Light-cone Research Articles

Traveling discontinuity at the quantum butterfly front

We formulate a kinetic theory of quantum information scrambling in the context of a paradigmatic model of interacting electrons in the vicinity of a superconducting phase transition. We carefully derive a set of coupled partial differential equations that effectively govern the dynamics of information spreading in generic dimensions. Their solutions show that scrambling propagates at the maximal speed set by the Fermi velocity. At early times, we find exponential growth at a rate set by the inelastic scattering. At late times, we find that scrambling is governed by shock-wave dynamics with traveling waves exhibiting a discontinuity at the boundary of the light cone. Notably, we find perfectly causal dynamics where the solutions do not spill outside of the light cone.

Learning From the Future: Light Cone Modeling for Sequential Recommendation.

Modeling sequential behaviors is the core of sequential recommendation. As users visit items in chronological order, existing methods typically capture a user's present interests from his/her past-to-present behaviors, i.e., making recommendations with only the unidirectional past information. This article argues that future information is another critical factor for the sequential recommendation. However, directly learning from future-to-present behaviors inevitably causes data leakage. Here, it is pointed out that future information can be learned from users' collaborative behaviors. Toward this end, this article introduces sequential graphs to depict item transition relationships: where and how each item transits from and will transit to. This temporal evolution information is called the light cone in special and general relativity. Then, a bidirectional sequential graph convolutional network (BiSGCN) is proposed to learn item representations by encoding past and future light cones. Finally, a manifold translating embedding (MTE) method is proposed to model item transition patterns in Riemannian manifolds, which helps to better capture the geometric structures of light cones and item transition patterns. Experimental comparisons and ablation studies verify the outstanding performance of BiSGCN, the benefits of learning from the future, and the improvements of learning in Riemannian manifolds.

Relativistic matter bispectrum of cosmic structures on the light cone

Upcoming surveys of cosmic structures will probe scales close to the cosmological horizon, which opens up new opportunities for testing the cosmological concordance model to high accuracy. In particular, constraints on the squeezed bispectrum could rule out the single-field hypothesis during inflation. However, the squeezed bispectrum is also sensitive to dynamical effects of general relativity as well as interactions of matter with residual radiation from the early Universe. In this paper, we present a relativistic simulation pipeline that includes these relativistic effects consistently. We produce light cones and calculate the observed number counts of cold dark matter for five redshift bins between z = 0.55-2.25. We compare the relativistic results against reference Newtonian simulations by means of angular power- and bispectra. We find that the dynamical relativistic effects scale roughly inversely proportional to the multipole in the angular power spectrum, with a maximum amplitude of 10% for ℓ ≲ 5. By using a smoothing method applied to the binned bispectrum we detect the Newtonian bispectrum with very high significance. The purely relativistic part of the matter bispectrum, obtained by subtracting the Newtonian bispectrum from the relativistic one, is detected with a significance of ∼ 3σ, mostly limited by cosmic variance. We find that the pure dynamical relativistic effects accounts for up to 3% and 10% of the total amplitude, respectively in the squeezed and equilateral limits. Our relativistic pipeline for modelling ultra-large scales yields gauge-independent results as we compute observables consistently on the past light cone, while the Newtonian treatment employs approximations that leave some residual gauge dependence. A gauge-invariant approach is required in order to meet the expected level of precision of forthcoming probes of cosmic structures on ultra-large scales.

The Hawking energy in a perturbed Friedmann-Lemaître universe

Hawking's quasi-local energy definition quantifies the energy enclosed by a spacelike 2-sphere in terms of the amount of lightbending on the sphere caused by the energy distribution inside the sphere. This paper establishes for the first time a direct connection between the formal mathematical definition of a quasi-local energy and observations, in the context of cosmological perturbation theory. This is achieved by studying the Hawking Energy of spherical sections of the past lightcone of a cosmic observer in a perturbed Friedmann-Lemaître spacetime. We express the Hawking Energy in terms of gauge-invariant perturbation variables and comment on the cosmic observables needed to in principle measure it. We then calculate its angular power spectrum and interpret its contributions.

The MillenniumTNG Project: the impact of baryons and massive neutrinos on high-resolution weak gravitational lensing convergence maps

ABSTRACT We study weak gravitational lensing convergence maps produced from the MillenniumTNG simulations by direct projection of the mass distribution on the past backwards lightcone of a fiducial observer. We explore the lensing maps over a large dynamic range in simulation mass and angular resolution, allowing us to establish a clear assessment of numerical convergence. By comparing full physics hydrodynamical simulations with corresponding dark-matter-only runs, we quantify the impact of baryonic physics on the most important weak lensing statistics. Likewise, we predict the impact of massive neutrinos reliably far into the non-linear regime. We also demonstrate that the ‘fixed & paired’ variance suppression technique increases the statistical robustness of the simulation predictions on large scales not only for time slices but also for continuously output lightcone data. We find that both baryonic and neutrino effects substantially impact weak lensing shear measurements, with the latter dominating over the former on large angular scales. Thus, both effects must explicitly be included to obtain sufficiently accurate predictions for stage IV lensing surveys. Reassuringly, our results agree accurately with other simulation results where available, supporting the promise of simulation modelling for precision cosmology far into the non-linear regime.

Global Stability for Charged Scalar Fields in an Asymptotically Flat Metric in Harmonic Gauge

We prove global stability for the charged scalar field system on a background spacetime, which is close to 1+3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1+3$$\\end{document}-dimensional Minkowski space and whose outward light cones converge to those for the Schwarzs-child metric at null infinity. The key technique to this proof is the use of a modified null frame, depending only on the mass M of the metric, which captures the asymptotic behavior of the metric at future null infinity. Our results are analogous to results obtained in Minkowski space by Lindblad and Sterbenz in (IMRP Int Math Res Pap 2006:52976, 2006) up to a change in coordinates, and will in the sequel be used to prove the full structure of the Einstein–charge scalar field system in these modified harmonic coordinates.

Extractions of |Vub|/|Vcb| from a combined study of the exclusive bto u(c){ell}^{-}{overline{nu}}_{ell } decays

We have extracted the ratio |Vub|/|Vcb| from a combined study of the available inputs on overline{B}to left(pi, rho, omega right){ell}^{-}{overline{nu}}_{ell } and overline{B}left({overline{B}}_sright)to left({D}^{left(ast right)},{D}_s^{left(ast right)}right){ell}^{-}{overline{nu}}_{ell } left(ell =mu textrm{or} eright) decays. We have done our analysis with and without the inclusion of the available experimental results on the branching fraction mathcal{BR}left({overline{B}}_sto {K}^{+}{mu}^{-}{overline{nu}}_{mu}right) or the ratio of the rates Gamma left({overline{B}}_sto {K}^{+}{ell}^{-}{overline{nu}}_{ell}right)/Gamma left({overline{B}}_sto {D}_s^{+}{ell}^{-}{overline{nu}}_{ell}right) . We have used all the available experimental data on the branching fractions in different q2-bins, the available theory inputs on the form factors from lattice and the light cone sum rule (LCSR) approach; analysed the data in different possible scenarios and presented the results. From a combined analysis of all the b → cℓ−νℓ exclusive decays, we have obtained |Vcb| = (40.5 ± 0.6) × 10−3 and from all the b → uℓ−νℓ modes, we obtain |Vub| = (3.46 ± 0.12) × 10−3 which changes to |Vub| = (3.51 ± 0.13) × 10−3 after dropping mathcal{BR}left({overline{B}}_sto {K}^{+}{mu}^{-}{overline{nu}}_{mu}right) . We hence report the values of the ratio |Vub|/|Vcb| = 0.085 ± 0.003 and 0.087 ± 0.003 with and without the input from {overline{B}}_sto {K}^{+}{mu}^{-}{overline{nu}}_{mu } modes, respectively. We have also predicted the ratio Gamma left({overline{B}}_sto {K}^{+}{ell}^{-}{overline{nu}}_{ell}right)/Gamma left({overline{B}}_sto {D}_s^{+}{ell}^{-}{overline{nu}}_{ell}right) using the fit results. In addition, we provide the predictions of mathcal{BR}left({overline{B}}_sto {K}^{+}{mu}^{-}{overline{nu}}_{mu}right) and mathcal{BR}left(overline{B}to left(rho, omega right){ell}^{-}{overline{nu}}_{ell}right) in the Standard Model (SM) in small q2-bins.

ALMACAL

It may be unsurprising that the most common approach to finding proto-clusters is to search for over-densities of galaxies. Upgrades to submillimetre (submm) interferometers and the advent of the James Webb Space Telescope will soon offer the opportunity to find more distant candidate proto-clusters in deep sky surveys without any spectroscopic confirmation. In this Letter, we report the serendipitous discovery of an extremely dense region centred on the blazar, J0217−0820, at z = 0.6 in the ALMACAL sky survey. Its density is eight times higher than that predicted by blind submm surveys. Among the seven submm-bright galaxies, three are as bright as conventional single-dish submm galaxies, with S870 μm > 3 mJy. The over-density is thus comparable to the densest known and confirmed proto-cluster cores. However, their spectra betray a wide range of redshifts. We investigate the likelihood of line-of-sight projection effects using light cones from cosmological simulations, finding that the deeper we search, the higher the chance that we will suffer from such projection effects. The extreme over-density around J0217−0820 demonstrates the strong cosmic variance we may encounter in the deep submm surveys. Thus, we should also question the fidelity of galaxy proto-cluster candidates selected via over-densities of galaxies, where the negative K correction eases the detection of dusty galaxies along an extraordinarily extended line of sight.

Time-like entanglement entropy in AdS/BCFT

We study the entanglement entropy for time-like subsystem in two-dimensional boundary conformal field theory (BCFT) both from the field theory and holographic point of view. In field theory, we compute the time-like entanglement entropy of a pure time-like interval at zero and finite temperature using the replica technique and analytical continuation. We find that, similar to the ordinary space-like entanglement entropy in BCFT, the time-like entropy also has a bulk phase and a boundary phase which corresponds respectively to the dominance of the identity block in the bulk and boundary OPE channels. However, we find that in Lorentzian BCFT, the time-like entanglement entropy posses a third Regge phase which arises in the Regge limit of the interval, when one endpoint of the time interval approaches the light cone of the mirror image of the other endpoint. We determine the phase diagram for the time-like entanglement entropy. We find that while the time-like entropy is complex in the bulk phase and has a boundary term in the boundary phase, there is no boundary entropy in the Regge phase. Moreover, it can be real or complex depending on which side the Regge limit is approached from. On the gravity side, we obtain the holographic time-like entanglement entropy from the corresponding bulk dual geometries and find exact agreement with the field theory results. The time-like entanglement entropy may be useful to describe the entanglement of a quantum dot on a half line.

Two dimensional wave-Klein–Gordon equations with a below-critical nonlinearity

In this paper we investigate the small data global existence and pointwise decay of solutions to two systems of coupled wave-Klein–Gordon equations in two spatial dimensions. In particular, we consider critical (in the sense of time decay) semilinear nonlinearities for the wave equation and below-critical semilinear nonlinearities for the Klein–Gordon equation, a situation that has not been studied before in the context of coupled wave and Klein–Gordon equations. An interesting feature of our two systems is that the below-critical nonlinearity causes the Klein–Gordon field to lose its linear behaviour close to the light cone, even though it enjoys optimal time decay.

Scalar topological photonic nested meta-crystals and skyrmion surface states in the light cone continuum.

Topological photonics is rapidly expanding. However, discovering three-dimensional topological electromagnetic systems can be more challenging than electronic systems for two reasons. First, the vectorial nature of electromagnetic waves results in complicated band dispersions, and simple tight-binding-type predictions usually fail. Second, topological electromagnetic surface modes inside the light cone have very low quality factors (Q factors). Here, we propose the concept of scalar topological photonics to address these challenges. Our approach is experimentally validated by employing a nested meta-crystal configuration using connected coaxial waveguides. They exhibit scalar-wave-like band dispersions, making the search for photonic topological phases an easier task. Their surface states have skyrmion-like electric field distributions, resulting in a whole, bright surface state band inside the light cone continuum. As such, the topological surface states in our three-dimensional nested crystals can be exposed to air, making such systems well-suited for practical applications.

Slowest and fastest information scrambling in the strongly disordered XXZ model

We present a perturbation method to compute the out-of-time-ordered correlator in the strongly disordered Heisenberg XXZ model in the deep many-body localized regime. We characterize the discrete structure of the information propagation across the eigenstates, revealing a highly structured light cone confined by the strictly logarithmic upper and lower bounds representing the slowest and fastest scrambling available in this system. We explain these bounds by deriving the closed-form expression of the effective interaction for the slowest scrambling and by constructing the effective model of a half length for the fastest scrambling. We extend our lowest-order perturbation formulations to the higher dimensions, proposing that the logarithmic upper and lower light cones may persist in a finite two-dimensional system in the limit of strong disorder and weak hopping.

Generalized parton distributions of sea quark at zero skewness in the light-cone model

We study the chiral-even generalized parton distributions (GPDs) of {bar{u}} and {bar{d}} quarks at zero skewness using the overlap representation within the light cone formalism. The GPDs of {bar{u}} and {bar{d}} quarks can be expressed as the convolution of the light cone wave functions which are obtained from the baryon-meson fluctuation model in terms of the |q{bar{q}}Brangle Fock states. We present the numerical results for H^{{bar{u}}/P}(x,xi ,Delta ^2), H^{{bar{d}}/P}(x,xi ,Delta ^2), E^{{bar{u}}/P}(x,xi ,Delta ^2) and E^{{bar{d}}/P}(x,xi ,Delta ^2). We apply the model resulting GPDs to calculate the orbital angular momentum of the {bar{u}} and {bar{d}} quarks, showing that L^{{bar{u}}/P}, L^{{bar{d}}/P} are positive and L^{{bar{u}}/P} is smaller than L^{{bar{d}}/P}. The sea quark OAM distributions in the impact parameter space L_{{bar{q}}}(x,{varvec{b}}_{varvec{T}}) are also calculated.

Mock X-Ray Observations of Hot Gas with L-Galaxies Semi-analytic Models of Galaxy Formation

We create mock X-ray observations of hot gas in galaxy clusters with a new extension of the L-Galaxies semi-analytic model of galaxy formation, which includes the radial distribution of hot gas in each halo. Based on the model outputs, we first build some mock light cones, then generate mock spectra with the SOXS package and derive the mock images in the light cones. Using the mock data, we simulate mock X-ray spectra for the ROSAT all-sky survey, and compare the mock spectra with the observational results. Then, we consider the design parameters of the HUBS mission and simulate the observation of the halo hot gas for HUBS as an important application of our mock work. We find: (1) our mock data match the observations by current X-ray telescopes. (2) The survey of hot baryons in resolved clusters by HUBS is effective below redshift 0.5, and the observations of the emission lines in point-like sources at z > 0.5 by HUBS help us understand the hot baryons in the early universe. (3) By taking advantage of the large simulation box and flexibility in semi-analytic models, our mock X-ray observations provide the opportunity to select targets and observation strategies for forthcoming X-ray facilities.

Long time behaviour of finite-energy radial solutions to energy subcritical wave equation in higher dimensions

We consider the defocusing, energy subcritical wave equation ∂t2u−Δu=−|u|p−1u in 4 to 6 dimensional spaces with radial initial data. We define w=r(d−1)/2u, reduce the equation above to one-dimensional equation of w and apply method of characteristic lines. This gives scattering of solutions outside any given light cone as long as the energy is finite. The scattering in the whole space can also be proved if we assume the energy decays at a certain rate as x→+∞. This generalizes the 3-dimensional results in Shen [32] to higher dimensions.

On the Cardinality of Future Worldlines in Discrete Spacetime Structures

We give an analysis over a variation of causal sets where the light cone of an event is represented by finitely branching trees with respect to any given arbitrary dynamics. We argue through basic topological properties of Cantor space that under certain assumptions about the universe, spacetime structure and causation, given any event x, the number of all possible future worldlines of x within the many-worlds interpretation is uncountable. However, if all worldlines extending the event x are ‘eventually deterministic’, then the cardinality of the set of future worldlines with respect to x is exactly $$\aleph _0$$ , i.e., countably infinite. We also observe that if there are countably many future worldlines with respect to x, then at least one of them must be necessarily ‘decidable’ in the sense that there is an algorithm which determines whether or not any given event belongs to that worldline. We then show that if there are only finitely many worldlines in the future of an event x, then they are all decidable. We finally point out the fact that there can be only countably many terminating worldlines.

Solutions with exponential singularity for (3 + 1)-D Protter problems

In the 1950s, Protter proposed multi-dimensional analogues of the classical Guderley–Morawetz problem for mixed-type hyperbolic-elliptic equations on the plane that models transonic flows in fluid dynamics. The multi-dimensional variants turn out to be different from the two-dimensional case and the situation there is still not clear. Here, we study Protter problems in the hyperbolic part of the domain. Unlike the planar analogues, the four-dimensional variant is not well-posed for classical solutions. The problem is not Fredholm — there is an infinite number of necessary conditions for classical solvability. Alternatively, the notion of a generalized solution that may have singularities was introduced. It is known that for smooth right-hand sides, the uniquely determined generalized solution may have a power-type growth at one boundary point. The singularity is isolated at the vertex of the boundary characteristic light cone and does not propagate along the cone. Here, we construct a new singular solution with an exponential growth at the point where the singularity appears.

Tight-focusing parabolic reflector schemes for petawatt lasers.

A comparative study of three different tight-focusing schemes for high-power lasers is performed numerically. Using the Stratton-Chu formulation, the electromagnetic field in the vicinity of the focus is evaluated for a short-pulse laser beam incident upon an on-axis high numerical aperture parabola (HNAP), an off-axis parabola (OAP), and a transmission parabola (TP). Linearly- and radially-polarized incident beams are considered. It is demonstrated that while all the focusing configurations yield intensities above 1023 W/cm2 for a 1 PW incident beam, the nature of the focused field can be drastically modified. In particular, it is shown that the TP, with its focal point behind the parabola, actually converts an incoming linearly-polarized beam into an m = 2 vector beam. The strengths and weaknesses of each configuration are discussed in the context of future laser-matter interaction experiments. Finally, a generalization of NA calculations up to 4π-illumination is proposed through the solid angle formulation, providing a universal way to compare light cones from any kind of optics.

Quenched Kitaev chain: Analogous model of gravitational collapse

We investigate generalized thermalization in an isolated free fermionic chain evolving from an out of equilibrium initial state through a sudden quench. We consider the quench where a fermionic chain is broken into two disjoint chains. We focus on the evolution of the local observables namely, occupation number, nearest neighbor hopping, information sharing and out-of-time-order correlations after the quench and study the relaxation of the observable, leading to generalized Gibbs ensemble for the system in the thermodynamic limit though it has been argued that noninteracting or free fermionic models in general do not relax to the generalized Gibbs ensemble (GGE). We obtain the light cone formed by the evolution of the observables along the fermionic lattice chain due to the sudden quench which abides by the Lieb-Robinson bound in quantum systems. We also analytically study a simpler model which captures the essential features of the system. Our analysis strongly suggest that the internal interactions within the system do not remain of much importance once the quench is sufficiently strong.

Electromagnetic field theory in superluminal spacetime

Recently, a number of experimental observations on the superluminal group velocities of pulses propagating in dispersive media have led to reconsidering electromagnetism theory in an unconventional framework. To consider faster-than-light phenomena, it is not necessary to replace the current relativistic theory, but it is sufficient to extend it to superluminal motions in a way that preserves the principle of causality. In the present paper, a new approach to study superluminal motions is proposed, which avoids introducing unphysical complex quantities and allows for the formulation of equations that are covariant according to a hyperbolic metric. In the framework of this formalism, Maxwell equations and the single-photon wave equation are obtained through superluminal transformations of ordinary equations. It is shown that the covariant and contravariant components of the superluminal electromagnetic field determine its magnitude and direction, respectively. Furthermore, the solutions of the transformed Maxwell equations are X-shaped ways propagating in the superluminal spacetime region that is delimited by the infinite light cone and the two-sheeted hyperboloid perpendicular to it. Instead, in quantum mechanics, the covariant and contravariant components of the electromagnetic field are proportional to the right- and left-handed helicities of the single photon, respectively.