Related papers: Locating Ruelle-Pollicott resonances
Spectrum cartography aims at estimating power propagation patterns over a geographical region across multiple frequency bands (i.e., a radio map)---from limited samples taken sparsely over the region. Classic cartography methods are mostly…
The spectral properties of interacting strongly chaotic systems are investigated for growing interaction strength. A very sensitive transition from Poisson statistics to that of random matrix theory is found. We introduce a new random…
We consider a sequence of matrices that are associated to Markov dynamical systems and use determinant-free linear algebra techniques (as well as some algebra and complex analysis) to rigorously estimate the eigenvalues of every matrix…
Perturbative expansions in physical applications are generically divergent, and their physical content can be studied using Borel analysis. Given just a finite number of terms of such an expansion, this input data can be analyzed in…
We describe extensive computational experiments on spectral properties of random objects - random cubic graphs, random planar triangulations, and Voronoi and Delaunay diagrams of random (uniformly distributed) point sets on the sphere). We…
We use scattering theoretic methods to prove strong dynamical and exponential localization for one dimensional, continuum, Anderson-type models with singular distributions; in particular the case of a Bernoulli distribution is covered. The…
We develop a universal approach enabling the study of any multimode quantum optical system evolving under a quadratic Hamiltonian. Our strategy generalizes the standard symplectic analysis and permits the treatment of multimode systems even…
We introduce a transfer matrix method for the spectral analysis of discrete Hermitian operators with locally finite hopping. Such operators can be associated with a locally finite graph structure and the method works in principle on any…
We propose numerical schemes for the approximate solution of problems defined on the edges of a one-dimensional graph. In particular, we consider linear transport and a drift-diffusion equations, and discretize them by extending Finite…
Unitary transformations are an essential tool for the theoretical understanding of many systems by mapping them to simpler effective models. A systematically controlled variant to perform such a mapping is a perturbative continuous unitary…
We suggest and implement an approach for the bottom-up description of systems undergoing large-scale structural changes and chemical transformations from dynamic atomically resolved imaging data, where only partial or uncertain data on…
The aim of the paper is firstly to study domains of definitions in terms of boundary conditions of minimal and maximal operators, as well as selfadjoint extensions of a minimal operator associated with the fourth-order differential operator…
We give sufficient conditions for the uniform hyperbolicity of certain nonuniformly hyperbolic dynamical systems. In particular, we show that local diffeomorphisms that are nonuniformly expanding on sets of total probability are necessarily…
We investigate spectral and dynamical localization of a quantum system of $ n $ particles on $ \mathbb{R}^d $ which are subject to a random potential and interact through a pair potential which may have infinite range. We establish two…
This work was intended as an attempt to extend the results on localization of Fourier-Laplace series to the spectral expansions of distributions on the unit sphere. It is shown that the spectral expansions of the distribution on the unit…
The structure of real-world networks is usually difficult to characterize owing to the variation of topological scales, the nondyadic complex interactions, and the fluctuations in the network. We aim to address these problems by introducing…
A new set of discrete ordinates is proposed for one-dimensional radiative transfer in spheres with central symmetry. The set is structured with un-normalized circular functions. This resulted in a conservative and closed set of discrete…
The content of this contribution is based on the course on numerical analysis techniques for non-linear dynamics. After introducing basic concepts as the visual analysis of trajectories in phase space and the importance of the nature of…
Spectral analysis in conjunction with discrete data in one and more dimensions can become a challenging task, because the methods are sometimes difficult to understand. This paper intends to provide an overview about the usage of the…
The mechanisms of information transmission are investigated in a lattice of coupled continuous maps, by analyzing the propagation of both finite and infinitesimal disturbances. Two distinct regimes are detected: in the former case, both…