Related papers: A Universal Route to Explosive Phenomena
In this paper we consider kinetically constrained models (KCM) on $\mathbb Z^2$ with general update families $\mathcal U$. For $\mathcal U$ belonging to the so-called "critical class" our focus is on the divergence of the infection time of…
In topological insulators and topological superconductors, the discrete jump of the topological invariant upon tuning a certain system parameter defines a topological phase transition. A unified framework is employed to address the quantum…
We consider the evolution of the unstable periodic orbit structure of coupled chaotic systems. This involves the creation of a complicated set outside of the synchronization manifold (the emergent set). We quantitatively identify a critical…
We study the interplay between ordered and chaotic dynamics at the critical point of a generic first-order quantum phase transition in the interacting boson model of nuclei. Classical and quantum analyses reveal a distinct behavior of the…
Catastrophes of all kinds can be roughly defined as short duration-large amplitude events following and followed by long periods of "ripening". Major earthquakes surely belong to the class of 'catastrophic' events. Because of the space-time…
Cascading failures in complex systems have been studied extensively using two different models: $k$-core percolation and interdependent networks. We combine the two models into a general model, solve it analytically and validate our…
Although cosmic expansion at very small distances is usually dismissed as entirely inconsequential, it appears that these extraordinarily small effects may in fact have a real and significant influence on our world. Calculations suggest…
Bifurcations can cause dynamical systems with slowly varying parameters to transition to far-away attractors. The terms ``critical transition'' or ``tipping point'' have been used to describe this situation. Critical transitions have been…
The dynamics at the critical-point of a general first-order quantum phase transition in a finite system is examined, from an algebraic perspective. Suitable Hamiltonians are constructed whose spectra exhibit coexistence of states…
The emergence of chaotic phenomena in a quantum system has long been an elusive subject. Experimental progresses in this subject have become urgently needed in recent years, when considerable theoretical studies have unveiled the vital…
The scaling theory of critical phenomena has been successfully extended for classical first order transitions even though the correlation length does not diverge in these transitions. In this paper we apply the scaling ideas to quantum…
The universal form for the average scattering intensity from systems undergoing order-disorder transitions is found by numerical integration of the Langevin dynamics. The result is nearly identical for simulations involving two different…
We propose a unifying theoretical framework for the analysis of first-passage time distributions in two important classes of stochastic processes in which the diffusivity of a particle evolves randomly in time. In the first class of…
We consider the semiclassical ballistic sigma-model as an effective theory describing the quantum mechanics of classically chaotic systems. Specifically, we elaborate on close analogies to the recently developed semiclassical theory of…
We study transformations of conventional (`classical') probabilities induced by context transitions. It is demonstrated that the transition from one complex of conditions to another induces a perturbation of the classical rule for the…
In a system of interdependent networks, an initial failure of nodes invokes a cascade of iterative failures that may lead to a total collapse of the whole system in a form of an abrupt first order transition. When the fraction of initial…
The fate of cities under natural hazards depends not only on hazard intensity but also on the coupling of structural damage, a collective process that remains poorly understood. Here we show that urban structural damage exhibits…
A paradigmatic framework to study the phenomenon of spontaneous collective synchronization is provided by the Kuramoto model comprising a large collection of limit-cycle oscillators of distributed frequencies that are globally coupled…
We construct a nontrivial generalization of the paradigmatic Kuramoto model by using an additional coupling term that explicitly breaks its rotational symmetry resulting in a variant of the Winfree Model. Consequently, we observe the…
We find a series of topological phase transitions of increasing order, beyond the more standard second-order phase transition in a one-dimensional topological superconductor. The jumps in the order of the transitions depend on the range of…