Space-time Phase Research Articles

Standard Model Gauge Couplings from Gauge-Dilatation Symmetry Breaking

We argue that there is a spontaneously broken rotational symmetry between space-time coordinates and gauge theoretical phases. The dilatonic mode acts as the massive Higgs boson, whose vacuum expectation value determines the gauge couplings. This mechanism requires that the quadratic divergences, or tadpoles of the three gauge-theory couplings, unify at a certain scale. We verify this statement, and find that this occurs at \Lambda_u ~ 4x10^7 GeV. The tadpole cancellation condition, together with the dilaton self-energy, fixes the value of the unified tadpole coefficient to be 1/[4 ln(\Lambda_cut/\Lambda_u)]. The observed values of the coupling constants at \Lambda_u then implies \Lambda_cut ~ 4x10^18 GeV, which is close to the value of the reduced Planck mass MR_Pl=M_Pl/sqrt(8 pi)=2.4 x 10^18 GeV. In other words, by assuming a cutoff at M_Pl or MR_Pl, we are able to obtain predictions for the gauge couplings which agree with the true values to within a few percent. It turns out that this symmetry breaking can only take place if mass is generated with the aid of some other means such as electroweak symmetry breaking. Assuming dynamical symmetry breaking originating at MR_Pl, we obtain M_chi ~ 10^9 GeV, which is not unreasonable but somewhat higher than \Lambda_u. The cancellation of an anomaly in the dilaton self-energy requires that the number of fermionic generations equals three.

Space-time phase transitions in the East model with a softened kinetic constraint

The East model has a dynamical phase transition between an active (fluid) and inactive (glass) state. We show that this phase transition generalizes to "softened" systems where constraint violations are allowed with small but finite probabilities. Moreover, we show that the first order coexistence line separating the active and inactive phases terminates in a finite-temperature space-time critical point. Implications of these results for equilibrium dynamics are discussed.

Green’s function of a massless scalar field in curved space-time and superluminal phase velocity of the retarded potential

We study a retarded potential solution of a massless scalar field in curved space-time. In a special ansatz for a particle at rest whose magnitude of the (scalar) charge is changing with time, we found an exact analytic solution. The solution indicates that the phase velocity of the retarded potential of a non-moving scalar charge is position dependent, and may easily be greater than the speed of light at a given point. In the case of the Schwarzschild space-time, at the horizon, the phase velocity becomes infinitely faster than the coordinate speed of light at that point. Superluminal phase velocity is relatively common phenomenon, with the the phase velocity of the massive Klein-Gordon field as the best known example. We discuss why it is possible to have modes with superluminal phase velocity even for a massless field.

Spatiotemporal representation of cardiac vectorcardiogram (VCG) signals

BackgroundVectorcardiogram (VCG) signals monitor both spatial and temporal cardiac electrical activities along three orthogonal planes of the body. However, the absence of spatiotemporal resolution in conventional VCG representations is a major impediment for medical interpretation and clinical usage of VCG. This is especially so because time-domain features of 12-lead ECG, instead of both spatial and temporal characteristics of VCG, are widely used for the automatic assessment of cardiac pathological patterns.Materials and methodsWe present a novel representation approach that captures critical spatiotemporal heart dynamics by displaying the real time motion of VCG cardiac vectors in a 3D space. Such a dynamic display can also be realized with only one lead ECG signal (e.g., ambulatory ECG) through an alternative lag-reconstructed ECG representation from nonlinear dynamics principles. Furthermore, the trajectories are color coded with additional dynamical properties of space-time VCG signals, e.g., the curvature, speed, octant and phase angles to enhance the information visibility.ResultsIn this investigation, spatiotemporal VCG signal representation is used to characterize various spatiotemporal pathological patterns for healthy control (HC), myocardial infarction (MI), atrial fibrillation (AF) and bundle branch block (BBB). The proposed color coding scheme revealed that the spatial locations of the peak of T waves are in the Octant 6 for the majority (i.e., 74 out of 80) of healthy recordings in the PhysioNet PTB database. In contrast, the peak of T waves from 31.79% (117/368) of MI subjects are found to remain in Octant 6 and the rest (68.21%) spread over all other octants. The spatiotemporal VCG signal representation is shown to capture the same important heart characteristics as the 12-lead ECG plots and more.ConclusionsSpatiotemporal VCG signal representation is shown to facilitate the characterization of space-time cardiac pathological patterns and enhance the automatic assessment of cardiovascular diseases.

New Advances of the Extended Minimum Cost Flow Phase Unwrapping Algorithm for SBAS-DInSAR Analysis at Full Spatial Resolution

We present an efficient space-time phase unwrapping (PhU) algorithm that allows us to process sequences of multitemporal full resolution differential synthetic aperture radar (SAR) interferograms for the generation of deformation time-series. The core of the proposed technique, dealing with sparse data grids, is represented by the extended minimum cost flow (MCF) (EMCF) PhU algorithm that was originally developed for the analysis of sequences of multilook interferograms. In particular, our method relies on the joint analysis of the spatial and temporal relationships among a set of properly selected multitemporal differential interferograms, which are compatible with the Small BAseline subset (SBAS) deformation time-series technique. The key point of the approach is the idea to split the complex MCF network problem, representing the overall PhU operation, into that of simpler subnetworks. More precisely, we start by identifying and solving a primary network that involves a proper selection of coherent pixels of the computed interferograms, representing the backbone structure of the overall network. Subsequently, this result is applied for constraining the solution of the subnetworks connected to the primary one, involving the entire set of analyzed pixels. To achieve this task, we solve a constrained optimization problem based on the computation of a constrained Delaunay triangulation in the azimuth/range domain. The overall procedure is implemented through two successive processing steps that are both carried out by using the EMCF PhU technique, which has been slightly modified to take into account the Doppler centroid differences of the exploited interferometric SAR data pairs. The experimental results, achieved by applying the proposed approach to a data set consisting of European Remote Sensing (ERS) SAR data acquired from June 1992 to August 2007 over the Napoli (Italy) bay area, confirm the effectiveness of the proposed PhU approach.

Quantum trajectory phase transitions in the micromaser

We study the dynamics of the single-atom maser, or micromaser, by means of the recently introduced method of thermodynamics of quantum jump trajectories. We find that the dynamics of the micromaser displays multiple space-time phase transitions, i.e., phase transitions in ensembles of quantum jump trajectories. This rich dynamical phase structure becomes apparent when trajectories are classified by dynamical observables that quantify dynamical activity, such as the number of atoms that have changed state while traversing the cavity. The space-time transitions can be either first order or continuous, and are controlled not just by standard parameters of the micromaser but also by nonequilibrium "counting" fields. We discuss how the dynamical phase behavior relates to the better known stationary-state properties of the micromaser.

MATHEMATICAL EXAMPLES OF SPACE-TIME PHASES

The space-time phases of a complex dynamic system are the probability distributions for state as a function of space and time which arise by evolving initial probability distributions from the distant past. Toom proved important results about space-time phases for a class of majority voter probabilistic cellular automata (PCA). Here, variants of the majority voter PCA are presented which are proved to exhibit a variety of types of space-time phase. These examples are expected to serve as useful steps on the way to a general theory of space-time phases.

Finite size scaling of current fluctuations in the totally asymmetric exclusion process

We study the fluctuations of the current J(t) of the totally asymmetric exclusion process with open boundaries. Using a density matrix renormalization group approach, we calculate the cumulant generating function of the current. This function can be interpreted as a free energy for an ensemble in which histories are weighted by exp ( − sJ(t)). We show that in this ensemble the model has a first-order spacetime phase transition at s = 0. We numerically determine the finite size scaling of the cumulant generating function near this phase transition, both in the non-equilibrium steady state and for large times.

Space-time phase transitions in driven kinetically constrained lattice models

Kinetically constrained models (KCMs) have been used to study and understand the origin of glassy dynamics. Despite having trivial thermodynamic properties, their dynamics slows down dramatically at low temperatures while displaying dynamical heterogeneity as seen in glass forming supercooled liquids. This dynamics has its origin in an ergodic-nonergodic first-order phase transition between phases of distinct dynamical "activity". This is a "space-time" transition as it corresponds to a singular change in ensembles of trajectories of the dynamics rather than ensembles of configurations. Here we extend these ideas to driven glassy systems by considering KCMs driven into non-equilibrium steady states through non-conservative forces. By classifying trajectories through their entropy production we prove that driven KCMs also display an analogous first-order space-time transition between dynamical phases of finite and vanishing entropy production. We also discuss how trajectories with rare values of entropy production can be realized as typical trajectories of a mapped system with modified forces.

Experimental and numerical study on a laminar fluid–structure interaction reference test case

With the rapid development of numerical codes for fluid–structure interaction computations, the demand for validation test cases increases. In this paper we present a comparison between numerical and experimental results for such a fluid–structure interaction reference test case. The investigated structural model consists of an aluminum front cylinder with an attached thin metal plate and a rear mass at the trailing edge. All the structure is free to rotate around the axle mounted in the center of the front cylinder. The model's geometry and mechanical properties are chosen in such a way as to attain a self-exciting periodical swiveling movement when exposed to a uniform laminar flow. Reproducibility of the coupled fluid–structure motion is the key criterion for the selection of the model in order to permit an accurate reconstruction of the results in the time-phase space. The Reynolds number of the tests varies up to 270 and within that range the structure undergoes large deformations and shows a strong nonlinear behavior. It also presents two different self-excitation mechanisms depending on the flow velocity. Hence, challenging tasks arise for both the numerical solution algorithm and the experimental measurements. To account for the two different excitation mechanisms observed on increasing the speed of the flow, results for two different velocities are considered: the first at 1.07 m/s (Re=140) and the second at 1.45 m/s (Re=195). The comparisons presented in this paper are carried out on the basis of the time trace of the front body angle, trailing edge coordinates, structure deformation and the time-phase resolved flow velocity field. They reveal very good agreement in some of the fluid–structure interaction modes whereas in others deficiencies are observed that need to be analyzed in more detail.

Un-spectral dimension and quantum spacetime phases

In this Letter, we propose a new scenario emerging from the conjectured presence of a minimal length ℓ in the spacetime fabric, on the one side, and the existence of a new scale invariant, continuous mass spectrum, of un-particles on the other side. We introduce the concept of un-spectral dimensionDU of a d-dimensional, euclidean (quantum) spacetime, as the spectral dimension measured by an “un-particle” probe. We find a general expression for the un-spectral dimension DU labelling different spacetime phases: a semi-classical phase, where ordinary spectral dimension gets contribution from the scaling dimension dU of the un-particle probe; a critical “Planckian phase”, where four-dimensional spacetime can be effectively considered two-dimensional when dU=1; a “Trans-Planckian phase”, which is accessible to un-particle probes only, where spacetime as we currently understand it looses its physical meaning.

Channel Equalization for Single Carrier MIMO Underwater Acoustic Communications

Multiple-input multiple-output (MIMO) underwater acoustic (UWA) channels introduce both space-time interference (STI) and time-varying phase distortion for transmitted signals. In such cases, the equalized symbols produced by conventional equalizer aiming for STI cancelation suffer phase rotation and thus cannot be reliably detected. In this paper, we propose a new equalization scheme for high data rate single carrier MIMO UWA channels. Different from existing methods employing joint equalization and symbolwise phase tracking technology, the proposed scheme decouples the interference cancelation (IC) operation and the phase compensation operation, leading to a generalized equalizer structure combining an IC equalizer with a phase compensator. The decoupling of the two functionalities leads to robust signal detection, which is most desirable in practical UWA applications. MIMO linear equalizer (LE) is adopted to remove space-time interference, and a groupwise phase estimation and correction method is used to compensate the phase rotation. In addition, the layered space-time processing technology is adopted to enhance the equalization performance. The proposed equalization scheme is tested to be very robust with extensive experimental data collected at Kauai, Hawaii, in September 2005, and Saint Margaret's Bay, Nova Scotia, Canada, in May 2006.

Metastable states and space-time phase transitions in a spin-glass model

We study large deviations of the dynamical activity in the random orthogonal model. This is a fully connected spin-glass model with one-step replica symmetry-breaking behavior, consistent with the random first-order transition scenario for structural glasses. We show that this model displays dynamical (space-time) phase transitions between active and inactive phases, as demonstrated by singularities in large deviation functions. We argue that such transitions are generic in systems with long-lived metastable states.

Oscillatory Spherical Traveling-Wave–Type Solutions to the Cardiac BVP

This study demonstrates how the assumption of a spherical traveling wave form for the general solution to the reaction–diffusion simplified cardiac system of PDEs can lead to a semi-analytical nonlinear iterative particular solution to an associated two-point boundary value problem (BVP). We demonstrate that a conventional traveling wave solution to this BVP does not exist in spherical geometry. Satisfaction, however, of a certain asymptotic parametric stability condition by the solution to the cardiac BVP is shown to be possible only when the spherical traveling wave speed is purely imaginary. The pertaining fundamentally oscillatory and bifurcative spherical traveling-wave–type solution yields further a direct iterative relation for the space–time phase of some associated scroll-type waves.

Higgs mechanism, quarks confinement and black holes as a Cantorian spacetime phase transition scenario

In a previous work it was argued that quarks confinement could be interpreted as a spacetime phase transition to a Planck Aether and thus removing the rather counter intuitive interpretation of asymptotic freedom at very tiny spacetime volume. In the present work we investigate this basic new interpretation both empirically using various experimental measurements as well as theoretically using E-infinity general theory. Extrapolating our model back to the Higgs field we argue that it may also be determined partially by the topology of spacetime itself and will involve physics that is black holes related.

Quarks confinement via Kaluza–Klein theory as a topological property of quantum classical spacetime phase transition

By introducing a curled fifth dimension, Kaluza–Klein theory predicted for the first time a connection between gravity and electromagnetism. An exacting look at this result shows that for a radius R of the fifth dimension equal to the Planck length, the coupling is exactly unity. The result is utilized to show that by introducing correction terms to the one loop renormalization equation of unification it can be made exact and subsequently quark confinement can be proven non-perturbatively as a property of the topology of quantum spacetime at the classical-quantum interface and the Planck phase transition.

Nonlinear Transformation of Differential Equations into Phase Space

Time-frequency representations transform a one-dimensional function into a two-dimensional function in the phase-space of time and frequency. The transformation to accomplish is a nonlinear transformation and there are an infinite number of such transformations. We obtain the governing differential equation for any two-dimensional bilinear phase-space function for the case when the governing equation for the time function is an ordinary differential equation with constant coefficients. This connects the dynamical features of the problem directly to the phase-space function and it has a number of advantages.

Operational time of arrival in quantum phase space

An operational time of arrival is introduced using a realistic position and momentum measurement scheme. The phase-space measurement involves the dynamics of a quantum particle probed by a measuring device. For such a measurement an operational positive operator-valued measure in phase space is introduced and investigated. In such an operational formalism a quantum-mechanical time operator is constructed and analyzed. A phase-space time and energy uncertainty relation is derived.

The Theory of Acceleration Within Its Context of Differential Invariants: The Root of the Problem with Cosmological Models?

Acceleration is an almost-sterile concept. However, since four-velocity is a four-dimensional (thus reduced) tangent vector field over geometric phase-spacetime (t, xi, ui), it yields a very rich concept of acceleration as a vector-valued 1-form. As in general relativity, the usual concept of acceleration comes out in the wash. By virtue of their nature, constants such as mass and charge are absent from this theory, though there is room for the concept of mass in the “renormalization” of the metric. Since, modulo these constants, force and acceleration become synonymous, the theory of acceleration (TOA) becomes a theory of “shadow” interactions: gravitational, electromagnetic (EM), and a third interaction that we refer to as “Third.” The TOA constitutes part of the theory of all the invariants associated with the above frames, namely, classical differential phase-space time geometry (PSTG). That is its context. The TOA connects with the remainder of PSTG through terms which appear in the acceleration 1-form but which fail to reach the equations of the motion. This absence splits the torsion into one part that we call “electromagnetic + Third” and another part, “Fourth,” which cannot manifest itself as a classical interaction. “Fourth,” which appears to shadow the weak interaction, nevertheless has gravitational effects through its contribution to the source side of Einstein's equations. It is, therefore, dark matter. Cosmological energy appears to be nothing but the energy of this particular type of dark matter, accounting for three quarters of the total. A cosmological term more sophisticated than the one involving the cosmological constant thus results.

Estimating the space-time phase fluctuations in radio waves generated by a turbulent propagation medium

Estimating the space-time phase fluctuations in radio waves generated by a turbulent propagation medium