Tracy–Widom at High Temperature

We investigate the marginal distribution of the bottom eigenvalues of the stochastic Airy operator when the inverse temperature \(\beta \) tends to \(0\) . We prove that the minimal eigenvalue, whose fluctuations are governed by the Tracy–Widom \(\beta \) law, converges weakly, when properly centered and scaled, to the Gumbel distribution. More generally we obtain the convergence in law of the marginal distribution of any eigenvalue with given index \(k\) . Those convergences are obtained after a careful analysis of the explosion times process of the Riccati diffusion associated to the stochastic Airy operator. We show that the empirical measure of the explosion times converges weakly to a Poisson point process using estimates proved in Dumaz and Virág (Ann Inst H Poincaré Probab Statist 49(4):915–933, 2013). We further compute the empirical eigenvalue density of the stochastic Airy ensemble on the macroscopic scale when \(\beta \rightarrow 0\) . As an application, we investigate the maximal eigenvalues statistics of \(\beta _N\) -ensembles when the repulsion parameter \(\beta _N\rightarrow 0\) when \(N\rightarrow +\infty \) . We study the double scaling limit \(N\rightarrow +\infty , \beta _N \rightarrow 0\) and argue with heuristic and numerical arguments that the statistics of the marginal distributions can be deduced following the ideas of Edelman and Sutton (J Stat Phys 127(6):1121–1165, 2007) and Ramírez et al. (J Am Math Soc 24:919–944, 2011) from our later study of the stochastic Airy operator.     

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).     

Embedding of Analytic Quasi-Periodic Cocycles into Analytic Quasi-Periodic Linear Systems and its Applications

In this paper, we prove that any analytic quasi-periodic cocycle close to constant is the Poincaré map of an analytic quasi-periodic linear system close to constant, which bridges both methods and results in quasi-periodic linear systems and cocycles. We also show that the almost reducibility of an analytic quasi-periodic linear system is equivalent to the almost reducibility of its corresponding Poincaré cocycle. By the local embedding theorem and the equivalence, we transfer the recent local almost reducibility results of quasi-periodic linear systems (Hou and You, in Invent Math 190:209–260, 2012) to quasi-periodic cocycles, and the global reducibility results of quasi-periodic cocycles (Avila, in Almost reducibility and absolute continuity, 2010; Avila et al., in Geom Funct Anal 21:1001–1019, 2011) to quasi-periodic linear systems. Finally, we give a positive answer to a question of Avila et al. (Geom Funct Anal 21:1001–1019, 2011) and use it to study point spectrum of long-range quasi-periodic operator with Liouvillean frequency. The embedding also holds for some nonlinear systems.     

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 \(\zeta _p\) .     

Quantum Random Walks with General Particle States

A convergence theorem is obtained for quantum random walks with particles in an arbitrary normal state. This unifies and extends previous work on repeated-interactions models, including that of Attal and Pautrat (Ann Henri Poincaré 7:59–104 2006) and Belton (J Lond Math Soc 81:412–434, 2010; Commun Math Phys 300:317–329, 2010). When the random-walk generator acts by ampliation and either multiplication or conjugation by a unitary operator, it is shown that the quantum stochastic cocycle which arises in the limit is driven by a unitary process.     

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.     

Hitting Matrix and Domino Tiling with Diagonal Impurities

As a continuation to our previous work (Nakano and Sadahiro in Fundam. Inform. 117:249–264, 2012; Nakano and Sadahiro in J. Stat. Phys. 139(4):565–597, 2010), we consider the domino tiling problem with impurities. (1) If we have more than two impurities on the boundary, we can compute the number of corresponding perfect matchings by using the hitting matrix method (Fomin in Trans. Am. Math. Soc. 353(9):3563–3583, 2001). (2) We have an alternative proof of the main result in Nakano and Sadahiro (Fundam. Inform. 117:249–264, 2012) and result in (1) above using the formula by Kenyon and Wilson (Trans. Am. Math. Soc. 363(3):1325–1364, 2011; Electron. J. Comb. 16(1):112, 2009) of counting the number of groves on circular planar graphs. (3) We study the behavior of the probability of finding the impurity at a given site when the size of the graph tends to infinity, as well as the scaling limit of those.     

Heterogeneous Memorized Continuous Time Random Walks in an External Force Fields

In this paper, we study the anomalous diffusion of a particle in an external force field whose motion is governed by nonrenewal continuous time random walks with correlated memorized waiting times, which involves Reimann–Liouville fractional derivative or Reimann–Liouville fractional integral. We show that the mean squared displacement of the test particle \(X_{x}\) which is dependent on its location \(x\) of the form (El-Wakil and Zahran, Chaos Solitons Fractals, 12, 1929–1935, 2001) 1 $$\begin{aligned} \langle \mathbb {X}_x^2\rangle (t)=\langle (\Delta X_x(t))^2\rangle _0\sim |x|^{-\theta }t^{\gamma }, \quad 0<\gamma <1, \quad \theta =d_w-2, \end{aligned}$$ where \(d_w>2\) is the anomalous exponent, the diffusion exponent \(\gamma \) is dependent on the model parameters. We obtain the Fokker–Planck-type dynamic equations, and their stationary solutions are of the Boltzmann–Gibbs form. These processes obey a generalized Einstein–Stokes–Smoluchowski relation and the second Einstein relation. We observe that the asymptotic behavior of waiting times and subordinations are of stretched Gaussian distributions. We also discuss the time averaged in the case of an harmonic potential, and show that the process exhibits aging and ergodicity breaking.     

Observation of the Antimatter Nuclei in Relativistic Heavy Ion Collisions

Recently antimatter hyper-triton nuclei ${(_{\bar{\Lambda}}^3\bar{H})}$ and antimatter helium nuclei ${(_2^4\bar{He})}$ are discovered with the Solenoidal Tracker At Rhic detector in relativistic heavy ion collisions at Relativistic Heavy Ion Collider (RHIC) (STAR Collaboration in Science 328(5974):58–62, 2010; STAR Collaboration in Nature 473:353–356, 2011). In this presentation, discoveries of antimatter particle are historically scanned and the recent observations at RHIC are reported in details as well as potential possibilities of discovery of antimatter nuclei at ALICE.     

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).     

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.     

Comment on Fractional Fokker–Planck Equation with Space and Time Dependent Drift and Diffusion

The purpose of this paper is to correct errors presented recently in the paper [Lv et al. J Stat Phys 149:619–628 (2012)], where the authors analyzed Fractional Fokker–Planck equation (FFPE) with space–time dependent drift $F(x,t)=F(x)f(t)$ and diffusion $D(x,t)=D(x)\tilde{d}(t)$ coefficients in the factorized form. We show an important drawback in the derivation of the stochastic representation of FFPE presented in the aforementioned paper, which makes the whole proof wrong. Moreover, we present a correct proof of their result in even more general case, when both drift and diffusion can have any, not necessarily factorized, form.     

Quantum Correlations and the Measurement Problem

The transition from classical to quantum mechanics rests on the recognition that the structure of information is not what we thought it was: there are operational, i.e., phenomenal, probabilistic correlations that lie outside the polytope of local correlations. Such correlations cannot be simulated with classical resources, which generate classical correlations represented by the points in a simplex, where the vertices of the simplex represent joint deterministic states that are the common causes of the correlations. The ‘no go’ hidden variable theorems tell us that we can’t shoe-horn phenomenal correlations outside the local polytope into a classical simplex by supposing that something has been left out of the story. The replacement of the classical simplex by the quantum convex set as the structure representing probabilistic correlations is the analogue for quantum mechanics of the replacement of Newton’s Euclidean space and time by Minkowski spacetime in special relativity. The nonclassical features of quantum mechanics, including the irreducible information loss on measurement, are generic features of correlations that lie outside the classical simplex. This paper is an elaboration of these ideas, which have their source in work by Pitowsky (J. Math. Phys. 27:1556, 1986; Math. Program. 50:395, 1991; Phys. Rev. A 77:062109, 2008), Garg and Mermin (Found. Phys. 14:1–39, 1984), Barrett (Phys. Rev. A 75:032304, 2007; Phys. Rev. A 7:022101, 2005) and others, e.g., Brunner et al. (arXiv:1303.2849, 2013), but the literature goes back to Boole (An Investigation of the Laws of Thought, Dover, New York, 1951). The final section looks at the measurement problem of quantum mechanics in this context. A large part of the problem is removed by seeing that the inconsistency in reconciling the entangled state at the end of a quantum measurement process with the definiteness of the macroscopic pointer reading and the definiteness of the correlated value of the measured micro-observable depends on a stipulation that is not required by the structure of the quantum possibility space. Replacing this stipulation by an alternative consistent stipulation is the first step to resolving the problem.     

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.     

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.     

Axially Symmetric Space-Time with Strange Quark Matter Attached to String Cloud in Self Creation Theory and General Relativity

The Axially symmetric space times with strange quark matter attached to string cloud in Barber’s (Gen. Relativ. Gravit. 14, 117, 1982) self-creation theory and general relativity have been studied. The field equations of the two theories have been solved by using the anisotropy feature of the universe in the axially symmetric space times. Some important features of the models, thus obtained, have been discussed and it is established that the additional condition, special law of variation of Hubble parameter proposed by Bermann (Nuovo Cimento B 74, 182, 1983), taken by Katore and Shaikh (Int. J. Teor. Phys. 51, 1881, 2012) in general relativity is superfluous.     

Probing compositeness with Higgs Boson decays at the LHC

We study how massive ghost-free gravity \(f(R)\) -modified theories, MGFTs, can be encoded into generic off-diagonal Einstein spaces. Using “auxiliary” connections completely defined by the metric fields and adapted to nonholonomic frames with associated nonlinear connection structure, we decouple and integrate in certain general forms the field equations in MGFT. Imposing additional nonholonomic constraints, we can generate Levi-Civita, LC, configurations and mimic MGFT effects via off-diagonal interactions of effective Einstein and/or Einstein–Cartan gravity with nonholonomically induced torsion. We show that imposing nonholonomic constraints it is possible reproduce very specific models of massive \(f(R)\) gravity studied in Cai et al. (arXiv:1307.7150, 2013), Klusoňet al. (Phys Lett B 726:918, 2013), Nojiri and Odintov (Phys Lett B 716:377, 2012) and Nojiri et al. (JCAP 1305:020, 2013). The cosmological evolution of ghost-free off-diagonal Einstein spaces is investigated. Certain compatibility of MGFT cosmology to small off-diagonal deformations of \(\Lambda \) CDM models is established.     

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.     

On the Geodesic Hypothesis in General Relativity

In this paper, we give a rigorous derivation of Einstein’s geodesic hypothesis in general relativity. We use small material bodies ${\phi^\epsilon}$ governed by the nonlinear Klein–Gordon equations to approximate the test particle. Given a vacuum spacetime ${([0, T]\times\mathbb{R}^3, h)}$ , we consider the initial value problem for the Einstein-scalar field system. For all sufficiently small ε and δ ≤ ε ^q , q > 1, where δ, ε are the amplitude and size of the particle, we show the existence of the solution ${([0, T]\times\mathbb{R}^3, g, \phi^\epsilon)}$ to the Einstein-scalar field system with the property that the energy of the particle ${\phi^\epsilon}$ is concentrated along a timelike geodesic. Moreover, the gravitational field produced by ${\phi^\epsilon}$ is negligibly small in C ¹, that is, the spacetime metric g is C ¹ close to the given vacuum metric h. These results generalize those obtained by Stuart in (Ann Sci École Norm Sup (4) 37(2):312–362, 2004, J Math Pures Appl (9) 83(5):541–587, 2004).