Related papers: Continuous percolation in a Hilbert space for a la…
Why does quantum theory need the complex numbers? With a view toward answering this question, this paper argues that the usual Hilbert-space formalism is a special case of the general method of Markovian embeddings. This paper then…
We present a systematic study of quantum system compression for the evolution of generic many-body problems. The necessary numerical simulations of such systems are seriously hindered by the exponential growth of the Hilbert space dimension…
In a new type of percolation phase transition, which was observed in a set of non-equilibrium models, each new connection between vertices is chosen from a number of possibilities by an Achlioptas-like algorithm. This causes preferential…
We consider the constrained-degree percolation (CDP) model on the hypercubic lattice. This is a continuous-time percolation model defined by a sequence $(U_e)_{e\in\mathcal{E}^d}$ of i.i.d. uniform random variables and a positive integer…
In this article, the concept of copulas is generalised to infinite dimensional Hilbert spaces. We show one direction of Sklar's theorem and explain that the other direction fails in infinite dimensional Hilbert spaces. We derive a necessary…
Recently it has been demonstrated that the connectivity transition from microscopic connectivity to macroscopic connectedness, known as percolation, is generically announced by a cascade of microtransitions of the percolation order…
We study the effect of superradiance in open quantum systems, i.e., the separation of short- and long-living eigenstates when a certain subspace of states in the Hilbert space acquires an increasing decay width. We use several Hamiltonian…
Porous media are often modelled as systems of overlapping obstacles, which leads to the problem of two percolation thresholds in such systems, one for the porous matrix and the other one for the void space. Here we investigate these…
We observed a phase transition-like behavior that is marked by the onset of the realization of the connectivity between two sites on a two-dimensional cross-section of a three-dimensional percolation cluster. This was found using…
A problem of the crossover from percolation to diffusion transport is considered. A general scaling theory is proposed. It introduces phenomenologically four critical exponents which are connected by two equations. One exponent is…
Continuous phase transitions in spin systems can be formulated as percolation of suitably defined clusters. We review this equivalence and then discuss how in a similar way, the color deconfinement transition in SU(2) gauge theory can be…
The localization transition and the critical properties of the Lorentz model in three dimensions are investigated by computer simulations. We give a coherent and quantitative explanation of the dynamics in terms of continuum percolation…
Quantum percolation describes the problem of a quantum particle moving through a disordered system. While certain similarities to classical percolation exist, the quantum case has additional complexity due to the possibility of Anderson…
We present a comprehensive and versatile theoretical framework to study site and bond percolation on clustered and correlated random graphs. Our contribution can be summarized in three main points. (i) We introduce a set of iterative…
We consider high-dimensional percolation at the critical threshold. We condition the origin to be disjointly connected to two points, $x$ and $x'$, and subsequently take the limit as $|x|$, $|x'|$ as well as $|x-x'|$ diverge to infinity.…
The properties of the pure-site clusters of spin models, i.e. the clusters which are obtained by joining nearest-neighbour spins of the same sign, are here investigated. In the Ising model in two dimensions it is known that such clusters…
We study nonequilibrium phase transitions of reaction-diffusion systems defined on randomly diluted lattices, focusing on the transition across the lattice percolation threshold. To develop a theory for this transition, we combine classical…
This paper is devoted to the study of quotients of finite metric spaces. The basic type of question we ask is: Given a finite metric space M, what is the largest quotient of (a subset of) M which well embeds into Hilbert space. We obtain…
While classical percolation is well understood, percolation effects in randomly packed or jammed structures are much less explored. Here we investigate both experimentally and theoretically the electrical percolation in a binary composite…
The statistical analysis of cosmic large-scale structure is most often based on simple two-point summary statistics, like the power spectrum or the two-point correlation function of a sample of galaxies or other types of tracers. In…