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Synchronization is a crucial phenomenon in many natural and artificial complex network systems. Applications include neuronal networks, formation control and coordination in robotics, and frequency synchronization in electrical power grids.…
Complex networks possess a rich, multi-scale structure reflecting the dynamical and functional organization of the systems they model. Often there is a need to analyze multiple networks simultaneously, to model a system by more than one…
A new type of collective excitations, due exclusively to the topology of a complex random network that can be characterized by a fractal dimension $D_F$, is investigated. We show analytically that these excitations generate phase…
Whether long-range interactions allow for a form of causality in non-relativistic quantum models remains an open question with far-reaching implications for the propagation of information and thermalization processes. Here, we study the…
We present a general theory for the onset of coherence in collections of heterogeneous maps interacting via a complex connection network. Our method allows the dynamics of the individual uncoupled systems to be either chaotic or periodic,…
Quantifying entanglement of multiple subsystems is a challenging open problem in interacting quantum systems. Here, we focus on two subsystems of length $\ell$ separated by a distance $r=\alpha\ell$ and quantify their entanglement…
We implement an efficient strong-disorder renormalization-group (SDRG) procedure to study disordered tight-binding models in any dimension and on the Erdos-Renyi random graphs, which represent an appropriate infinite dimensional limit. Our…
We study nonequilibrium dynamical properties of inhomogeneous systems, in particular at a free surface or at a defect plane. Thereby we consider nonconserved (model-A) dynamics of a system which is prepared in the high-temperature phase and…
We consider a percolation model, the vacant set $\mathcal{V}^u$ of random interlacements on $\mathbb{Z}^d$, $d \geq 3$, in the regime of parameters $u>0$ in which it is strongly percolative. By definition, such values of $u$ pinpoint a…
For networks of pulse-coupled oscillators with complex connectivity, we demonstrate that in the presence of coupling heterogeneity precisely timed periodic firing patterns replace the state of global synchrony that exists in homogenous…
Quantum cluster theories are a set of approaches for the theory of correlated and disordered lattice systems, which treat correlations within the cluster explicitly, and correlations at longer length scales either perturbatively or within a…
We present a unifying, consistent, finite-size-scaling picture for percolation theory bringing it into the framework of a general, renormalization-group-based, scaling scheme for systems above their upper critical dimensions $d_c$.…
In the last decade, the quantum chemical version of the density matrix renormalization group (DMRG) method has established itself as the method of choice for calculations of strongly correlated molecular systems. Despite its favourable…
We study the strong-coupling (SC) interaction between two like-charged membranes of finite thickness embedded in a medium of higher dielectric constant. A generalized SC theory is applied along with extensive Monte-Carlo simulations to…
The density matrix renormalization group (DMRG) method allows an efficient computation of the properties of interacting 1D quantum systems. Two-dimensional (2D) systems, capable of displaying much richer quantum behavior, generally lie…
We present the results of extensive Monte Carlo simulations of Ising models with algebraically decaying ferromagnetic interactions in the regime where classical critical behavior is expected for these systems. We corroborate the values for…
In many real, directed networks, the strongly connected component of nodes which are mutually reachable is very small. This does not fit with current theory, based on random graphs, according to which strong connectivity depends on mean…
Networks in the real world do not exist as isolated entities, but they are often part of more complicated structures composed of many interconnected network layers. Recent studies have shown that such mutual dependence makes real networked…
Real-world networks often exhibit strong transitivity with nontrivial local clustering spectra and degree correlations. Such features are not easily modeled in tractable network models, creating an obstacle to the theoretical understanding…
Interacting quantum systems evolving from an uncorrelated composite initial state generically develop quantum correlations -- entanglement. As a consequence, a local description of interacting quantum system is impossible as a rule. A…