to the combined Yang-Mills and non-Yang-Mills symmetries of the (2+1)-dimensional Jackiw-Pi model within the framework of augmented superfield formalism. The absolute anticommutativity of the (anti-)BRST symmetries is ensured by the existence of two sets of Curci-Ferrari (CF) type of conditions which emerge naturally in this formalism. The presence of CF conditions enables us to derive the coupled but equivalent Lagrangian densities. We also capture the (anti-)BRST invariance of the coupled Lagrangian densities in the superfield formalism. The derivation of the (anti-)BRST transformations of the auxiliary field ρ is one of the key findings which can neither be generated by the nilpotent (anti-)BRST charges nor by the requirements of the nilpotency and/or absolute anticommutativity of the (anti-)BRST transformations. Finally, we provide a bird’s-eye view on the role of auxiliary field for various massive models and point out few striking similarities and some glaring differences among them.     

Ab initio calculations of Born charges in ferroelectrics with a perovskite structure

A method has been proposed for calculating Born effective charges in compounds with a cubic perovskite structure. The method is based on the first-principles calculation of individual contributions from the short-range interaction and the intercell dipole-dipole interaction to the Born tensor Z _ii (s) for crystalline dielectrics. It has been shown that the contribution from the short-range interaction Z _ii ^sr (s) to the Born tensor components can be derived from ab initio calculations performed for polyatomic clusters. The results of the calculations of the short-range interactions Z _ii ^sr (s) for the cubic phases of the BaTiO₃, SrTiO₃, CaTiO₃, PbTiO₃, BaZrO₃, PbZrO₃, KNbO₃, and KTaO₃ compounds with the use of the electronic structure calculations within the Hartree-Fock approximation and the density functional theory are presented. For the BaTiO₃, SrTiO₃, CaTiO₃, PbTiO₃, KNbO₃, and KTaO₃ compounds, the components of the complete Born tensor have been also calculated. The obtained values of Z _ii (s) are in good agreement with the results of the calculations in terms of the linear response theory and the Berry phase approach.