相关论文: Markov spectra for modular billiards

A circular Andreev billiard in a uniform magnetic field is studied. It is demonstrated that the classical dynamics is pseudointegrable in the same sense as for rational polygonal billiards. The relation to a specific polygon, the asymmetric…

In this semi-expository paper we review the notion of a spherical space. In particular we present some recent results of Wedhorn on the classification of spherical spaces over arbitrary fields. As an application, we introduce and classify…

We study the Lawn Mowing Problem restricted to periodic billiard paths in the unit square. Given the combinatorial data of a trajectory, we determine the optimal covering radius, and identify the shortest path that covers the square for any…

In a unifying way, the doorway mechanism explains spectral properties in a rich variety of open mesoscopic quantum systems, ranging from atoms to nuclei. A distinct state and a background of other states couple to each other which…

The paper is devoted to the derivation of random unitary matrices whose spectral statistics is the same as statistics of quantum eigenvalues of certain deterministic two-dimensional barrier billiards. These random matrices are extracted…

Some of the subtleties of the integrability of the elliptic quantum billiard are discussed. A well known classical constant of the motion has in the quantum case an ill-defined commutator with the Hamiltonian. It is shown how this problem…

Random-matrix theory is used to show that the proximity to a superconductor opens a gap in the excitation spectrum of an electron gas confined to a billiard with a chaotic classical dynamics. In contrast, a gapless spectrum is obtained for…

We prove lower bounds on the error incurred when approximating any oscillating function using piecewise polynomial spaces. The estimates are explicit in the polynomial degree and have optimal dependence on the meshwidth and frequency when…

We give some properties of skew spectrum of a graph, especially, we answer negatively a problem concerning the skew characteristic polynomial and matching polynomial in [M. Cavers et al., Skew-adjacency matrices of graphs, Linear Algebra…

We investigate one of the simplest multi-species generalizations of the one dimensional exclusion process with reflective boundaries. The Markov matrix governing the dynamics of the system splits into blocks (sectors) specified by the…

The billiard systems within quadrics, playing the role of discrete analogues of geodesics on ellipsoids, are incorporated into the theory of integrable quad-graphs. An initial observation is that the Six-pointed star theorem, as the…

Black holes carrying a magnetic monopole charge are a subject of interest for a long time. In this work we explore the possibility of an observational evidence of such black holes carrying a magnetic monopole, namely the Bardeen rotating…

We obtain a lower bound for a number of primes in tuples. As applications, we obtain a lower bound for the Romanoff type representation functions.

I prove lower bounds of some parameters of elliptic curve over finite field. There parameters are closely interrelated with cryptographic stability of elliptic curve.

In this article, we illustrate how the concept of slope limiter can be interpreted graphically, i.e., how the slope of reconstructed piecewise linear function is limited by four bounding lines that connect cell-averaged data and its…

We develop a spectral analysis of a class of block Jacobi operators based on the conjugate operator method of Mourre. We give several applications including scalar Jacobi operators with periodic coefficients, a class of difference operators…

In this paper we provide some more details on the numerical analysis and we present some enlightening numerical results related to the spectrum of a finite element least-squares approximation of the linear elasticity formulation introduced…

For strictly convex billiard maps of smooth boundaries, we get a Birkhoff normal form via a list of constructive generating functions. Based on this, we get an explicit formula for the beta function (locally), and explored the relation…

We find an upper estimate for a splitting time of a thin parallel beam for irrational triangle billiards in terms of some number-theoretic function of angles. We provide an upper estimate on this function for some class of angles.

We give an upper bound on the largest eigenvalue of a graph of given order, size, and girth.