Related papers: Loop correlations in random wire models
A disordered medium is often constructed by $N$ points independently and identically distributed in a $d$-dimensional hyperspace. Characteristics related to the statistics of this system is known as the random point problem. As $d \to…
We consider the homogenization of a Poisson problem or a Stokes system in a randomly punctured domain with Dirichlet boundary conditions. We assume that the holes are spherical and have random centres and radii. We impose that the average…
The random walk loop soup is a Poissonian ensemble of lattice loops; it has been extensively studied because of its connections to the discrete Gaussian free field, but was originally introduced by Lawler and Trujillo Ferreras as a discrete…
The distribution of higher order level spacings, i.e. the distribution of $\{s_{i}^{(n)}=E_{i+n}-E_{i}\}$ with $n\geq 1$ is derived analytically using a Wigner-like surmise for Gaussian ensembles of random matrix as well as Poisson…
We consider bond percolation on the square lattice with perfectly correlated random probabilities. According to scaling considerations, mapping to a random walk problem and the results of Monte Carlo simulations the critical behavior of the…
We perform a detailed numerical study of the conductance $G$ through one-dimensional (1D) tight-binding wires with on-site disorder. The random configurations of the on-site energies $\epsilon$ of the tight-binding Hamiltonian are…
Nearest-neighbor spin correlations are considered near the surface of a semi-infinite spin-$\frac12$ Heisenberg antiferromagnet on a simple cubic lattice. In the spin-wave approximation, the excitation spectrum of this model involves bulk…
We study the distribution of sizes of erased loops for loop-erased random walks on regular and fractal lattices. We show that for arbitrary graphs the probability $P(l)$ of generating a loop of perimeter $l$ is expressible in terms of the…
The problem of long-range correlations of particles produced in high- energy collisions is discussed. Long-range correlations involve large groups of particles. Among them are, e.g., those correlations which lead to ring-like and elliptic…
We simulate the bond and site percolation models on several three-dimensional lattices, including the diamond, body-centered cubic, and face-centered cubic lattices. As on the simple-cubic lattice [Phys. Rev. E, \textbf{87} 052107 (2013)],…
An infinite chain of driven-dissipative condensate spins with uniform nearest-neighbor coherent coupling is solved analytically and investigated numerically. Above a critical occupation threshold the condensates undergo spontaneous spin…
We give heuristic arguments and computer results to support the hypothesis that, after appropriate rescaling, the statistics of spacings between adjacent prime numbers follows the Poisson distribution. The scaling transformation removes the…
We exploit the inherent entanglement of the ground state of a spin chain with dimerized XX or XXZ Hamiltonian to investigate the entanglement generation between the ends of the chain. We follow the strategy has been introduced in Ref. [14]…
We consider a pair of identical fermions with a short-range attractive interaction on a finite lattice cluster in the presence of strong site disorder. This toy model imitates a low density regime of the strongly disordered Hubbard model.…
We consider a general random walk loop soup which includes, or is related to, several models of interest, such as the Spin O(N) model, the double dimer model and the Bose gas. The analysis of this model is challenging because of the…
We prove that under an easily verifiable set of conditions a sequence of associated random fields converges under rescaling to the Poisson Point Process and give a couple of examples.
Consider the following random spatial network: in a large disk, construct a network using a stationary and isotropic Poisson line process of unit intensity. Connect pairs of points using the network, with initial / final segments of the…
We show that local correlators in a wide class of kicked chains can be calculated exactly at light cone edges. Extending previous works on dual-unitary systems, the correlators between local operators are expressed through the expectation…
The two-dimensional dense O(n) loop model for $n=1$ is equivalent to the bond percolation and for $n=0$ to the dense polymers or spanning trees. We consider the boundary correlations on the half space and calculate the probability $P_b$…
The purpose of this short note is to establish a connection between a one-dimensional random walk in a random sparse environment and the random pinning model. We show that the grand canonical partition function of the pinning model…