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.     

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.     

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)     

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.     

Yes,More Decoherence: A Reply to Critics

Recently I published an article in this journal entitled “Less interpretation and more decoherence in quantum gravity and inflationary cosmology” (Crull in Found Phys 45(9):1019–1045, 2015). This article generated responses from three pairs of authors: Vassallo and Esfeld (Found Phys 45(12):1533–1536, 2015), Okon and Sudarsky (Found Phys 46(7):852–879, 2016) and Fortin and Lombardi (Found Phys, 2017). In what follows, I reply to the criticisms raised by these authors.     

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.     

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.     

Towards apparent convergence in asymptotically safe quantum gravity

The asymptotic safety scenario in gravity is accessed within the systematic vertex expansion scheme for functional renormalisation group flows put forward in Christiansen et al. (Phys Lett B 728:114, 2014), Christiansen et al. (Phy Rev D 93:044036, 2016), and implemented in Christiansen et al. (Phys Rev D 92:121501, 2015) for propagators and three-point functions. In the present work this expansion scheme is extended to the dynamical graviton four-point function. For the first time, this provides us with a closed flow equation for the graviton propagator: all vertices and propagators involved are computed from their own flows. In terms of a covariant operator expansion the current approximation gives access to \(\Lambda \), R, \(R^2\) as well as \(R_{\mu \nu }^2\) and higher derivative operators. We find a UV fixed point with three attractive and two repulsive directions, thus confirming previous studies on the relevance of the first three operators. In the infrared we find trajectories that correspond to classical general relativity and further show non-classical behaviour in some fluctuation couplings. We also find signatures for the apparent convergence of the systematic vertex expansion. This opens a promising path towards establishing asymptotically safe gravity in terms of apparent convergence.     

Inflation and reheating in scale-invariant scalar-tensor gravity

We consider the scale-invariant inflationary model studied in Rinaldi and Vanzo (Phys Rev D 94: 024009, 2016). The Lagrangian includes all the scale-invariant operators that can be built with combinations of \(R, R^{2}\) and one scalar field. The equations of motion show that the symmetry is spontaneously broken after an arbitrarily long inflationary period and a fundamental mass scale is generated. Upon symmetry breaking, and in the Jordan frame, both Hubble function and the scalar field undergo damped oscillations that can eventually amplify Standard Model fields and reheat the Universe. In the present work, we study in detail inflation and the reheating mechanism of this model in the Einstein frame and we compare some of the results with the latest observational data.     

Fractional quiver W-algebras

We introduce quiver gauge theory associated with the non-simply laced type fractional quiver and define fractional quiver W-algebras by using construction of Kimura and Pestun (Lett Math Phys, 2018.  https://doi.org/10.1007/s11005-018-1072-1; Lett Math Phys, 2018.  https://doi.org/10.1007/s11005-018-1073-0) with representation of fractional quivers.     

A Free Boundary Problem with Non Local Interaction

We prove local existence for classical solutions of a free boundary problem which arises in one of the biological selection models proposed by Brunet and Derrida, (Phys. Rev. E 56, 2597D2604, 1997) and Durrett and Remenik, (Ann. Probab. 39, 2043–2078, 2011). The problem we consider describes the limit evolution of branching brownian particles on the line with death of the leftmost particle at each creation time as studied in De Masi et al. (2017). We use extensively results in Cannon (1984) and Fasano (2008).     

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.     

Totally Asymmetric Limit for Models of Heat Conduction

We consider one dimensional weakly asymmetric boundary driven models of heat conduction. In the cases of a constant diffusion coefficient and of a quadratic mobility we compute the quasi-potential that is a non local functional obtained by the solution of a variational problem. This is done using the dynamic variational approach of the macroscopic fluctuation theory (Bertini et al. in Rev Mod Phys 87:593, 2015). The case of a concave mobility corresponds essentially to the exclusion model that has been discussed in Bertini et al. (J Stat Mech L11001, 2010; Pure Appl Math 64(5):649–696, 2011; Commun Math Phys 289(1):311–334, 2009) and Enaud and Derrida (J Stat Phys 114:537–562, 2004). We consider here the convex case that includes for example the Kipnis-Marchioro-Presutti (KMP) model and its dual (KMPd) (Kipnis et al. in J Stat Phys 27:6574, 1982). This extends to the weakly asymmetric regime the computations in Bertini et al. (J Stat Phys 121(5/6):843–885, 2005). We consider then, both microscopically and macroscopically, the limit of large externalfields. Microscopically we discuss some possible totally asymmetric limits of the KMP model. In one case the totally asymmetric dynamics has a product invariant measure. Another possible limit dynamics has instead a non trivial invariant measure for which we give a duality representation. Macroscopically we show that the quasi-potentials of KMP and KMPd, which are non local for any value of the external field, become local in the limit. Moreover the dependence on one of the external reservoirs disappears. For models having strictly positive quadratic mobilities we obtain instead in the limit a non local functional having a structure similar to the one of the boundary driven asymmetric exclusion process.     

On Convergence to SLE<Subscript>6</Subscript> II: Discrete Approximations and Extraction of Cardy’s Formula for General Domains

We show how to extract Cardy’s Formula for a general class of domains given the requisite interior analyticity statement. This is accomplished by a careful study of the interplay between discretization schemes and extraction of limiting boundary values. Of particular importance to the companion work (Binder et al. in J. Stat. Phys., 2010) we establish these results for slit domains and for the critical percolation models introduced in Chayes and Lei (Rev. Math. Phys. 19:511–565, 2007).     

Physics Without Physics

David Finkelstein was very fond of the new information-theoretic paradigm of physics advocated by John Archibald Wheeler and Richard Feynman. Only recently, however, the paradigm has concretely shown its full power, with the derivation of quantum theory (Chiribella et al., Phys. Rev. A 84:012311, 2011; D’Ariano et al., 2017) and of free quantum field theory (D’Ariano and Perinotti, Phys. Rev. A 90:062106, 2014; Bisio et al., Phys. Rev. A 88:032301, 2013; Bisio et al., Ann. Phys. 354:244, 2015; Bisio et al., Ann. Phys. 368:177, 2016) from informational principles. The paradigm has opened for the first time the possibility of avoiding physical primitives in the axioms of the physical theory, allowing a re-foundation of the whole physics over logically solid grounds. In addition to such methodological value, the new information-theoretic derivation of quantum field theory is particularly interesting for establishing a theoretical framework for quantum gravity, with the idea of obtaining gravity itself as emergent from the quantum information processing, as also suggested by the role played by information in the holographic principle (Susskind, J. Math. Phys. 36:6377, 1995; Bousso, Rev. Mod. Phys. 74:825, 2002). In this paper I review how free quantum field theory is derived without using mechanical primitives, including space-time, special relativity, Hamiltonians, and quantization rules. The theory is simply provided by the simplest quantum algorithm encompassing a countable set of quantum systems whose network of interactions satisfies the three following simple principles: homogeneity, locality, and isotropy. The inherent discrete nature of the informational derivation leads to an extension of quantum field theory in terms of a quantum cellular automata and quantum walks. A simple heuristic argument sets the scale to the Planck one, and the currently observed regime where discreteness is not visible is the so-called “relativistic regime” of small wavevectors, which holds for all energies ever tested (and even much larger), where the usual free quantum field theory is perfectly recovered. In the present quantum discrete theory Einstein relativity principle can be restated without using space-time in terms of invariance of the eigenvalue equation of the automaton/walk under change of representations. Distortions of the Poincaré group emerge at the Planck scale, whereas special relativity is perfectly recovered in the relativistic regime. Discreteness, on the other hand, has some plus compared to the continuum theory: 1) it contains it as a special regime; 2) it leads to some additional features with GR flavor: the existence of an upper bound for the particle mass (with physical interpretation as the Planck mass), and a global De Sitter invariance; 3) it provides its own physical standards for space, time, and mass within a purely mathematical adimensional context. The paper ends with the future perspectives of this project, and with an Appendix containing biographic notes about my friendship with David Finkelstein, to whom this paper is dedicated.     

Impact of topology in foliated quantum Einstein gravity

We use a functional renormalization group equation tailored to the Arnowitt–Deser–Misner formulation of gravity to study the scale dependence of Newton’s coupling and the cosmological constant on a background spacetime with topology \(S^1 \times S^d\). The resulting beta functions possess a non-trivial renormalization group fixed point, which may provide the high-energy completion of the theory through the asymptotic safety mechanism. The fixed point is robust with respect to changing the parametrization of the metric fluctuations and regulator scheme. The phase diagrams show that this fixed point is connected to a classical regime through a crossover. In addition the flow may exhibit a regime of “gravitational instability”, modifying the theory in the deep infrared. Our work complements earlier studies of the gravitational renormalization group flow on a background topology \(S^1 \times T^d\) (Biemans et al. Phys Rev D 95:086013, 2017, Biemans et al. arXiv:1702.06539, 2017) and establishes that the flow is essentially independent of the background topology.     

Quantum Games under Decoherence

Quantum systems are easily influenced by ambient environments. Decoherence is generated by system interaction with external environment. In this paper, we analyse the effects of decoherence on quantum games with Eisert-Wilkens-Lewenstein (EWL) (Eisert et al., Phys. Rev. Lett. 83(15), 3077 1999) and Marinatto-Weber (MW) (Marinatto and Weber, Phys. Lett. A 272, 291 2000) schemes. Firstly, referring to the analytical approach that was introduced by Eisert et al. (Phys. Rev. Lett. 83(15), 3077 1999), we analyse the effects of decoherence on quantum Chicken game by considering different traditional noisy channels. We investigate the Nash equilibria and changes of payoff in specific two-parameter strategy set for maximally entangled initial states. We find that the Nash equilibria are different in different noisy channels. Since Unruh effect produces a decoherence-like effect and can be perceived as a quantum noise channel (Omkar et al., arXiv:1408.1477v1), with the same two parameter strategy set, we investigate the influences of decoherence generated by the Unruh effect on three-player quantum Prisoners’ Dilemma, the non-zero sum symmetric multiplayer quantum game both for unentangled and entangled initial states. We discuss the effect of the acceleration of noninertial frames on the the game’s properties such as payoffs, symmetry, Nash equilibrium, Pareto optimal, dominant strategy, etc. Finally, we study the decoherent influences of correlated noise and Unruh effect on quantum Stackelberg duopoly for entangled and unentangled initial states with the depolarizing channel. Our investigations show that under the influence of correlated depolarizing channel and acceleration in noninertial frame, some critical points exist for an unentangled initial state at which firms get equal payoffs and the game becomes a follower advantage game. It is shown that the game is always a leader advantage game for a maximally entangled initial state and there appear some points at which the payoffs become zero.     

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.     

Replica Bounds by Combinatorial Interpolation for Diluted Spin Systems

In two papers Franz et al. proved bounds for the free energy of diluted random constraints satisfaction problems, for a Poisson degree distribution (Franz and Leone in J Stat Phys 111(3–4):535–564, 2003) and a general distribution (Franz et al. in J Phys A 36(43), 10967, 2003). Panchenko and Talagrand (Probab Theo Relat Fields 130(3):319–336, 2004) simplified the proof and generalized the result of Franz and Leone (J Stat Phys 111(3–4):535–564, 2003) for the Poisson case. We provide a new proof for the general degree distribution case and as a corollary, we obtain new bounds for the size of the largest independent set (also known as hard core model) in a large random regular graph. Our proof uses a combinatorial interpolation based on biased random walks (Salez in Combin Probab Comput 25(03):436–447, 2016) and allows to bypass the arguments in Franz et al. (J Phys A 36(43):10967, 2003) based on the study of the Sherrington–Kirkpatrick (SK) model.     

Energy Statistics in Open Harmonic Networks

We relate the large time asymptotics of the energy statistics in open harmonic networks to the variance-gamma distribution and prove a full large deviation principle. We consider both Hamiltonian and stochastic dynamics, the later case including electronic RC networks. We compare our theoretical predictions with the experimental data obtained by Ciliberto et al. (Phys. Rev. Lett. 110:180601, 2013).