Related papers: Fractal Weyl law for three-dimensional chaotic har…
In this paper, we study an inverse scattering problem at fixed energy on three-dimensional asymptotically hyperbolic St{\"a}ckel manifolds having the topology of toric cylinders and satisfying the Robertson condition. On these manifolds the…
This review is dedicated to some recent results on Weyl theory, inverse problems, evolution of the Weyl functions and applications to integrable wave equations in a semistrip and quarter-plane. For overdetermined initial-boundary value…
We prove the Weyl law for the volume spectrum for $1$-cycles in $n$-dimensional manifolds which was conjectured by Gromov. We follow the strategy of Guth and Liokumovich of obtaining the Weyl law from parametric versions of the coarea…
The correlation between the values of wavefunctions at two different spatial points is examined for chaotic systems with time-reversal symmetry. Employing a supermatrix method, we find that there exist long-range Friedel oscillations of the…
When a Dirac semimetal is subject to a circularly polarized laser, it is predicted that the Dirac cone splits into two Weyl nodes and a nonequilibrium transient state called the Floquet Weyl semimetal is realized. We focus on the previously…
Inspired by the similarity between the fractal Weierstrass function and quantum systems with discrete scaling symmetry, we establish general conditions under which the dynamics of a quantum system will exhibit fractal structure in the time…
Unconventional Weyl semimetals have attracted intensive research interest in condensed matter physics and materials science, but they are very rare in two dimensions. In this work, based on symmetry analysis and the first-principles…
Self-similar sets with open set condition, the linear objects of fractal geometry, have been considered mainly for crystallographic data. Here we introduce new symmetry classes in the plane, based on rotation by irrational angles. Examples…
This is a brief introduction to fractals, multifractals and wavelets in an accessible way, in order that the founding ideas of those strange and intriguing newcomers to science as fractals may be communicated to a wider public. Fractals are…
The Weyl equation describes chiral massless relativistic particles, called Weyl fermions, which have important relations to neutrinos. A direct observation of the dynamics of Weyl fermions in an experiment is difficult to achieve. This…
Fractional supersymmetric quantum mechanics is developed from a generalized Weyl-Heisenberg algebra. The Hamiltonian and the supercharges of fractional supersymmetric dynamical systems are built in terms of the generators of this algebra.…
We present a method of constructing discrete integrable systems with crystallographic reflection group (Weyl) symmetries, thus clarifying the relationship between different discrete integrable systems in terms of their symmetry groups.…
It has recently been demonstrated that it is possible to open a gap in a magnetic Weyl semimetal, while preserving the chiral anomaly along with the charge conservation and translational symmetries, which all protect the gapless nodes in a…
We consider a billiard model of a self-bound, interacting three-body system in two spatial dimensions. Numerical studies show that the classical dynamics is chaotic. The corresponding quantum system displays spectral fluctuations that…
In these lecture notes we present connections between the theory of iterated function systems, in particular those attractors that are graphs of multivariate real-valued fractal functions, foldable figures and affine Weyl groups, and…
This paper presents a new Lie theoretic approach to fractal calculus, which in turn yields such new results as a Fractal Noether's Theorem, a setting for fractal differential forms, for vector fields, and Lie derivatives, as well as…
This review article will present some recent results and methods in the study of 1-particle quantum or wave scattering systems, in the semiclassical/high frequency limit, in cases where the corresponding classical/ray dynamics is chaotic.…
Weyl semimetals are a new paradigmatic topological phase of matter featuring a gapless spectrum. One of its most distinctive features is the presence of Fermi arc surface states. Here, we report on atomistic simulations of the dc…
Atomization stretches and folds the liquid-gas interface before fragmenting it into ligaments and droplets, making fractal measures a natural descriptor of the breakup state. We examine this idea in two-dimensional volume-of-fluid direct…
A variety of quantum systems exhibits Weyl points in their spectra where two bands cross in a point of three-dimensional parameters space with conical dispersion in the vicinity of the point. We consider theoretically the soft constraint…