Related papers: Fractal Weyl law for three-dimensional chaotic har…
For a Riemannian manifold $(M,g)$ which is isometric to the Euclidean space outside of a compact set, and whose trapped set has Liouville measure zero, we prove Weyl type asymptotics for the scattering phase with remainder depending on the…
The distribution of eigenvalues of the wave equation in a bounded domain is known as Weyl's problem. We describe several computational projects related to the cumulative state number, defined as the number of states having wavenumber up to…
Numerical calculation and analysis of extremely high-lying energy spectra, containing thousands of levels with sequential quantum number up to 62,000 per symmetry class, of a generic chaotic 3D quantum billiard is reported. The shape of the…
We study the properties of spectrum and eigenstates of the Google matrix of a directed network formed by the procedure calls in the Linux Kernel. Our results obtained for various versions of the Linux Kernel show that the spectrum is…
On a closed manifold $M$, we consider a smooth vector field $X$ that generates an Anosov flow. Let $V\in C^{\infty}\left(M;\mathbb{R}\right)$ be a smooth function called potential. It is known that for any $C>0$, there exists some…
Recently, intense efforts have been devoted to realizing classical analogues of various topological phases of matter. In this Letter, we explore the intriguing Weyl physics by a simple one-dimensional sonic crystal, in which two extra…
This paper focuses on the well-posedness (or lack thereof) of three-dimensional time-harmonic wave propagation problems modeled by the Helmholtz equation. It is well-known that if the problem is set in bounded domain with Dirichlet boundary…
We propose a scheme to simulate and explore Weyl semimetal physics with ultracold fermionic atoms in a two-dimensional square optical lattice subjected to experimentally realizable spin-orbit coupling and an artificial dimension from an…
Previous studies have shown that fractal scatterings in weak interactions of solitary waves in the generalized nonlinear Schr\"odinger equations are described by a universal second-order separatrix map. In this paper, this separatrix map is…
We construct meta-intransitive systems of independent random variables of any finite order from basic tuple of random variables which generalize intransitive dice. Under this construction, the equality of some linear functional is…
Friedel's law guarantees an inversion-symmetric diffraction pattern for thin, light materials where a kinematic approximation or a single-scattering model holds. Typically, breaking Friedel symmetry is ascribed to multiple scattering events…
We survey a number of Weyl type laws that have recently been established in low-dimensional symplectic geometry. These have had a number of applications, which we also introduce. We sketch a number of proofs so that the reader can get a…
We assume that the energy spectrum of a chaotic system undergoing symmetry breaking transitions can be represented as a superposition of independent level sequences, one increasing on the expense of the others. The relation between the…
Two-dimensional random Lorentz gases with absorbing traps are considered in which a moving point particle undergoes elastic collisions on hard disks and annihilates when reaching a trap. In systems of finite spatial extension, the…
We investigate the dynamics of the Weyl quasiparticles emerged in an optical lattice where the topological Weyl semimental and trivial band insulator phases can be adjusted with the on-site energy. The evolution of the density distribution…
We investigate the properties of the semiclassical short periodic orbit approach for the study of open quantum maps that was recently introduced in [M. Novaes, J.M. Pedrosa, D. Wisniacki, G.G. Carlo, and J.P. Keating, Phys. Rev. E 80,…
Fractal scatterings in weak solitary wave interactions is analyzed for generalized nonlinear Schr\"odiger equations (GNLS). Using asymptotic methods, these weak interactions are reduced to a universal second-order map. This map gives the…
We combine theories of scattering for linearized water waves and flexural waves in thin plates to characterize and achieve control of water wave scattering using floating plates. This requires manipulating a sixth-order partial differential…
Friedel's law states that the modulus of the Fourier transform of real functions is centrosymmetric, while the phase is antisymmetric. As a consequence of this, elastic scattering of plane wave photons or electrons within the first-order…
Our first experience of dimension typically comes in the intuitive Euclidean sense: a line is one dimensional, a plane is two-dimensional, and a volume is three-dimensional. However, following the work of Mandelbrot \cite{mandelbrot},…