Locally Anisotropic Structures and Nonlinear Connections in Einstein and Gauge Gravity

We analyze locally anisotropic configurations modeled by anholonomic frames with associated nonlinear connections in general relativity, affine–Poincarè and/or de Sitter gauge gravity and Kaluza–Klein theories. A suitable geometrical formalism for theories with higher order anisotropies and non compactified extra dimensions is introduced. We give a mostly self–containing review of some aspects of gauge models of gravity and discuss their anholonomic generalizations and the conditions of equivalence with the Einstein gravity in arbitrary dimensions. New classes of cosmological solutions describing Friedmann–Robertson–Walker like universes with resolution ellipsoid or torus symmetry.     

Higher dimensional Vaidya metric in Einstein and de Sitter background

Spherically symmetric non-static higher dimensional metrics are considered in connection with Einstein’s field equations. Two exact solutions are derived. One of them corresponds to a mixture of perfect fluid and pure radiation field and represents higher dimensional Vaidya metric in the cosmological background of Einstein static universe. The other corresponds to a pure radiation field and represents higher dimensional Vaidya metric in the background de Sitter universe. For both of these solutions, the cosmological constant is taken to be non-zero. Many known solutions are derived as particular cases.     

Black Holes in Bose–Einstein Condensates

It is shown that there exist both dynamically stable and unstable dilute-gas Bose–Einstein condensates that, in the hydrodynamic limit, exhibit a behavior completely analogous to that of gravitational black holes. The dynamical instabilities involve creation of quasiparticle pairs in positive and negative energy states. We illustrate these features in two qualitatively different one-dimensional models. We have also simulated the creation of a stable sonic black hole by solving the Gross–Pitaevskii equation numerically for a condensate subject to a trapping potential that is adiabatically deformed. A sonic black hole could in this way be created experimentally with state-of-the-art or planned technology.     

Bimetric renormalization group flows in quantum Einstein gravity

The formulation of an exact functional renormalization group equation for quantum Einstein gravity necessitates that the underlying effective average action depends on two metrics, a dynamical metric giving the vacuum expectation value of the quantum field, and a background metric supplying the coarse graining scale. The central requirement of “background independence” is met by leaving the background metric completely arbitrary. This bimetric structure entails that the effective average action may contain three classes of interactions: those built from the dynamical metric only, terms which are purely background, and those involving a mixture of both metrics. This work initiates the first study of the full-fledged gravitational RG flow, which explicitly accounts for this bimetric structure, by considering an ansatz for the effective average action which includes all three classes of interactions. It is shown that the non-trivial gravitational RG fixed point central to the asymptotic safety program persists upon disentangling the dynamical and background terms. Moreover, upon including the mixed terms, a second non-trivial fixed point emerges, which may control the theory’s IR behavior.     

Quantum-phase dynamics of two-component Bose–Einstein condensates: Collapse–revival of macroscopic superposition states

We investigate the long-time dynamics of two-component dilute gas Bose–Einstein condensates with relatively different two-body interactions and Josephson couplings between the two components. Although in certain parameter regimes the quantum state of the system is known to evolve into macroscopic superposition, i.e., Schrödinger cat state, of two states with relative atom number differences between the two components, the Schrödinger cat state is also found to repeat the collapse and revival behavior in the long-time region. The dynamical behavior of the Pegg–Barnett phase difference between the two components is shown to be closely connected with the dynamics of the relative atom number difference for different parameters. The variation in the relative magnitude between the Josephson coupling and intra- and inter-component two-body interaction difference turns out to significantly change not only the size of the Schrödinger cat state but also its collapse–revival period, i.e., the lifetime of the Schrödinger cat state.     

On higher order gravities, their analogy to GR, and dimensional dependent version of Duff’s trace anomaly relation

An almost brief, though lengthy, review introduction about the long history of higher order gravities and their applications, as employed in the literature, is provided. We review the analogous procedure between higher order gravities and GR, as described in our previous works, in order to highlight/manipulate its important achievements. Amongst which are presentation of an easy classification of higher order Lagrangians and its employment as a criteria in order to distinguish correct metric theories of gravity. For example, it does not permit the inclusion of only one of the second order Lagrangians in isolation. But, it does allow the inclusion of the cosmological term. We also discuss on the compatibility of our procedure and the Mach idea. We derive a dimensional dependent version of Duff’s trace anomaly relation, which in four-dimension is the same as the usual Duff relation. The Lanczos Lagrangian satisfies this new constraint in any dimension. The square of the Weyl tensor identically satisfies it independent of dimension, however, this Lagrangian satisfies the previous relation only in three and four dimensions.     

f(R) theories of gravity in the Palatini approach matched with observations

We investigate the viability of f(R) theories in the framework of the Palatini approach as solutions to the problem of the observed accelerated expansion of the universe. Two physically motivated popular choices for f(R) are considered,: power law, f(R) = β R ⁿ , and logarithmic, f(R) = α ln R. Under the Palatini approach, both Lagrangians give rise to cosmological models comprising only standard matter and undergoing a present phase of accelerated expansion. We use the Hubble diagram of type Ia Supernovae and the data on the gas mass fraction in relaxed galaxy clusters to see whether these models are able to reproduce what is observed and to constrain their parameters. It turns out that they are indeed able to fit the data with values of the Hubble constant and of the matter density parameter in agreement with some model independent estimates, but the today deceleration parameter is higher than what is measured in the concordance ΛCDM model.     

Phase transition in dually weighted colored tensor models

Tensor models are a generalization of matrix models (their graphs being dual to higher-dimensional triangulations) and, in their colored version, admit a 1/N expansion and a continuum limit. We introduce a new class of colored tensor models with a modified propagator which allows us to associate weight factors to the faces of the graphs, i.e. to the bones (or hinges) of the triangulation, where curvature is concentrated. They correspond to dynamical triangulations in three and higher dimensions with generalized amplitudes. We solve analytically the leading order in 1/N of the most general model in arbitrary dimensions. We then show that a particular model, corresponding to dynamical triangulations with a non-trivial measure factor, undergoes a third-order phase transition in the continuum characterized by a jump in the susceptibility exponent.     

A unified approach to quantum and classical TTW systems based on factorizations

A unifying method based on factorization properties is introduced for finding symmetries of quantum and classical superintegrable systems using the example of the Tremblay–Turbiner–Winternitz (TTW) model. It is shown that the symmetries of the quantum system can be implemented in a natural way to its classical version. Besides, by this procedure we get also other type of constants of motion depending explicitly on time that allow to find directly the motion of the system whose corresponding trajectories coincide with those obtained previously by using its symmetries.     

Einstein as Engineer:The Case of the Little Machine

I first discuss Albert Einstein’s practical and educational background in engineering and then his invention of his “little machine,” an electrostatic induction machine, while working in the Patent Office in Bern, Switzerland, between 1902 and 1909. He believed that it could be used as a voltage or potential multiplier in experiments to test his new theory of Brownian motion of 1905. I then discuss Einstein’s search for collaborators to produce it and the work that his friends Conrad and Paul Habicht, in particular, did in designing and testing it. Although the initial response to it was promising, it never became a success after Paul Habicht manufactured a few specimens of it beginning in 1912.Today only three specimens are known to exist; these are preserved at the Zürcher Hochschule Winterthur, Switzerland, in the Physics Institute of the University of Tübingen, Germany, and in the Museum Boerhaave in Leiden,The Netherlands.     

Critical behavior of colored tensor models in the large N limit

Colored tensor models have been recently shown to admit a large N expansion, whose leading order encodes a sum over a class of colored triangulations of the D-sphere. The present paper investigates in details this leading order. We show that the relevant triangulations proliferate like a species of colored trees. The leading order is therefore summable and exhibits a critical behavior, independent of the dimension. A continuum limit is reached by tuning the coupling constant to its critical value while inserting an infinite number of pairs of D-simplices glued together in a specific way. We argue that the dominant triangulations are branched polymers.     

Analytical results of the generalized mean-field theory for diluted magnetic semiconductors with RKKY interaction

Analytical results have been obtained in the framework of the generalized mean-field theory for diluted semiconductors with RKKY interaction. That theory accounts for the non-equivalency of different lattice sites by introducing the distribution function of local effective magnetic fields for non-regular (random) systems with magnetic interaction. The procedure is described that permits to deduce the analytical expression for that function. Corresponding improvement of the traditional mean-field theory could be observed by comparing results of such a generalized analytical model with exact results known for some simple cases, with numerical results of different authors considering the disorder of magnetic impurities’ arrangement, and with experimental data, as well.     

New-synthesized pyrazoloquinoline as promising luminescent materials

A new theoretical method for searching the light-emitting diodes with the desired technological parameters is proposed. This method is grounded on the complex use of molecular dynamics and quantum chemical methods for the prediction of the main directions of the design of the corresponding light sources. Comparison of the theoretical simulations and measured parameters is made. A crucial role of the solvents on the performed theoretical simulations was shown. It was found that several observed discrepancies between the theoretical simulations and experimental data may be explained within the red Stocks shifts of the emission spectra. Generally, the simulated spectra within a framework of the proposed approach describe well the observed experimental dependences. Depending on the substituted group (hydrogen, phenyl, methyl and their combination), we have established a correlation between the spectral shift of blue luminescence from 161 up to . A quantum efficiency (about 0.20%) allows to propose the investigated materials’ blue-light luminophore. The approach may be recommended for searching the organic chromophore for light-emitting diodes.     

Intermediate statistics as a consequence of deformed algebra

We present a formulation of deformed oscillator algebra which leads to intermediate statistics as a continuous interpolation between Bose-Einstein and Fermi-Dirac statistics. It is deduced that a generalized permutation or exchange symmetry leads to the introduction of the basic number and it is then established that this in turn leads to the deformed algebra of oscillators. We obtain the mean occupation number describing the particles obeying intermediate statistics which thus establishes the interpolating statistics and describe boson-like and fermion-like particles obeying intermediate statistics. We also obtain an expression for the mean occupation number in terms of an infinite continued fraction, thus clarifying successive approximations.     

Complete spacelike hypersurfaces in conformally stationary Lorentz manifolds

We derive, for the square operator of Yau, an analogue of the Omori–Yau maximum principle for the Laplacian. We then apply it to obtain nonexistence results concerning complete noncompact spacelike hypersurfaces immersed with constant higher order mean curvature in a conformally stationary Lorentz manifold.     

Proving AGT conjecture as HS duality: Extension to five dimensions

We extend the proof from Mironov et al. (2011) [25], which interprets the AGT relation as the Hubbard-Stratonovich duality relation to the case of 5d gauge theories. This involves an additional q-deformation. Not surprisingly, the extension turns out to be straightforward: it is enough to substitute all relevant numbers by q-numbers in all the formulas, Dotsenko-Fateev integrals by the Jackson sums and the Jack polynomials by the MacDonald ones. The problem with extra poles in individual Nekrasov functions continues to exist, therefore, such a proof works only for β=1, i.e. for q=t in MacDonald?s notation. For β≠1 the conformal blocks are related in this way to a non-Nekrasov decomposition of the LMNS partition function into a double sum over Young diagrams.     

Description of the transport critical current density behavior of polycrystalline superconductors as a function of the applied magnetic field

A model to describe the critical current density behavior of high-T_c polycrystalline superconductors is proposed for all magnetic field values. The main features of the model are as follows: the transport critical current density is controlled by the weak-link network at grain boundaries. The size distribution of weak links is well represented by a Gamma-type distribution. Finally, the tunneling critical current between grains follows a Fraunhofer diffraction pattern or a modified pattern if the applied magnetic field is lower or higher than the first critical field H_c1.