Related papers: Continuous Limit of Discrete Sawtooth Maps and its…
The study of hypersurfaces in a torus leads to the beautiful zoo of amoebas and their contours, whose possible configurations are seen from combinatorial data. There is a deep connection to the logarithmic Gauss map and its critical points.…
We study the ergodic properties of quantized ergodic maps of the torus. It is known that these satisfy quantum ergodicity: For almost all eigenstates, the expectation values of quantum observables converge to the classical phase-space…
Quantum walks can be defined in two quite distinct ways: discrete-time and continuous-time quantum walks (DTQWs and CTQWs). For classical random walks, there is a natural sense in which continuous-time walks are a limit of discrete-time…
The concept of fixed-area states has proven useful for recent studies of quantum gravity, especially in connection with gravitational holography. We explore the Lorentz-signature spacetime geometry intrinsic to such fixed-area states in…
On a family of classical dynamical systems on the 2-torus, we perform a discretization procedure similar to the Anti-Wick quantization. Such a discretization is performed by using a particular class of states, fulfilling an appropriate…
In this paper, we efficiently compute overapproximating reachable sets for control systems evolving on Lie groups, building off results from monotone systems theory and geometric integration theory. We consider intervals in the tangent…
Mixing properties of discrete-time quantum walks on two-dimensional grids with torus-like boundary conditions are analyzed, focusing on their connection to the complexity of the corresponding abstract search algorithm. In particular, an…
We study the cover time $\tau_{\mathrm{cov}}$ by (continuous-time) random walk on the 2D box of side length $n$ with wired boundary or on the 2D torus, and show that in both cases with probability approaching 1 as $n$ increases,…
The structure of the set of local dimensions of a self-similar measure has been studied by numerous mathematicians, initially for measures that satisfy the open set condition and, more recently, for measures on $\mathbb{R}$ that are of…
We address the problem related to the extraction of the information in the simulation of complex dynamics quantum computation. Here we present an example where important information can be extracted efficiently by means of quantum…
We investigate special lcs and twisted Hamiltonian torus actions on strict lcs manifolds and characterize them geometrically in terms of the minimal presentation. We prove a convexity theorem for the corresponding twisted moment map,…
The continuous limit of one dimensional discrete-time quantum walks with time- and space-dependent coefficients is investigated. A given quantum walk does not generally admit a continuous limit but some families (1-jets) of quantum walks…
We define the generalized logarithmic Gauss map for algebraic varieties of the complex algebraic torus of any codimension. Moreover, we describe the set of critical points of the logarithmic mapping restricted to our variety, and we show an…
A motion of a mechanism is a curve in its configuration space (c-space). Singularities of the c-space are kinematic singularities of the mechanism. Any mobility analysis of a particular mechanism amounts to investigating the c-space…
A generalized moment map is proposed for arbitrary symplectic actions of compact connected Lie groups on closed symplectic manifolds, in the spirit of the circle -valued maps introduced by D. McDuff in the case of non-Hamiltonian circle…
We discuss the simulation of a complex dynamical system, the so-called quantum sawtooth map model, on a quantum computer. We show that a quantum computer can be used to efficiently extract relevant physical information for this model. It is…
We consider the strong solution of the 2D Navier-Stokes equations in a torus subject to an additive noise. We implement a fully implicit time numerical scheme and a finite element method in space. We prove that the rate of convergence of…
The work that consists of two parts is devoted to the problem of enumerating unrooted $r$-regular maps on the torus up to all its symmetries. We begin with enumerating near-$r$-regular rooted maps on the torus, projective plane and the…
In this paper we construct a sequence of eigenfunctions of the ``quantum Arnold's cat map'' that, in the semiclassical limit, show a strong scarring phenomenon on the periodic orbits of the dynamics. More precisely, those states have a…
Classical and quantum properties of a discontinuous perturbed twist map are investigated. Different classical diffusive regimes, quasilinear and slow respectively, are observed. The regime of slow classical diffusion gives rise to two…