A Small and Non-simple Geometric Transition

Following notation introduced in the recent paper (Rossi Int. J. Geom. Methods Mod. Phys. 12(5), 2015), this paper is aimed to present in detail an example of a small geometric transition which is not a simple one i.e. a deformation of a conifold transition. This is realized by means of a detailed analysis of the Kuranishi space of a Namikawa cuspidal fiber product, which in particular improves the conclusion of Y. Namikawa in Remark 2.8 and Example 1.11 of Namikawa (Topology 41(6), 1219–1237, 2002). The physical interest of this example is presenting a geometric transition which can’t be immediately explained as a massive black hole condensation to a massless one, as described by Strominger (Nucl. Phys. B451, 97–109, 1995).     

Leptogenesis in inflationary models with non-Abelian gauge fields

A scenario of leptogenesis was introduced in Alexander et al. (Phys Rev Lett 96:081301, 2006) which works during inflationary period within standard model of particle physics setup. In this scenario lepton number is created by the gravitational chiral anomaly which has a non-zero expectation value for models of inflation driven by pseudoscalar field(s). Here, we observe that models of inflation involving non-Abelian gauge fields, e.g. the chromo-natural inflation (Adshead and Wyman in Phys Rev Lett 108:261302, 2012) or the gauge-flation (Maleknejad and Sheikh-Jabbari in Phys Lett B 723:224, 2013. arXiv:1102.1513 [hep-ph]), have a parity-violating tensor mode (graviton) spectrum and naturally lead to a non-vanishing expectation value for the gravitational chiral anomaly. Therefore, one has a natural leptogenesis scenario associated with these inflationary setups, inflato-natural leptogenesis. We argue that the observed value of baryon-to-photon number density can be explained in a natural range of parameters in these models.     

Two-Dimensional Anisotropic Random Walks: Fixed Versus Random Column Configurations for Transport Phenomena

We consider random walks on the square lattice of the plane along the lines of Heyde (J Stat Phys 27:721–730, 1982, Stochastic processes, Springer, New York, 1993) and den Hollander (J Stat Phys 75:891–918, 1994), whose studies have in part been inspired by the so-called transport phenomena of statistical physics. Two-dimensional anisotropic random walks with anisotropic density conditions á  la Heyde (J Stat Phys 27:721–730, 1982, Stochastic processes, Springer, New York, 1993) yield fixed column configurations and nearest-neighbour random walks in a random environment on the square lattice of the plane as in den Hollander (J Stat Phys 75:891–918, 1994) result in random column configurations. In both cases we conclude simultaneous weak Donsker and strong Strassen type invariance principles in terms of appropriately constructed anisotropic Brownian motions on the plane, with self-contained proofs in both cases. The style of presentation throughout will be that of a semi-expository survey of related results in a historical context.     

A Ping-Pong Quantum Dialogue Scheme Using Genuine Four-Particle Entangled States

Based on the genuine four-particle entangled state (Yeo and Chua in Phys. Rev. Lett. 96:060502, 2006) and the ping-pong protocol (Boström and Felbinger in Phys. Rev. Lett. 89:187902, 2002), an efficient quantum dialogue scheme is proposed. Since some subtle methods are employed, the information leakage doesn’t exist in this scheme. There are two security-check processes in this scheme, one is accomplished by using the four-particle entanglement pairs and the other by using the d particles.     

Reconstruction of a kinetic k-essence Lagrangian from a modified of dark energy equation of state

In this paper the Lagrangian density of a purely kinetic k-essence model that describes the behavior of dark energy described by four parameterized equations of state proposed by Cooray and Huterer (Astrophys J 513:L95, 1999), Zhang and Wu (Mod Phys Lett A 27:1250030, 2012), Linder (Phys Rev Lett 90:091301, 2003), Efstathiou (Mon Not R Astron Soc 310:842, 2000), and Feng and Lu (J Cosmol Astropart Phys 1111:34, 2011) has been reconstructed. This reconstruction is performed using the method outlined by de Putter and Linder (Astropart Phys 28:263, 2007), which makes it possible to solve the equations that relate the Lagrangian density of the k-essence with the given equation of state (EoS) numerically. Finally, we discuss the observational constraints for the models based on 1049 SNIa data points from the Pantheon data set compiled by Scolnic et al. (Astrophys J 859(2):101, 2018)     

Topological Hall Effect of Spin-2 Condensate in a Time and Space-Dependent Magnetic Field

We simulate the dynamics of spin-2 ⁸⁷Rb condensate in a time and space-dependent magnetic field with a time-dependent variational approach. The topological Hall effect is observed, which has been realized in the experiment of spin-1 ²³Na condensate [Phys. Rev. Lett. 111, 245301 (2013)]. A driving-induced resonance behavior is observed.     

Gravitational Rutherford scattering and Keplerian orbits for electrically charged bodies in heterotic string theory

Properties of the motion of electrically charged particles in the background of the Gibbons–Maeda–Garfinkle–Horowitz–Strominger black hole is presented in this paper. Radial and angular motions are studied analytically for different values of the fundamental parameter. Therefore, gravitational Rutherford scattering and Keplerian orbits are analyzed in detail. Finally, this paper complements previous work by Fernando for null geodesics (Phys Rev D 85:024033, 2012), Olivares and Villanueva (Eur Phys J C 73:2659, 2013) and Blaga (Automat Comp Appl Math 22:41–48, 2013; Serb Astron 190:41, 2015) for time-like geodesics.     

The Operator Product Expansion Converges in Massless {\varphi_{4}^{4}}-Theory

It has been shown recently (Hollands and Kopper, Commun. Math. Phys. 313:257–290, 2012) that the mathematical status of the operator product expansion (OPE) is better than had previously been expected: namely considering massive Euclidean \({\varphi_4^4}\)-theory in the perturbative loop expansion, the OPE converges at any loop order when considering (as is usually done) composite operator insertions into correlation functions. In the present paper we prove the same result for the massless theory. While the short-distance properties of massive and massless theories may be expected to be similar on physical grounds, the proof in the massless case requires entirely new techniques, becausewe have to control with sufficient precision the exceptional momentum singularities of the massless correlation functions. Thebounds we state are organised in terms of weight factors associated to certain tree graphs (“tree dominance”). Our proof is again based on the flow equations of the renormalisation group, which we combine with such graph structures.     

A Generalization of Powers–Størmer Inequality

In this note, we prove the following inequality: \({2\Vert\Delta_{\eta\varphi}^{\frac s2}\xi_{\varphi}\Vert ^2 \ge \varphi(1)+\eta(1)- \vert\varphi-\eta\vert(1)}\) , where \({\varphi}\) and η are positive normal linear functionals over a von Neumann algebra. This is a generalization of the famous Powers–Størmer inequality (Powers and Størmer proved the inequality for \({L({\mathcal H})}\) in Commun Math Phys 16:1–33, 1970; Takesaki in Theory of Operator Algebras II, 2001). For matrices, this inequality was proven by Audenaert et al. (Phys Rev Lett 98:160501, 2007). We extend their result to general von Neumann algebras.     

Deflection of light by black holes and massless wormholes in massive gravity

Weak gravitational lensing by black holes and wormholes in the context of massive gravity (Bebronne and Tinyakov, JHEP 0904:100, 2009) theory is studied. The particular solution examined is characterized by two integration constants, the mass M and an extra parameter S namely ‘scalar charge’. These black hole reduce to the standard Schwarzschild black hole solutions when the scalar charge is zero and the mass is positive. In addition, a parameter \(\lambda \) in the metric characterizes so-called ‘hair’. The geodesic equations are used to examine the behavior of the deflection angle in four relevant cases of the parameter \(\lambda \). Then, by introducing a simple coordinate transformation \(r^\lambda =S+v^2\) into the black hole metric, we were able to find a massless wormhole solution of Einstein–Rosen (ER) (Einstein and Rosen, Phys Rev 43:73, 1935) type with scalar charge S. The programme is then repeated in terms of the Gauss–Bonnet theorem in the weak field limit after a method is established to deal with the angle of deflection using different domains of integration depending on the parameter \(\lambda \). In particular, we have found new analytical results corresponding to four special cases which generalize the well known deflection angles reported in the literature. Finally, we have established the time delay problem in the spacetime of black holes and wormholes, respectively.     

Statistical Mechanics and the Climatology of the Arctic Sea Ice Thickness Distribution

We study the seasonal changes in the thickness distribution of Arctic sea ice, g(h), under climate forcing. Our analytical and numerical approach is based on a Fokker–Planck equation for g(h) (Toppaladoddi and Wettlaufer in Phys Rev Lett 115(14):148501, 2015), in which the thermodynamic growth rates are determined using observed climatology. In particular, the Fokker–Planck equation is coupled to the observationally consistent thermodynamic model of Eisenman and Wettlaufer (Proc Natl Acad Sci USA 106:28–32, 2009). We find that due to the combined effects of thermodynamics and mechanics, g(h) spreads during winter and contracts during summer. This behavior is in agreement with recent satellite observations from CryoSat-2 (Kwok and Cunningham in Philos Trans R Soc A 373(2045):20140157, 2015). Because g(h) is a probability density function, we quantify all of the key moments (e.g., mean thickness, fraction of thin/thick ice, mean albedo, relaxation time scales) as greenhouse-gas radiative forcing, \(\Delta F_0\), increases. The mean ice thickness decays exponentially with \(\Delta F_0\), but much slower than do solely thermodynamic models. This exhibits the crucial role that ice mechanics plays in maintaining the ice cover, by redistributing thin ice to thick ice-far more rapidly than can thermal growth alone.     

On the type N twisting vacuum solution of the Einstein equations

One of the problems in the catalogue of solutions to the vacuum solutions of the Einstein equations is the dearth of solutions to what is known as the type N twisting metric. Were it to be found in its general form it would then, according to the Peeling theorem of Sachs (Proc R Soc Lond A270:103, 1962), describe the asymptotic gravitational field of an isolated source. The only known mathematical solution was found by Hauser (Phys Rev Lett 33:1112, 1974) and (Phys Rev Lett 33:1525, 1974). In this article the general equations are reduced to one third order complex equation for one complex variable plus one simple condition.     

Specific Heat Anomalies in Solids Described by a Multilevel Model

In the field of condensed matter physics, specific heat measurements can be considered as a pivotal experimental technique for characterizing the fundamental excitations involved in a certain phase transition. Indeed, phase transitions involving spin (de Souza et al. Phys. B Condens. Matter 404, 494 (2009) and Manna et al. Phys. Rev. Lett. 104, 016403 (2010)), charge (Pregelj et al. Phys. Rev. B 82, 144438 (2010)), lattice (Jesche et al. Phys. Rev. B 81, 134525 (2010)) (phonons) and orbital degrees of freedom, the interplay between ferromagnetism and superconductivity (Jesche et al. Phys. Rev. B 86, 020501 (2012)), Schottky-like anomalies in doped compounds (Lagos et al. Phys. C Supercond. 309, 170 (1998)), electronic levels in finite correlated systems (Macedo and Lagos J. Magn. Magn. Mater. 226, 105 (2001)), among other features, can be captured by means of high-resolution calorimetry. Furthermore, the entropy change associated with a first-order phase transition, no matter its nature, can be directly obtained upon integrating the specific heat over T, i.e., C(T)/T, in the temperature range of interest. Here, we report on a detailed analysis of the two-peak specific heat anomalies observed in several materials. Employing a simple multilevel model, varying the spacing between the energy levels Δ_i = (E_i?E₀) and the degeneracy of each energy level g_i, we derive the required conditions for the appearance of such anomalies. Our findings indicate that a ratio of \({\Delta }_{2}/{\Delta }_{1}\thickapprox \) 10 between the energy levels and a high degeneracy of one of the energy levels define the two-peaks regime in the specific heat. Our approach accurately matches recent experimental results. Furthermore, using a mean-field approach, we calculate the specific heat of a degenerate Schottky-like system undergoing a ferromagnetic (FM) phase transition. Our results reveal that as the degeneracy is increased the Schottky maximum in the specific heat becomes narrow while the peak associated with the FM transition remains unaffected.     

The Second Order Upper Bound for the Ground Energy of a Bose Gas

Consider N bosons in a finite box Λ=[0,L]³?R ³ interacting via a two-body smooth repulsive short range potential. We construct a variational state which gives the following upper bound on the ground state energy per particle

$\overline{\lim}_{\rho\to0}\overline{\lim}_{L\to\infty,\,N/L^3\to \rho}\biggl(\frac{e_0(\rho)-4\pi a\rho}{(4\pi a)^{5/2}(\rho)^{3/2}}\biggr )\leq\frac{16}{15\pi^2},$

where a is the scattering length of the potential. Previously, an upper bound of the form C16/15π ² for some constant C>1 was obtained in (Erdös et al. in Phys. Rev. A 78:053627, 2008). Our result proves the upper bound of the prediction by Lee and Yang (Phys. Rev. 105(3):1119–1120, 1957) and Lee et al. (Phys. Rev. 106(6):1135–1145, 1957).

     

<Emphasis Type="Italic">C</Emphasis><Superscript>1</Superscript>-Classification of Gapped Parent Hamiltonians of Quantum Spin Chains

We consider the C ¹-classification of gapped Hamiltonians introduced in Fannes et al. (Commun Math Phys 144:443–490, 1992) and Nachtergaele (Commun Math Phys 175:565–606, 1996) as parent Hamiltonians of translation invariant finitely correlated states. Within this family, we show that the number of edge modes, which is equal at the left and right edge, is the complete invariant. The construction proves that translation invariance of the ‘bulk’ ground state does not need to be broken to establish C ¹-equivalence, namely that the spin chain does not need to be blocked.     

Multihop Teleportation via the Composite of Asymmetric W State and Bell State

In this article, quantum teleportation schemes of a single qubit, two-qubit and N-qubit state are presented in a multihop communication network. All the schemes can be completed deterministicly. The shared entanglement resource between two adjacent nodes is the composition of the asymmetric W state and Bell state. It is not equivalent to the composite of GHZ state and Bell state used by Zou et al. (Phys. Lett. A 381, 76–81 2017).     

Hypersurface-homogeneous Universe filled with perfect fluid in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>, <Emphasis Type="Italic">T</Emphasis>) theory of gravity

The exact solutions of the field equations with respect to hypersurface-homogeneous Universe filled with perfect fluid in the framework of f(R, T) theory of gravity (Harko et al, Phys. Rev. D 84, 024020 (2011)) is derived. The physical behaviour of the cosmological model is studied.     

Constraints on tidal charge of the supermassive black hole at the Galactic Center with trajectories of bright stars

As it was pointed out recently in Hees et al. (Phys Rev Lett 118:211101, 2017), observations of stars near the Galactic Center with current and future facilities provide an unique tool to test general relativity (GR) and alternative theories of gravity in a strong gravitational field regime. In particular, the authors showed that the Yukawa gravity could be constrained with Keck and TMT observations. Some time ago, Dadhich et al. (Phys Lett B 487:1, 2001) showed that the Reissner–Nordström metric with a tidal charge is naturally appeared in the framework of Randall–Sundrum model with an extra dimension (\(Q^2\) is called tidal charge and it could be negative in such an approach). Astrophysical consequences of presence of black holes with a tidal charge are considerered, in particular, geodesics and shadows in Kerr–Newman braneworld metric are analyzed in Schee and Stuchlík (Intern J Mod Phys D 18:983, 2009), while profiles of emission lines generated by rings orbiting braneworld Kerr black hole are considered in Schee and Stuchlík (Gen Relat Grav 52:1795, 2009). Possible observational signatures of gravitational lensing in a presence of the Reissner–Nordström black hole with a tidal charge at the Galactic Center are discussed in papers (Bin-Nun in Phys Rev D 81:123011, 2010; Bin-Nun in Phys Rev D 82:064009, 2010; Bin-Nun in Class Quant Grav 28:114003, 2011). Here we are following such an approach and we obtain analytical expressions for orbital precession for Reissner–Nordström–de-Sitter solution in post-Newtonian approximation and discuss opportunities to constrain parameters of the metric from observations of bright stars with current and future astrometric observational facilities such as VLT, Keck, GRAVITY, E-ELT and TMT.     

Mixing Times of Monotone Surfaces and SOS Interfaces: A Mean Curvature Approach

We consider stochastic spin-flip dynamics for: (i) monotone discrete surfaces in \({\mathbb {Z}^3}\) with planar boundary height and (ii) the one-dimensional discrete Solid-on-Solid (SOS) model confined to a box. In both cases we show almost optimal bounds O(L ²polylog(L)) for the mixing time of the chain, where L is the natural size of the system. The dynamics at a macroscopic scale should be described by a deterministic mean curvature motion such that each point of the surface feels a drift which tends to minimize the local surface tension (Spohn in J Stat Phys 71:1081–1132, 1993). Inspired by this heuristics, our approach consists in bounding the dynamics with an auxiliary one which, with very high probability, follows quite closely the deterministic mean curvature evolution. Key technical ingredients are monotonicity, coupling and an argument due to Wilson (Ann Appl Probab 14:274–325, 2004) in the framework of lozenge tiling Markov Chains. Our approach works equally well for both models despite the fact that their equilibrium maximal height fluctuations occur on very different scales (log L for monotone surfaces and \({\sqrt L}\) for the SOS model). Finally, combining techniques from kinetically constrained spin systems (Cancrini et al. in Probab Th Rel Fields 140:459–504, 2008) together with the above mixing time result, we prove an almost diffusive lower bound of order 1/L ²polylog(L) for the spectral gap of the SOS model with horizontal size L and unbounded heights.     

Spinning Earth and its Coriolis effect on the circuital light beams: Verification of the special relativity theory

Bilger et al (1995), Anderson et al (1994) and Michelson–Gale assisted by Pearson (1925) measure / mention Sagnac effect on the circuital light /laser beams on the spinning Earth. But from the consideration of classical electrodynamics, the effect measured /mentioned by those experimenters is the Coriolis effect, not the Sagnac effect. A simple experiment is suggested here that can easily settle the problem.