Related papers: Topological Resonances in Scattering on Networks (…
Transmission through a complex network of nonlinear one-dimensional leads is discussed by extending the stationary scattering theory on quantum graphs to the nonlinear regime. We show that the existence of cycles inside the graph leads to a…
Quantized, compact graphs were shown to be excellent paradigms for quantum chaos in bounded systems. Connecting them with leads to infinity we show that they display all the features which characterize scattering systems with an underlying…
Synchronization and resonance on networks are some of the most remarkable collective dynamical phenomena. The network topology, or the nature and distribution of the connections within an ensemble of coupled oscillators, plays a crucial…
Can one hear the shape of a graph? This is a modification of the famous question of Mark Kac "Can one hear the shape of a drum?" which can be asked in the case of scattering systems such as quantum graphs and microwave networks. It…
The irreducible complexity of natural phenomena has led Graph Neural Networks to be employed as a standard model to perform representation learning tasks on graph-structured data. While their capacity to capture local and global patterns is…
We address the two-dimensional band-structure of graphene above the vacuum level in the context of discrete states immersed in the three-dimensional continuum. Scattering resonances are discovered that originate from the coupling of the…
We connect quantum graphs with infinite leads, and turn them to scattering systems. We show that they display all the features which characterize quantum scattering systems with an underlying classical chaotic dynamics: typical poles, delay…
In this paper, we try to put the results of Smilansky and al. on "Topological resonances" on a mathematical basis.A key role in the asymptotic of resonances near the real axis for Quantum Graphs is played by the set of metrics for which…
A complex network is said to show topological isotropy if the topological structure around a particular node looks the same in all directions of the whole network. Topologically anisotropic networks are those where the local neighborhood…
We investigate the topological properties of dynamical states evolving on periodic oriented graphs. This evolution, that encodes the scattering processes occurring at the nodes of the graph, is described by a single-step global operator, in…
Network-topology inference from (vertex) signal observations is a prominent problem across data-science and engineering disciplines. Most existing schemes assume that observations from all nodes are available, but in many practical…
Turing patterns, arising from the interplay between competing species of diffusive particles, has long been an important concept for describing non-equilibrium self-organization in nature, and has been extensively investigated in many…
Recent evidence indicates that the abundance of recurring elementary interaction patterns in complex networks, often called subgraphs or motifs, carry significant information about their function and overall organization. Yet, the…
Wave propagation through nodes and links of a network forms the basis of spectral graph theory. Nevertheless, the sound emitted by nodes within the resonating chamber formed by a network are not well studied. The sound emitted by vibrations…
Quantum graphs with leads to infinity serve as convenient models for studying various aspects of systems which are usually attributed to chaotic scattering. They are also studied in several experimental systems and practical applications.…
Quantum walks that depend smoothly on a small parameter $\varepsilon\ge0$ are considered on directed graphs. The asymptotic behavior of the scattering matrix of the quantum walk as $\varepsilon\to+0$ is investigated. It is shown that, in…
We study the resonant scattering for discrete time quantum walks on graphs with some tails. In our arguments, we reduce the study of resonances to the perturbation of eigenvalues of a finite rank matrix associated with the internal graph.…
A common feature of biological networks is the geometric property of self-similarity. Molecular regulatory networks through to circulatory systems, nervous systems, social systems and ecological trophic networks, show self-similar…
We connect quantum compact graphs with infinite leads, and turn them into scattering systems. We derive an exact expression for the scattering matrix, and explain how it is related to the spectrum of the corresponding closed graph. The…
This work develops a flexible and mathematically sound framework for the design and analysis of graph scattering networks with variable branching ratios and generic functional calculus filters. Spectrally-agnostic stability guarantees for…