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.     

Weak and Strong Connectivity Regimes for a General Time Elapsed Neuron Network Model

For large fully connected neuron networks, we study the dynamics of homogenous assemblies of interacting neurons described by time elapsed models. Under general assumptions on the firing rate which include the ones made in previous works (Pakdaman et al. in Nonlinearity 23(1):55–75, 2010; SIAM J Appl Math 73(3):1260–1279, 2013, Mischler and Weng in Acta Appl Math, 2015), we establish accurate estimate on the long time behavior of the solutions in the weak and the strong connectivity regime both in the case with and without delay. Our results improve (Pakdaman et al. 2010, 2013) where a less accurate estimate was established and Mischler and Weng (2015) where only smooth firing rates were considered. Our approach combines several arguments introduced in the above previous works as well as a slightly refined version of the Weyl’s and spectral mapping theorems presented in Voigt (Monatsh Math 90(2):153–161, 1980) and Mischler and Scher (Ann Inst H Poincaré Anal Non Linéaire 33(3):849–898, 2016).     

Finite vs. Infinite Decompositions in Conformal Embeddings

We revisit two old and apparently little known papers by Basuev (Teoret Mat Fiz 37(1):130–134, 1978, Teoret Mat Fiz 39(1):94–105, 1979) and show that the results contained there yield strong improvements on current lower bounds of the convergence radius of the Mayer series for continuous particle systems interacting via a very large class of stable and tempered potentials, which includes the Lennard-Jones type potentials. In particular we analyze the case of the classical Lennard-Jones gas under the light of the Basuev scheme and, using also some new results (Yuhjtman in J Stat Phys 160(6): 1684–1695, 2015) on this model recently obtained by one of us, we provide a new lower bound for the Mayer series convergence radius of the classical Lennard-Jones gas, which improves by a factor of the order 10⁵ on the current best lower bound recently obtained in de Lima and Procacci (J Stat Phys 157(3):422–435, 2014).     

A Second Order Expansion of the Separatrix Map for Trigonometric Perturbations of a Priori Unstable Systems

In this paper we study a so-called separatrix map introduced by Zaslavskii–Filonenko (Sov Phys JETP 27:851–857, 1968) and studied by Treschev (Physica D 116(1–2):21–43, 1998; J Nonlinear Sci 12(1):27–58, 2002), Piftankin (Nonlinearity (19):2617–2644, 2006) Piftankin and Treshchëv (Uspekhi Mat Nauk 62(2(374)):3–108, 2007). We derive a second order expansion of this map for trigonometric perturbations. In Castejon et al. (Random iteration of maps of a cylinder and diffusive behavior. Preprint available at arXiv:1501.03319, 2015), Guardia and Kaloshin (Stochastic diffusive behavior through big gaps in a priori unstable systems (in preparation), 2015), and Kaloshin et al. (Normally Hyperbolic Invariant Laminations and diffusive behavior for the generalized Arnold example away from resonances. Preprint available at http://www.terpconnect.umd.edu/vkaloshi/, 2015), applying the results of the present paper, we describe a class of nearly integrable deterministic systems with stochastic diffusive behavior.     

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).     

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.     

Traces of Intertwiners for Quantum Affine {\mathfrak{sl}}_2 and Felder–Varchenko Functions

We show that the traces of \({U_q({\widehat{\mathfrak{sl}}}_2)}\)-intertwiners of [ESV02] valued in the three-dimensional evaluation representation converge in a certain region of parameters and give a representation-theoretic construction of Felder–Varchenko’s hypergeometric solutions to the q-KZB heat equation given in [FV02]. This gives the first proof that such a trace function converges and resolves the first case of the Etingof–Varchenko conjecture of [EV00]. As applications, we prove a symmetry property for traces of intertwiners and prove Felder–Varchenko’s conjecture in [FV04] that their elliptic Macdonald polynomials are related to the affine Macdonald polynomials defined as traces over irreducible integrable \({U_q({\widehat{\mathfrak{sl}}}_2)}\)-modules in [EK95]. In the trigonometric and classical limits, we recover results of [EK94,EV00]. Our method relies on an interplay between the method of coherent states applied to the free field realization of the q-Wakimoto module of [Mat94], convergence properties given by the theta hypergeometric integrals of [FV02], and rationality properties originating from the representation-theoretic definition of the trace function.     

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)     

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.     

Superdiffusion in the Periodic Lorentz Gas

We introduce the dynamical sine-Gordon equation in two space dimensions with parameter \({\beta}\), which is the natural dynamic associated to the usual quantum sine-Gordon model. It is shown that when \({\beta^{2} \in (0, \frac{16\pi}{3})}\) the Wick renormalised equation is well-posed. In the regime \({\beta^{2} \in (0, 4\pi)}\), the Da Prato–Debussche method [J Funct Anal 196(1):180–210, 2002; Ann Probab 31(4):1900–1916, 2003] applies, while for \({\beta^{2} \in [4\pi, \frac{16\pi}{3})}\), the solution theory is provided via the theory of regularity structures [Hairer, Invent Math 198(2):269–504, 2014]. We also show that this model arises naturally from a class of \({2 + 1}\) -dimensional equilibrium interface fluctuation models with periodic nonlinearities. The main mathematical difficulty arises in the construction of the model for the associated regularity structure where the role of the noise is played by a non-Gaussian random distribution similar to the complex multiplicative Gaussian chaos recently analysed in Lacoin et al. [Commun Math Phys 337(2):569–632, 2015].     

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.     

Frobenius manifolds and Frobenius algebra-valued integrable systems

The notion of integrability will often extend from systems with scalar-valued fields to systems with algebra-valued fields. In such extensions the properties of, and structures on, the algebra play a central role in ensuring integrability is preserved. In this paper, a new theory of Frobenius algebra-valued integrable systems is developed. This is achieved for systems derived from Frobenius manifolds by utilizing the theory of tensor products for such manifolds, as developed by Kaufmann (Int Math Res Not 19:929–952, 1996), Kontsevich and Manin (Inv Math 124: 313–339, 1996). By specializing this construction, using a fixed Frobenius algebra \({\mathcal {A}},\) one can arrive at such a theory. More generally, one can apply the same idea to construct an \({\mathcal {A}}\)-valued topological quantum field theory. The Hamiltonian properties of two classes of integrable evolution equations are then studied: dispersionless and dispersive evolution equations. Application of these ideas are discussed, and as an example, an \({\mathcal {A}}\)-valued modified Camassa–Holm equation is constructed.     

Generalized Quantum Probability and Entanglement Enhancement Witnessing

It has been suggested (cf. Sinha et al. in Science 329:418, 2010) that the Born rule for quantum probability could be violated. It has also been suggested that, in a generalized version of quantum mechanical probability theory such as that proposed by Sorkin (Mod. Phys. Lett. A 9:3119, 1994) there might occur deviations from the predictions of quantum probability in cases where more than two paths are available to a self-interfering system. These would lead to additional contributions to interference. Here, these ideas, some in the theoretical context and some in the experimental context, are briefly reviewed and pragmatically extended to situations involving bipartite systems, so that corresponding interference enhancement due to entanglement might be witnessed.     

The Corolla Polynomial for Spontaneously Broken Gauge Theories

In Kreimer and Yeats (Electr. J. Comb. 41–41, 2013), Kreimer et al. (Annals Phys. 336, 180–222, 2013) and Sars (2015) the Corolla Polynomial \( \mathcal C ({\Gamma }) \in \mathbb C [a_{h_{1}}, \ldots , a_{h_{\left \vert {\Gamma }^{[1/2]} \right \vert }}]\) was introduced as a graph polynomial in half-edge variables \(\{a_{h}\}_{h \in {\Gamma }^{[1/2]}}\) over a 3-regular scalar quantum field theory (QFT) Feynman graph Γ. It allows for a covariant quantization of pure Yang-Mills theory without the need for introducing ghost fields, clarifies the relation between quantum gauge theory and scalar QFT with cubic interaction and translates back the problem of renormalizing quantum gauge theory to the problem of renormalizing scalar QFT with cubic interaction (which is super renormalizable in 4 dimensions of spacetime). Furthermore, it is, as we believe, useful for computer calculations. In Prinz (2015) on which this paper is based the formulation of Kreimer and Yeats (Electr. J. Comb. 41–41, 2013), Kreimer et al. (Annals Phys. 336, 180–222, 2013) and Sars (2015) gets slightly altered in a fashion specialized in the case of the Feynman gauge. It is then formulated as a graph polynomial \(\mathcal C ({\Gamma } ) \in \mathbb C [a_{h_{1 \pm }}, \ldots , a_{h_{\left \vert {\Gamma }^{[1/2]} \right \vert } \vphantom {h}_{\pm }}, b_{h_{1}}, \ldots , b_{h_{\left \vert {\Gamma }^{[1/2]} \right \vert }}] \) in three different types of half-edge variables \( \{a_{h_{+}} , a_{h_{-}} , b_{h}\}_{h \in {\Gamma }^{[1/2]}} \). This formulation is also suitable for the generalization to the case of spontaneously broken gauge theories (in particular all bosons from the Standard Model), as was first worked out in Prinz (2015) and gets reviewed here.     

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 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.     

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.     

Quantum Axiomatics: Topological and Classical Properties of State Property Systems

The definition of ‘classical state’ from (Aerts in K. Engesser, D. Gabbay and D. Lehmann (Eds.), Handbook of Quantum Logic and Quantum Structures. Elsevier, Amsterdam, 2009), used e.g. in Aerts et al. (http://arxiv.org/abs/quant-ph/0503083, 2010) to prove a decomposition theorem internally in the language of State Property Systems, presupposes as an additional datum an orthocomplementation on the property lattice of a physical system. In this paper we argue on the basis of the (ε,d)-model on the Poincaré sphere that a notion of topologicity for states can be seen as an alternative (operationally foundable) classicality notion in the absence of an orthocomplementation, and compare it to the known and operationally founded concept of classicality.     

A Nonlinear Transfer Operator Theorem

In recent papers, Kenyon et al. (Ergod Theory Dyn Syst 32:1567–1584 2012), and Fan et al. (C R Math Acad Sci Paris 349:961–964 2011, Adv Math 295:271–333 2016) introduced a form of non-linear thermodynamic formalism based on solutions to a non-linear equation using matrices. In this note we consider the more general setting of Hölder continuous functions.