Related papers: Approximations by graphs and emergence of global s…
We develop a new framework for generalizing approximation algorithms from the structural graph algorithm literature so that they apply to graphs somewhat close to that class (a scenario we expect is common when working with real-world…
A spin system is a framework in which the vertices of a graph are assigned spins from a finite set. The interactions between neighbouring spins give rise to weights, so a spin assignment can also be viewed as a weighted graph homomorphism.…
We study fluctuation properties in the energy spectra of finite-size honeycomb lattices, graphene billiards, subject to the Haldane-model onsite potential and next-nearest neighbor interaction at critical points, referred to as Haldane…
Inspired by previous work of Diaz, Petit, Serna, and Trevisan (Approximating layout problems on random graphs Discrete Mathematics, 235, 2001, 245--253), we show that several well-known graph layout problems are approximable to within a…
We study quantum-mechanical tunneling between symmetry-related pairs of regular phase space regions that are separated by a chaotic layer. We consider the annular billiard, and use scattering theory to relate the splitting of…
We propose an approach to quantize discrete networks (graphs with discrete edges). We introduce a new exact solution of discrete Schrodinger equation that is used to write the solution for quantum graphs. Formulation of the problem and…
We obtained the spectrum of the Sinai billiard as the zeroes of a secular equation, which is based on the scattering matrix of a related scattering problem. We show that this quantization method provides an efficient numerical scheme, and…
We consider a Sinai billiard where the usual hard disk scatterer is replaced by a repulsive potential with $V(r)\sim\lambda r^{-\alpha}$ close to the origin. Using periodic orbit theory and numerical evidence we show that its spectral…
We consider an elliptic billiard whose shape slowly changes. During slow evolution of the billiard certain resonance conditions can be fulfilled. We study the phenomena of capture into a resonance and scattering on resonances which lead to…
We study how the structure of the interaction graph of a game affects the existence of pure Nash equilibria. In particular, for a fixed interaction graph, we are interested in whether there are pure Nash equilibria arising when random…
Many real-world networks of interest are embedded in physical space. We present a new random graph model aiming to reflect the interplay between the geometries of the graph and of the underlying space. The model favors configurations with…
The seminal physical model for investigating formulations of nonlinear dynamics is the billiard. Gravitational billiards provide an experimentally accessible arena for their investigation. We present a mathematical model that captures the…
Quantum cavities or dots have markedly different properties depending on whether their classical counterparts are chaotic or not. Connecting a superconductor to such a cavity leads to notable proximity effects, particularly the appearance,…
In a graphical game agents play with their neighbors on a graph to achieve an appropriate state of equilibrium. Here relevant problems are characterizing the equilibrium set and discovering efficient algorithms to find such an equilibrium…
In the tight-binding approximation we consider multi-channel transmission through a billiard coupled to leads. Following Dittes we derive the coupling matrix, the scattering matrix and the effective Hamiltonian, but take into account the…
The periodic discrete Toda equation defined over finite fields has been studied. We obtained the finite graph structures constructed by the network of states where edges denote possible time evolutions. We simplify the graphs by introducing…
Theoretical quest of flat-band tight-binding models usually relies on lattice structures on which electrons reside. Typical examples of candidate lattice structures include the Lieb-type lattices and the line graphs. Meanwhile, there can be…
Nonlinear coupling between eigenmodes of a system leads to spectral energy redistribution. For multi-wavespeed chaotic billiards the average coupling strength can exhibit sharp discontinuities as a function of frequency related to…
We give polynomial-time approximation schemes for monotone maximization problems expressible in terms of distances (up to a fixed upper bound) and efficiently solvable in graphs of bounded treewidth. These schemes apply in all fractionally…
In distributed systems, knowledge of the network structure of the connections among the unitary components is often a requirement for an accurate prediction of the emerging collective dynamics. However, in many real-world situations, one…