Related papers: Matter Correlations in Branched Polymers
The structure and degree of order in soft matter and other materials is intimately connected to the nature of the interactions between the particles. One important research goal is to find suitable control mechanisms, to enhance or suppress…
In this article, addressing large $n$ systems, we report that in numerous systems hosting long and short range interactions, multiple correlation lengths may appear. The largest correlation lengths often monotonically increase with…
We consider a toy model to analyze the consequences of dark matter interaction with a dark energy background on the overall rotation of galaxy clusters and the misalignment between their dark matter and baryon distributions when compared to…
We discuss structural correlations in mixtures of free polymer and colloidal particles based on a microscopic, 2-component liquid state integral equation theory. Whereas in the case of polymers much smaller than the spherical particles the…
In these lecture notes we present some connections between random matrices, the asymmetric exclusion process, random tilings. These three apparently unrelated objects have (sometimes) a similar mathematical structure, an interlacing…
In a system with long-ranged correlations, the behavior of correlation functions is sensitive to the presence of a boundary. We show that surface deformations strongly modify this behavior as compared to a flat surface. The modified near…
We study the thermodynamic behavior of branched polymers. We first study random walks in order to clarify the thermodynamic relation between the canonical ensemble and the grand canonical ensemble. We then show that correlation functions…
We show that correlation functions for branched polymers correspond to those for $\phi^3$ theory with a single mass insertion, not those for the $\phi^3$ theory themselves, as has been widely believed. In particular, the two-point function…
Functional geometry is a framework using concepts from geometry to understand the invariance of amplitudes in quantum field theory under a large class of field redefinitions, including those involving derivatives. It is inspired by…
Geometrical measurements of biological objects form the basis of many quantitative analyses. Hausdorff measures such as the volume and the area of objects are simple and popular descriptors of individual objects, however, for most…
We examine the behavior of correlation functions for a massless scalar field in de Sitter space with a quartic interaction. We find that two-loop corrections are relevant, and that the resummation of these corrections generates a…
We derive an exact formula for the covariance of cartesian distances in two simple polymer models, the freely-jointed chain and a discrete flexible model with nearest-neighbor interaction. We show that even in the interaction-free case…
We study the fluctuations of the directed polymer in 1+1 dimensions in a Gaussian random environment with a finite correlation length {\xi} and at finite temperature. We address the correspondence between the geometrical transverse…
In this paper, we explore the interplay between symmetry and fracton order, motivated by the analogous close relationship for topologically ordered systems. Specifically, we consider models with 3D planar subsystem symmetry, and show that…
We show point processes generated in different ways and having different structure, presenting very similar power-law two--point correlation functions at small scales and quite different shapes at large scales.
We survey some principal results and open problems related to colorings of algebraic and geometric objects endowed with symmetries.
Polymers are among the most important materials in the modern society being found almost in every activity of our daily life. Understanding their chemical and physical properties lead to improvements of their usage. The correlation…
With the increasing interplay between experimental and computational approaches at multiple length scales, new research directions are emerging in materials science and computational mechanics. Such cooperative interactions find many…
We consider the dynamics of a simple one dimensional model and we discuss the phenomenon of aging (i.e., the strong dependence of the dynamical correlation functions over the waiting time). Our model is the so-called random random walk, the…
Measuring bipartite fluctuations of a conserved charge, such as the particle number, is a powerful approach to understanding quantum systems. When the measured region has sharp corners, the bipartite fluctuation receives an additional…