Search results for "discrete [space-time]"
showing 10 items of 2035 documents
Anomaly and global inconsistency matching: θ angles, SU(3)/U(1)2 nonlinear sigma model, SU(3) chains, and generalizations
2018
We discuss the SU(3)/[U(1)×U(1)] nonlinear sigma model in 1+1D and, more broadly, its linearized counterparts. Such theories can be expressed as U(1)×U(1) gauge theories and therefore allow for two topological θ angles. These models provide a field theoretic description of the SU(3) chains. We show that, for particular values of θ angles, a global symmetry group of such systems has a 't Hooft anomaly, which manifests itself as an inability to gauge the global symmetry group. By applying anomaly matching, the ground-state properties can be severely constrained. The anomaly matching is an avatar of the Lieb-Schultz-Mattis (LSM) theorem for the spin chain from which the field theory descends, …
Symmetry, winding number, and topological charge of vortex solitons in discrete-symmetry media
2009
[EN] We determine the functional behavior near the discrete rotational symmetry axis of discrete vortices of the nonlinear Schrodinger equation. We show that these solutions present a central phase singularity whose charge is restricted by symmetry arguments. Consequently, we demonstrate that the existence of high-charged discrete vortices is related to the presence of other off-axis phase singularities, whose positions and charges are also restricted by symmetry arguments. To illustrate our theoretical results, we offer two numerical examples of high-charged discrete vortices in photonic crystal fibers showing hexagonal discrete rotational invariance
A nonlocal problem describing spherical system of stars
2014
We prove in this note the existence and uniqueness of solutions of a nonlocal problem appearing as a model of galaxy in early stage of evolution. Some properties of solutions are also given.
Engineering the Success of Quantum Walk Search Using Weighted Graphs
2016
Continuous-time quantum walks are natural tools for spatial search, where one searches for a marked vertex in a graph. Sometimes, the structure of the graph causes the walker to get trapped, such that the probability of finding the marked vertex is limited. We give an example with two linked cliques, proving that the captive probability can be liberated by increasing the weights of the links. This allows the search to succeed with probability 1 without increasing the energy scaling of the algorithm. Further increasing the weights, however, slows the runtime, so the optimal search requires weights that are neither too weak nor too strong.
Weyl Asymptotics for the Damped Wave Equation
2019
The damped wave equation is closely related to non-self-adjoint perturbations of a self-adjoint operator P of the form $$\displaystyle P_\epsilon =P+i\epsilon Q. $$ Here, P is a semi-classical pseudodifferential operator of order 0 on L2(X), where we consider two cases: X = Rn and P has the symbol P ∼ p(x, ξ) + hp1(x, ξ) + ⋯ . in S(m), as in Sect. 6.1, where the description is valid also in the case n > 1. We assume for simplicity that the order function m(x, ξ) tends to + ∞, when (x, ξ) tends to ∞. We also assume that P is formally self-adjoint. Then by elliptic theory (and the ellipticity assumption on P) we know that P is essentially self-adjoint with purely discrete spectrum. X is a com…
Teaching Fourier optics through ray matrices
2005
In this work we examine the use of ray-transfer matrices for teaching and for deriving some topics in a Fourier optics course, exploiting the mathematical simplicity of ray matrices compared to diffraction integrals. A simple analysis of the physical meaning of the elements of the ray matrix provides a fast derivation of the conditions to obtain the optical Fourier transform. We extend this derivation to fractional Fourier transform optical systems, and derive the order of the transform from the ray matrix. Some examples are provided to stress this point of view, both with classical and with graded index lenses. This formulation cannot replace the complete explanation of Fourier optics prov…
Nodal solitons and the nonlinear breaking of discrete symmetry
2005
We present a new type of soliton solutions in nonlinear photonic systems with discrete point-symmetry. These solitons have their origin in a novel mechanism of breaking of discrete symmetry by the presence of nonlinearities. These so-called nodal solitons are characterized by nodal lines determined by the discrete symmetry of the system. Our physical realization of such a system is a 2D nonlinear photonic crystal fiber owning C6v symmetry.
White-light optical implementation of the fractional fourier transform with adjustable order control.
2000
An optical implementation of the fractional Fourier transform (FRT) with broadband illumination is proposed by use of a single imaging element, namely, a blazed diffractive lens. The setup displays an achromatized version of the FRT of order P of any two-dimensional input function. This fractional order can be tuned continuously by shifting of the input along the optical axis. Our compact and flexible configuration is tested with a chirplike input signal, and the good experimental results obtained support the theory.
Theory for the control of dark rays by means of discrete symmetry diffractive elements
2013
We present an analytical theory that describes the disintegration of a highly charged phase singularity by the presence of a thin discrete symmetry diffractive element, i.e., an optical diffractive element possessing rotational symmetry of finite order. The process is described in terms of dark rays, defined as the trajectories where there is no light, i.e., those for which the complex optical field vanishes. We provide explicit analytical expressions for the equations that describe the dark ray trajectories. We show that dark rays follow straight line trajectories asymptotically, like ordinary rays, but with properties which differ in essential features with respect to their bright counter…
Local dimensions in Moran constructions
2015
We study the dimensional properties of Moran sets and Moran measures in doubling metric spaces. In particular, we consider local dimensions and $L^q$-dimensions. We generalize and extend several existing results in this area.