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A general scheme to calculate dynamical susceptibilities of strongly correlated electron systems within the dynamical mean field theory is developed. Approach is based on an expansion over electron hopping around the atomic limit (within…
Using random matrices, we study the reduced dynamics of a two level system interacting with a generic environment. In the weak coupling limit, the result can be obtained directly from known results for purity decay, and result in Markovian…
Markovian population models are suitable abstractions to describe well-mixed interacting particle systems in situation where stochastic fluctuations are significant due to the involvement of low copy particles. In molecular biology,…
Random metastability occurs when an externally forced or noisy system possesses more than one state of apparent equilibrium. This work investigates fluctuations in a class of random dynamical systems, arising from randomly perturbing a…
We characterize the macroscopic attractor of infinite populations of noisy maps subjected to global and strong coupling by using an expansion in order parameters. We show that for any noise amplitude there exists a large region of strong…
Photons strongly coupled to material systems constitute a novel system for studying the dynamics of non-equilibrium quantum many-body systems. We give a fully analytical description of the dynamics of photons coupled to a one-dimensional…
This paper investigates the stability and stabilization of diffusively coupled network dynamical systems. We leverage Lyapunov methods to analyze the role of coupling in stabilizing or destabilizing network systems. We derive critical…
The study of the interplay between the structure and dynamics of complex multilevel systems is a pressing challenge nowadays. In this paper, we use a semi-annealed approximation to study the stability properties of Random Boolean Networks…
We analyst in detail a new approach to the monitoring and forecasting of the onset of transitions in high dimensional complex systems (see Phys. Rev. Lett . vol. 113, 264102 (2014)) by application to the Tangled Nature Model of evolutionary…
In many complex systems, the dynamical evolution of the different components can result in adaptation of the connections between them. We consider the problem of how a fully connected network of discrete-state dynamical elements which can…
The paper presents a method by which the mean field dynamics of a population of dynamical systems with parameter diversity and global coupling can be described in terms of a few macroscopic degrees of freedom. The method applies to…
The thermodynamic framework of repeated interactions is generalized to an arbitrary open quantum system in contact with a heat bath. Based on these findings the theory is then extended to arbitrary measurements performed on the system. This…
The Hamiltonian of a recently proposed supersymmetric matrix model has been shown to become block-diagonal in the large-N, infinite 't Hooft coupling limit. We show that (most of) these blocks can be mapped into seemingly non-supersymmetric…
In this paper we present a rigorous analysis of a class of coupled dynamical systems in which two distinct types of components, one excitatory and the other inhibitory, interact with one another. These network models are finite in size but…
A quantum system weakly interacting with a fast environment usually undergoes a relaxation with complex frequencies whose imaginary parts are damping rates quadratic in the coupling to the environment, in accord with Fermi's ``Golden…
A fundamental concept in control theory is that of controllability, where any system state can be reached through an appropriate choice of control inputs. Indeed, a large body of classical and modern approaches are designed for controllable…
We prove an invariance principle for non-stationary random processes and establish a rate of convergence under a new type of mixing condition. The dependence is exponentially decaying in the gap between the past and the future and is…
When describing the effective dynamics of an observable in a many-body system, the repeated randomness assumption, which states that the system returns in a short time to a maximum entropy state, is a crucial hypothesis to guarantee that…
This note illustrates the possibility in simple loaded string models of trapping most of the system energy in a single degree of freedom for very long times, demonstrating in particular that the robustness of the trapping is enhanced by…
We investigate the dynamics of a two-level system in the presence of an overall environment composed of two layers. The first layer is just one single-mode cavity which decays to memoryless reservoir while the second layer is the two…