相关论文: Refracting profiles and generalized holodiagrams
We develop the formalism of derived divided power algebras, and revisit the theory of derived De Rham and derived crystalline cohomology in this framework. We characterize derived De Rham cohomology of a derived commutative algebra $A$ over…
The holographic principle is represented as the well-known de Alfaro, Fubini and Furlan correspondence between the generating functional for the Green functions of the Euclidean quantum field theory in $D$ dimensions and the Gibbs average…
A generalized notion of oscillatory integrals that allows for inhomogeneous phase functions of arbitrary positive order is introduced. The wave front set of the resulting distributions is characterized in a way that generalizes the…
Diffraction images with continuous rotation symmetry arise from amorphous systems, but also from regular crystals when investigated by powder diffraction. On the theoretical side, pinwheel patterns and their higher dimensional…
This short note revisits the classical result that the complete caustic by refraction of a circle is the evolute of Cartesian ovals. We provide additional details to the statement and geometric proof of this fact, as presented in G.…
We construct a semiclassical theory for propagation of an optical wavepacket in non-conducting media with periodic structures of dielectric permittivity and magnetic permeability, i.e., non-conducting photonic crystals. We employ a…
We introduce several possible generalizations of tomography for quadratic surfaces. We analyze different types of elliptic, hyperbolic and hybrid tomograms. In all cases it is possible to consistently define the inverse tomographic map. We…
In AdS/CFT corresponding, the UV divergence of generating functional on the field theory can be removed as the IR divergence in the gravity. This geometric process is well known as holographic renormalization. The standard method of…
Binary systems of two compact objects circularize and spiral toward each other via the emission of gravitational waves. The coupling of the spins of each object with the orbital angular momentum causes the orbital plane to precess, which…
Holography has emerged as a vital approach to fully engineer the wavefronts of light since its invention dating back to the last century. However, the typically large pixel size, small field of view and limited space-bandwidth impose…
We consider the inverse problem of the broken ray transform (sometimes also referred to as the V-line transform). Explicit image reconstruction formulas are derived and tested numerically. The obtained formulas are generalizations of the…
Tomography is the three-dimensional reconstruction of an object from images taken at different angles. The term classical tomography is used, when the imaging beam travels in straight lines through the object. This assumption is valid for…
The generalization of (super)integrable Euclidean classical Hamiltonian systems to the two-dimensional sphere and the hyperbolic space by preserving their (super)integrability properties is reviewed. The constant Gaussian curvature of the…
Bifurcations of classical orbits introduce divergences into semiclassical spectra which have to be smoothed with the help of uniform approximations. We develop a technique to extract individual energy levels from semiclassical spectra…
In this article we classify normal forms and unfoldings of linear maps in eigenspaces of (anti)-automorphisms of order two. Our main motivation is provided by applications to linear systems of ordinary differential equations, general and…
This paper presents investigations on the generalized laws of refraction and reflection for metasurfaces made of diffractive elements. It introduces a phenomenological model that reproduces all the features of the experiments dedicated to…
Despite the advances in the development of numerical methods analytical approaches still play the key role on the way towards a deeper understanding of many-particle systems. In this regards, diagonalization schemes for Hamiltonians…
This paper concerns diffraction-tomographic reconstruction of an object characterized by its scattering potential. We establish a rigorous generalization of the Fourier diffraction theorem in arbitrary dimension, giving a precise relation…
The main purpose of this paper is to lay the foundations of a general theory which encompasses the features of the classical Hough transform and extend them to general algebraic objects such as affine schemes. The main motivation comes from…
A general type of localized excitations, folded solitary waves and foldons, are defined and studied both analytically and graphically. The folded solitary waves and foldons may be "folded" in quite complicated ways and possess quite rich…