Universe Filled with a Binary Mixture of Perfect Fluid and Dark Energy

We consider a self consistent system of Bianchi type-V gravitational field and a binary mixture of perfect fluid and dark energy. The perfect fluid is taken to be the one obeying the usual equation of state, i.e., p=γρ, with γ∈[0,1] whereas, the dark energy is considered to be either the quintessence like equation of state or Chaplygin gas. The equation of state parameter for dark energy ω is found to be consistent with the recent observations of SNe I_a data (Knop et al., Astrophys. J. 598:102, 2003), SNe I_a data with CMBR anisotropy and galaxy clustering statistics (Tegmark et al., Astrophys. J. 606:702, 2004) and latest a combination of cosmological datasets coming from CMB anisotropies, luminosity distances of high redshift type I_a supernovae and galaxy clustering (Hinshaw et al., Astrophys. J. Suppl. 180:225, 2009; Komatsu et al., Astrophys. J. Suppl. Ser. 180:330, 2009). The physical and geometrical aspects of the models are also discussed in detail.     

Bianchi Type-II Dark Energy Model in Scale Covariant Theory of Gravitation

Spatially Homogeneous and anisotropic Bianchi type-II space time with variable equation of state (EoS) parameter and constant deceleration parameter has been investigated in scale covariant theory of gravitation formulated by Canuto et al. (Phys. Rev. Lett. 39:429, 1977). With the help of special law of variation for Hubble’s parameter proposed by Bermann (Nuovo Cimento 74B:182, 1983) a dark energy cosmological model is obtained in this theory. We use the power law relation between scalar field ? and scale factor R to find the solutions. Some physical and kinematical properties of the model are also discussed.     

Thermodynamics and holography of tachyon cosmology

Recently, we have investigated the dynamics of the universe in tachyon cosmology with non-minimal coupling to matter (Farajollahi et al. in Mod Phys Lett A 26(15):1125–1135, 2011; Phys Lett B 711(3–4)15:225–231,2012; Phys Rev D 83:124042, 2011; JCAP 10:014, 20112011; JCAP 05:017, 2011). In particular, for the interacting holographic dark energy (IHDE), the model is studied in Farajollahi et al. (Astrophys Space Sci 336(2):461–467, 2011). In the current work, a significant observational program has been conducted to unveil the model’s thermodynamic properties. Our result shows that the IHDE version of our model better fits the observational data than $\Lambda $ CDM model. The first and generalized second thermodynamics laws for the universe enveloped by cosmological apparent and event horizon are revisited. From the results, both first and generalized second laws, constrained by the observational data, are satisfied on cosmological apparent horizon.In addition, the total entropy is verified with the observation only if the horizon of the universe is taken as apparent horizon. Then, due to validity of generalized second law, the current cosmic acceleration is also predicted.     

The Parafermionic Observable in SLE

The parafermionic observable has recently been used by number of authors to study discrete models, believed to be conformally invariant and to prove convergence results for these processes to SLE (Beffara and Duminil-Copin in arXiv:1010.0526v2, 2011; Duminil-Copin and Smirnov in arXiv:1007.0575v2, 2011; Hongler and Smirnov in arXiv:1008.2645v3, 2011; Ikhlef and Cardy in J. Phys. A 42:102001, 2009; Lawler in preprint, 2011; Rajabpour and Cardy in J. Phys. A 40:14703, 2007; Riva and Cardy in J. Stat. Mech. Theory Exp., 2006; Smirnov in International Congress of Mathematicians, vol. II, pp. 1421?C1451, 2006; Smirnov in Ann. Math. 172(2):1435?C1467, 2010; Smirnov in Proceedings of the International Congress of Mathematicians, Hyderabad 2010, vol.?I, pp. 595?C621, 2010). We provide a definition for a one parameter family of continuum versions of the parafermionic observable for SLE, which takes the form of a normalized limit of expressions identical to the discrete definition. We then show the limit defining the observable exists, compute the value of the observable up to a finite multiplicative constant, and prove this constant is non-zero for a wide range of ??. Finally, we show our observable for SLE becomes a holomorphic function for a particular choice of the parameter, which provides a new point of view on a fundamental property of the discrete observable.     

C-Field Cosmological Model for Barotropic Fluid Distribution with Varying Λ in FRW Space Time

A cosmological model for barotropic fluid distribution in creation field cosmology with varying cosmological constant (Λ) in FRW space-time is investigated. To get the deterministic model satisfying conservation equation, we have assumed $\varLambda = \frac{1}{R^{2}}$ as considered by Chen and Wu (in Phys. Rev. D 41:695, 1990) where R is scale factor. We find that creation field (C) increases with time, which matches with the result of HN Theory (in Hoyle and Narlikar, Proc. R. Astron. Soc. A 282:178, 1964), $\varLambda\sim\frac{1}{t^{2}}$ , the spatial volume increases with time and deceleration parameter q<0 which shows that universe is accelerating. This result matches with recent observations. The inflationary scenario exists in the models and the results so obtained match with astronomical observations. The various special cases of the model (21) viz. dust filled universe (γ=0) and radiation dominated era (ρ=3p), ρ=p (stiff fluid universe) are also discussed. The models are free from horizon.     

High harmonic generation in a gas-filled hollow-core photonic crystal fiber

High harmonic generation (HHG) of intense infrared laser radiation (Ferray et al., J. Phys. B: At. Mol. Opt. Phys. 21:L31, 1988; McPherson et al., J. Opt. Soc. Am. B 4:595, 1987) enables coherent vacuum-UV (VUV) to soft-X-ray sources. In the usual setup, energetic femtosecond laser pulses are strongly focused into a gas jet, restricting the interaction length to the Rayleigh range of the focus. The average photon flux is limited by the low conversion efficiency and the low average power of the complex laser amplifier systems (Keller, Nature 424:831, 2003; Südmeyer et al., Nat. Photonics 2:599, 2008; Röser et al., Opt. Lett. 30:2754, 2005; Eidam et al., IEEE J. Sel. Top. Quantum Electron. 15:187, 2009) which typically operate at kilohertz repetition rates. This represents a severe limitation for many experiments using the harmonic radiation in fields such as metrology or high-resolution imaging. Driving HHG with novel high-power diode-pumped multi-megahertz laser systems has the potential to significantly increase the average photon flux. However, the higher average power comes at the expense of lower pulse energies because the repetition rate is increased by more than a thousand times, and efficient HHG is not possible in the usual geometry. So far, two promising techniques for HHG at lower pulse energies were developed: external build-up cavities (Gohle et al., Nature 436:234, 2005; Jones et al., Phys. Rev. Lett. 94:193, 2005) and resonant field enhancement in nanostructured targets (Kim et al., Nature 453:757, 2008). Here we present a third technique, which has advantages in terms of ease of HHG light extraction, transverse beam quality, and the possibility to substantially increase conversion efficiency by phase-matching (Paul et al., Nature 421:51, 2003; Ren et al., Opt. Express 16:17052, 2008; Serebryannikov et al., Phys. Rev. E (Stat. Nonlinear Soft Matter Phys.) 70:66611, 2004; Serebryannikov et al., Opt. Lett. 33:977, 2008; Zhang et al., Nat. Phys. 3:270, 2007). The interaction between the laser pulses and the gas occurs in a Kagome-type Hollow-Core Photonic Crystal Fiber (HC-PCF) (Benabid et al., Science 298:399, 2002), which reduces the detection threshold for HHG to only 200 nJ. This novel type of fiber guides nearly all of the light in the hollow core (Couny et al., Science 318:1118, 2007), preventing damage even at intensities required for HHG. Our fiber guided 30-fs pulses with a pulse energy of more than 10 μJ, which is more than five times higher than for any other photonic crystal fiber (Hensley et al., Conference on Lasers and Electro-Optics (CLEO), IEEE Press, New York, 2008).     

Decoherent Histories of Spin Networks

The decoherent histories formalism, developed by Griffiths, Gell-Mann, and Hartle (in Phys. Rev. A 76:022104, 2007; arXiv:1106.0767v3 [quant-ph], 2011; Consistent Quantum Theory, Cambridge University Press, 2003; arXiv:gr-qc/9304006v2, 1992) is a general framework in which to formulate a timeless, ‘generalised’ quantum theory and extract predictions from it. Recent advances in spin foam models allow for loop gravity to be cast in this framework. In this paper, I propose a decoherence functional for loop gravity and interpret existing results (Bianchi et al. in Phys. Rev. D 83:104015, 2011; Phys. Rev. D 82:084035, 2010) as showing that coarse grained histories follow quasiclassical trajectories in the appropriate limit.     

A Higher Dimensional Cosmological Model in a Scale-Covariant Theory of Gravitation

Kaluza-Klein space-time is considered in the presence of a perfect fluid distribution in the scale-covariant theory of gravitation by Canuto et al. (Phys. Rev. Lett. 39:429, 1977). With the help of special law of variation for Hubble’s parameter proposed by Bermann (Nuovo Cimento 74B:182, 1983), a cosmological model in five dimensions with a negative constant deceleration parameter is presented in this theory. Some physical and kinematical properties of the model are also discussed.     

Bianchi Type-II Dark Energy Model in f(R,T) Gravity

The spatially homogeneous and totally anisotropic Bianchi Type-II space-time dark energy model with EoS parameter is considered in the presence of a perfect fluid source in the framework of f(R,T) gravity proposed by Harko et al. (Phys. Rev. D, 84:024020, 2011). With the help of special law of variation for Hubble’s parameter proposed by Berman (Nuovo Cimento B, 74:182, 1983) a dark energy cosmological model is obtained in this theory. We consider f(R,T) model and investigate the modification R+f(T) in Bianchi type-II cosmology with an appropriate choice of a function f(T)=λT. We use the power law relation between average Hubble parameter H and average scale factor R to find the solution. The assumption of constant deceleration parameter leads to two models of universe, i.e. power law model and exponential model. Some physical and kinematical properties of the model are also discussed.     

LRS Bianchi Type II Massive String Cosmological Model for Stiff Fluid Distribution with Decaying Vacuum Energy (Λ)

An LRS Bianchi Type II model formed by massive strings with decaying vacuum energy (Λ) for stiff fluid distribution is studied in the context of general relativity. To get the deterministic model, we have assumed that $\frac{\sigma}{\theta} =\mathrm{constant}$ where σ is shear and θ the expansion in the model and decaying vacuum energy (Λ) is proportional to H ² (H is Hubble parameter) as used in Arbab (Gen. Relativ. Gravit. 29:51, 1997). We find that the model represents decelerating and accelerating phases of universe. The decaying vacuum energy (Λ) is proportional to $\frac{1}{\tau^{2}}$ as obtained by Bertolami (Nuovo Cimento B 93:36, 1986) and Hubble parameter is proportional to $\frac{1}{\tau}$ which matches with the observation. The model in general represents anisotropic space-time. However, in special case, it isotropizes. The particle density (ρ _p ) and string tenson (λ) are initially large but decrease due to lapse of time. The model also admits particle horizon and entropy is inversely proportional absolute temperature. Thus the model is in good agreement with present age of universe.     

Asymptotic Expansion of β Matrix Models in the One-cut Regime

We prove the existence of a 1/N expansion to all orders in β matrix models with a confining, offcritical potential corresponding to an equilibrium measure with a connected support. Thus, the coefficients of the expansion can be obtained recursively by the “topological recursion” derived in Chekhov and Eynard (JHEP 0612:026, 2006). Our method relies on the combination of a priori bounds on the correlators and the study of Schwinger-Dyson equations, thanks to the uses of classical complex analysis techniques. These a priori bounds can be derived following (Boutet de Monvel et al. in J Stat Phys 79(3–4):585–611, 1995; Johansson in Duke Math J 91(1):151–204, 1998; Kriecherbauer and Shcherbina in Fluctuations of eigenvalues of matrix models and their applications, 2010) or for strictly convex potentials by using concentration of measure (Anderson et al. in An introduction to random matrices, Sect. 2.3, Cambridge University Press, Cambridge, 2010). Doing so, we extend the strategy of Guionnet and Maurel-Segala (Ann Probab 35:2160–2212, 2007), from the hermitian models (β = 2) and perturbative potentials, to general β models. The existence of the first correction in 1/N was considered in Johansson (1998) and more recently in Kriecherbauer and Shcherbina (2010). Here, by taking similar hypotheses, we extend the result to all orders in 1/N.     

Non-Equilibrium Statistical Mechanics of Turbulence

The macroscopic study of hydrodynamic turbulence is equivalent, at an abstract level, to the microscopic study of a heat flow for a suitable mechanical system (Ruelle, PNAS 109:20344–20346, 2012). Turbulent fluctuations (intermittency) then correspond to thermal fluctuations, and this allows to estimate the exponents \(\tau _p\) and \(\zeta _p\) associated with moments of dissipation fluctuations and velocity fluctuations. This approach, initiated in an earlier note (Ruelle, 2012), is pursued here more carefully. In particular we derive probability distributions at finite Reynolds number for the dissipation and velocity fluctuations, and the latter permit an interpretation of numerical experiments (Schumacher, Preprint, 2014). Specifically, if \(p(z)dz\) is the probability distribution of the radial velocity gradient we can explain why, when the Reynolds number \(\mathcal{R}\) increases, \(\ln p(z)\) passes from a concave to a linear then to a convex profile for large \(z\) as observed in (Schumacher, 2014). We show that the central limit theorem applies to the dissipation and velocity distribution functions, so that a logical relation with the lognormal theory of Kolmogorov (J. Fluid Mech. 13:82–85, 1962) and Obukhov is established. We find however that the lognormal behavior of the distribution functions fails at large value of the argument, so that a lognormal theory cannot correctly predict the exponents \(\tau _p\) and \(\zeta _p\) .     

Solution to Information Leakage in a Quantum Network System of QSS-QDC Using χ-Type Entangled States

Recently, Hong et al. (Chin. Phys. Lett. 29:050303, 2012) put forward two quantum secret sharing (QSS) protocols of quantum direct communication (QDC) by using χ-type entangled states. Later, some studies (Gao et al. in Chin. Phys. Lett. 29:110305, 2012; Chin. Phys. Lett. 30:079904, 2013; Liu et al. in Chin. Phys. Lett. 30:039901, 2013; Hong and Yang in Chin. Phys. Lett. 30:069901, 2013; Liu and Chen in Chin. Phys. Lett. 30:079903, 2013) made up for the drawbacks of Hong et al.’s two protocols to some extent. However, the information leakage weakness is still not thoroughly solved. In this Letter, the author analyzes the inner reason of information leakage weakness in detail at first. And then he suggests an effective encoding rule to avoid this weakness.     

An Alternative Approach to Understanding the Observed Positron Fraction

Space-based observations by PAMELA (Adriani et al., Nature 458, 607, 2009), Fermi-LAT (Ackerman et al., Phys. Rev. Lett. 105, 01103, 2012), and AMS (Aguilar et al., Phys. Rev. Lett. 110, 141102, 2013) have demonstrated that the positron fraction (e+/total-e) increases with increasing energy above about 10 GeV. According to the propagation model for Galactic cosmic rays in widespread use (Moskalenko & Strong, Astrophys. J. 493, 693, 1998), the production of secondary positrons from interaction of cosmic-ray protons and heavier nuclei with the interstellar medium gives a generally falling positron fraction between 10 and 100 GeV, with secondary positrons accounting for only ～20 % of the observed positron fraction at 100 GeV; so some other physical phenomena have been proposed to explain the data. An alternative approach to interpreting the positron observations is to consider these data as presenting an opportunity for re-examining models of Galactic cosmic-ray propagation. Following release of the PAMELA data, three groups published propagation models (Shaviv, et al., Phys. Rev. Lett. 103, 111302, 2009, Cowsik and Burch, Phys. Rev. D. 82, 023009, 2010, Katz et al., Mon. Not. R. Aston. Soc. 405, 1458 2010) in which the observed positron fraction is explained entirely by secondary positrons produced in the interstellar medium. In May of this year, stimulated by the AMS extension of the positron data to higher energy with excellent statistics, two of those groups presented further development of their calculations (Cowsik et al. 2013, Blum et al. 2013), again concluding that the observed positrons can be understood as secondaries. None of the authors of these five papers was registered for the 33rd International Cosmic Ray Conference (ICRC). Although I am not an author of any of these papers, I have some close familiarity with one of these recent papers, so the conference organizers invited me to bring this alternative approach to the attention of the conference. The present paper is a summary of the material I presented, along with a brief comment about reaction at the conference to this approach.     

Open Gromov-Witten Invariants of Toric Calabi-Yau 3-Folds

We present a proof of the mirror conjecture of Aganagic and Vafa (Mirror Symmetry, D-Branes and Counting Holomorphic Discs. http://arxiv.org/abs/hep-th/0012041v1, 2000) and Aganagic et al. (Z Naturforsch A 57(1–2):128, 2002) on disk enumeration in toric Calabi-Yau 3-folds for all smooth semi-projective toric Calabi-Yau 3-folds. We consider both inner and outer branes, at arbitrary framing. In particular, we recover previous results on the conjecture for (i) an inner brane at zero framing in ${K_{\mathbb{P}^2}}$ K P 2 (Graber-Zaslow, Contemp Math 310:107–121, 2002), (ii) an outer brane at arbitrary framing in the resolved conifold ${\mathcal{O}_{\mathbb{P}^1}(-1)\oplus \mathcal{O}_{\mathbb{P}^1}(-1)}$ O P 1 ( - 1 ) ⊕ O P 1 ( - 1 ) (Zhou, Open string invariants and mirror curve of the resolved conifold. http://arxiv.org/abs/1001.0447v1 [math.AG], 2010), and (iii) an outer brane at zero framing in ${K_{\mathbb{P}^2}}$ K P 2 (Brini, Open topological strings and integrable hierarchies: Remodeling the A-model. http://arxiv.org/abs/1102.0281 [hep-th], 2011).     

A note on the area spectrum of d-dimensional pure de Sitter Space-time

Consistent supercurrent multiplets are naturally associated with linearized off-shell supergravity models. In S.M. Kuzenko, J. High Energy Phys. 1004, 022 (2010) we presented the hierarchy of such supercurrents which correspond to all the models for linearized 4D $\mathcal{N}=1$ supergravity classified a few years ago. Here we analyze the correspondence between the most general supercurrent given in S.M. Kuzenko, J. High Energy Phys. 1004, 022 (2010) and the one obtained eight years ago in M. Magro et al., Ann. Phys. 298, 123 (2002) using the superfield Noether procedure. We apply the Noether procedure to the general $\mathcal{N}=1$ supersymmetric nonlinear sigma-model and show that it naturally leads to the so-called $\mathcal{S}$ -multiplet, revitalized in Z. Komargodski, N. Seiberg, J. High Energy Phys. 1007, 017 (2010).     

The νMSM and muon to electron conversion experiments

We review briefly the different constraints on the three right-handed neutrinos of the νMSM, an extension of the Standard Model that can explain baryon asymmetry, dark matter and neutrino masses. We include in the discussion the proposed experiments on muon to electron conversion Mu2e (Carey et al., Mu2e Collaboration, 2012), COMET and PRISM (Hungerford, COMET Collaboration, AIP Conf Proc 1182:694, 2009; Cui et al., COMET Collaboration, 2012). We find that the expected sensitivity of these experiments is weaker by about two orders of magnitude than the constraints coming from successful baryogenesis.     

Multilocal Fermionization

We present a simple isomorphism between the algebra of one real chiral Fermi field and the algebra of n real chiral Fermi fields. The isomorphism preserves the vacuum state. This is possible by a “change of localization”, and gives rise to new multilocal symmetries generated by the corresponding multilocal current and stress–energy tensor. The result gives a common underlying explanation of several remarkable recent results on the representation of the free Bose field in terms of free Fermi fields (Anguelova, arXiv:1112.3913, 2011; Anguelova, arXiv:1206.4026, 2012), and on the modular theory of the free Fermi algebra in disjoint intervals (Casini and Huerta, Class Quant Grav 26:185005, 2009; Longo et al., Rev Math Phys 22:331–354, 2010)     

Sharp parameter bounds for certain maximal point lenses

Starting from an $n$ -point circular gravitational lens having $3n+1$ images, Rhie (ArXiv Astrophysics e-prints, 2003) used a perturbation argument to construct an $(n+1)$ -point lens producing $5n$ images. In this work we give a concise proof of Rhie’s result, and we extend the range of parameters in Rhie’s model for which maximal lensing occurs. We also study a slightly different construction given by Bayer and Dyer (Gen Relativ Gravit 39(9):1413–1418, 2007) arising from the $(3n+1)$ -point lens. In particular, we extend their results and give sharp parameter bounds for their lens model. By a substitution of variables and parameters we show that both models are equivalent in a certain sense.     

n-Orthodistributivity in Orthomodular Lattices

A useful generalization of distributivity in lattices n-distributivity, \(n \in \mathbb{N}\) , was introduced in Huhn (Acta Sci. Math. 33:297–305, 1972). In Mayet and Roddy (Contrib. Gen. Algebra 5:285–294, 1987), ‘orthogonalized’ versions, n-orthodistributivity, \(n \in \mathbb{N}\) , of these equations were introduced and discussed. The discussion and results of Mayet and Roddy (Contrib. Gen. Algebra 5:285–294, 1987) centered on the class of modular ortholattices. In this paper we discuss and present some preliminary results for these conditions in orthomodular lattices. In particular, we completely classify the n-(ortho)distributive orthomodular lattices arising from Greechie’s classical 1971 construction, and we prove that a certain simple atomless orthomodular lattice, presented in Roddy (Algebra Univers. 29:564–597, 1992), is 4-orthodistributive. It is not 3-orthodistributive.