Related papers: Caustics and wave propagation in curved spacetimes
We develop a theoretical model to investigate wave propagation in media with random time-varying properties, where temporal fluctuations lead to complex scattering dynamics. Focusing on the ensemble-averaged field, we derive an exact…
We explore the description of bulk causal structure in a dual field theory. We observe that in the spacetime dual to a spacelike non-commutative field theory, the causal structure in the boundary directions is modified asymptotically. We…
We construct stationary flat three-dimensional Lorentzian manifolds with singularities that are obtained from Euclidean surfaces with cone singularities and closed one-forms on these surfaces. In the application to (2+1)-gravity, these…
We exhibit simple lattice systems, motivated by recently proposed cold atom experiments, whose continuum limits interpolate between real and $p$-adic smoothness as a spectral exponent is varied. A real spatial dimension emerges in the…
In the stringy cosmology, we investigate singularities in geodesic surface congruences for the time-like and null strings to yield the Raychaudhuri type equations possessing correction terms associated with the novel features owing to the…
We consider how causality and micro-causality are realised in QED in curved spacetime. The photon propagator is found to exhibit novel non-analytic behaviour due to vacuum polarization, which invalidates the Kramers-Kronig dispersion…
Using a five dimensional (5D) warped model with two branes along the extra dimension, we study the Green's functions for gauge bosons with a mass gap $m_g = \rho/2$ and a continuum for $s > m_g^2$. We find that the Green's functions exhibit…
In a 4-dimensional (4D) weak field geometry governed by the linearized Einstein's equations and sourced primarily by a static, spatially localized, but otherwise arbitrary mass density $T_{00}$, it is known that the leading order tail part…
This paper establishes uniqueness results of inverse elastic scattering problem with phaseless near-field data in periodic structures in $\mathbb{R}^2$ and periodic/biperiodic structures in $\mathbb{R}^3$. We use a superposition of two…
A rotating cosmic string spacetime has a singularity along a timelike curve corresponding to a one-dimensional source of angular momentum. Such spacetimes are not globally hyperbolic: they admit closed timelike curves near the string. This…
First theoretical and numerical results on the global structure of the energy shell, the Green function spectra and the eigenfunctions, both localized and ergodic, in a generic conservative quantum system are presented. In case of quantum…
Consider a discrete uniformly elliptic divergence form equation on the $d$ dimensional lattice $\Z^d$ with random coefficients. It has previously been shown that if the random environment is translational invariant, then the averaged…
The pointwise space-time behaviors of the Green's function and the global solution to the Vlasov-Poisson-Fokker-Planck (VPFP) system in spatial three dimension are studied in this paper. It is shown that the Green's function consists of the…
Conjugate points play an important role in the proofs of the singularity theorems of Hawking and Penrose. We examine the relation between singularities and conjugate points in FLRW spacetimes with a singularity. In particular we prove a…
Singularity theorems of general relativity utilize the notion of causal geodesic incompleteness as a criterion of the presence of a spacetime singularity. The incompleteness of a causal curve implies the end and/or beginning of the…
We investigate linear matter density perturbations in models of structure formation with causal seeds. Under the fluid approximation, we obtain the analytic solutions using Green-function technique. Some incorrect solutions in the…
This paper studies singularity structures of the linear inviscid damping of two-dimensional Euler equations in a finite periodic channel. We introduce a recursive definition of singularity structures which characterize the singularities of…
We study several quantities associated to the Green's function of a multiply connected domain in the complex plane. Among them are some intrinsic properties such as geodesics, curvature, and $L^2$-cohomology of the capacity metric and…
For Anderson Localization models with multifractal eigenvectors on disordered samples containing $N$ sites, we analyze in a unified framework the consequences for the statistical properties of the Green function. We focus in particular on…
The so-called ``analogue models of general relativity'' provide a number of specific physical systems, well outside the traditional realm of general relativity, that nevertheless are well-described by the differential geometry of curved…