Related papers: A graph-theoretic approach to chaos and complexity…
We address the properties of continuous-time quantum walks with Hamiltonians of the form $\mathcal{H}= L + \lambda L^2$, being $L$ the Laplacian matrix of the underlying graph and being the perturbation $\lambda L^2$ motivated by its…
Traditional traffic optimization solutions assume that the graph structure of road networks is static, missing opportunities for further traffic flow optimization. We are interested in optimizing traffic flows as a new type of graph-based…
In classical dynamical systems, chaotic behavior is often associated with exponential sensitivity to initial conditions together with global phase-space structure. Translating this geometric concept to the strictly linear framework of…
Adapting a method developed for the study of quantum chaos on {\it quantum (metric)} graphs \cite {KS}, spectral $\zeta$ functions and trace formulae for {\it discrete} Laplacians on graphs are derived. This is achieved by expressing the…
In this work we study the relationship between quantum random walks on graphs and Krylov/spread complexity. We show that the latter's definition naturally emerges through a canonical method of reducing a graph to a chain, on which we can…
It was recently shown how graphs can be used to provide descriptions of psychopathologies, where symptoms of, say, depression, affect each other and certain configurations determine whether someone could fall into a sudden depression. To…
Holographic theories with classical gravity duals are maximally chaotic; i.e., they saturate the universal bound on the rate of growth of chaos. It is interesting to ask whether this property is true only for leading large $N$ correlators…
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…
We study the complexity of a classic problem in computational topology, the homology problem: given a description of some space $X$ and an integer $k$, decide if $X$ contains a $k$-dimensional hole. The setting and statement of the homology…
Dynamical systems appear in nearly every aspect of the physical world. As such, understanding the properties of dynamical systems is of great importance. Typically, a dynamical system is described by a system of ordinary differential…
Chaotic functions are characterized by sensitivity to initial conditions, transitivity, and regularity. Providing new functions with such properties is a real challenge. This work shows that one can associate with any Boolean network a…
This paper presents graph theoretic conditions for the controllability and accessibility of bilinear systems over the special orthogonal group, the special linear group and the general linear group, respectively, in the presence of drift…
The out-of-time ordered correlator (OTOC) is a measure of scrambling of quantum information. Scrambling is intuitively considered to be a significant feature of chaotic systems and thus the OTOC is widely used as a measure of chaos. For…
Chaos transition, as an important topic, has become an active research subject in non-linear science. By considering a Dicke Hamiltonian coupled to a bath of harmonic oscillator, we have been able to introduce a logistic map with quantum…
Time-continuous dynamical systems defined on graphs are often used to model complex systems with many interacting components in a non-spatial context. In the reverse sense attaching meaningful dynamics to given 'interaction diagrams' is a…
Discrete versions of the Laplace and Dirac operators haven been studied in the context of combinatorial models of statistical mechanics and quantum field theory. In this paper we introduce several variations of the Laplace and Dirac…
The control of bilinear systems has attracted considerable attention in the field of systems and control for decades, owing to their prevalence in diverse applications across science and engineering disciplines. Although much work has been…
We present and validate simple and efficient methods to estimate the chaoticity of orbits in low dimensional dynamical systems from computations of Lagrangian descriptors (LDs) on short time scales. Two quantities are proposed for…
We study the finite-temperature scrambling behavior of a quantum system described by a Hamiltonian chosen from a random matrix ensemble. This effectively (0+1)-dimensional model admits an exact calculation of various ensemble-averaged…
Continuous cellular automata (CCAs) have evolved from discrete lookup tables to continuous partial differential equation (PDE) formulations in the search for novel forms of complexity. Despite innovations in qualitative behavior, analytical…