相关论文: Cluster expansions and correlation functions
The Tomita-Takesaki modular theory is used to establish a cluster estimate extending and modifying that of Thomas and Wichmann, so as to extend it to regions within which the relevant observables are not necessarily spacelike separated.…
We generalize the classical probability frame by adopting a wider family of random variables that includes nondeterministic ones. The frame that emerges is known to host a ''classical'' extension of quantum mechanics. We discuss the notion…
We compare the different convergence criteria available for cluster expansions of polymer gases subjected to hard-core exclusions, with emphasis on polymers defined as finite subsets of a countable set (e.g. contour expansions and more…
Correlations in interacting many-particle systems can lead to the formation of clusters, in particular bound states and resonances. Systematic quantum statistical approaches allow to combine the nuclear statistical equilibrium description…
We prove clustering estimates for the truncated correlations, i.e., cumulants of an unbounded spin system on the lattice. We provide a unified treatment, based on cluster expansion techniques, of four different regimes: large mass, small…
A variant of coupled-cluster theory is described here, wherein the degrees of freedom are fluctuations of fragments between internally correlated states. The effects of intra-fragment correlation on the inter-fragment interaction are…
We show the validity of the cluster expansion in the canonical ensemble for the Ising model. We compare the lower bound of its radius of convergence with the one computed by the virial expansion working in the grand-canonical ensemble.…
We prove that for a general $N$-component model on a $d$-dimensional lattice $\bZ^d$ with pairwise nearest-neighbor coupling and general local interaction obeying a stability bound the linked cluster expansion has a finite radius of…
We have developed a model to describe two-point correlation functions of clusters of galaxies in X-ray flux-limited surveys. Our model properly takes account of nonlinear gravitational evolution of mass fluctuations, redshift-space…
We perform a cluster expansion in the canonical ensemble with periodic boundary conditions, introducing a new choice of polymer activities that differs from the standard ones. This choice leads to an improved bound for the convergence of…
The unitary coupled cluster (UCC) approximation is one of the more promising wave-function ans\"atze for electronic structure calculations on quantum computers via the variational quantum eigensolver algorithm. However, for large systems…
We study the dependence of a cluster algebra on the choice of coefficients. We write general formulas expressing the cluster variables in any cluster algebra in terms of the initial data; these formulas involve a family of polynomials…
Especially in lattice structured populations, homogeneous mixing represents an inadequate assumption. Various improvements upon the ordinary pair approximation based on a number of assumptions concerning the higher-order correlations have…
The Atomic Cluster Expansion (Drautz, Phys. Rev. B 99, 2019) provides a framework to systematically derive polynomial basis functions for approximating isometry and permutation invariant functions, particularly with an eye to modelling…
Methods which aim at universal applicability must be able to describe both weak and strong electronic correlation with equal facility. Such methods are in short supply. The combination of symmetry projection for strong correlation and…
In this master's thesis, we introduce expansion systems as a general framework to describe a large variety of approximation algorithms, such as Taylor approximation, decimal expansion and continued fraction. We consider some basic…
Taylor expansions of analytic functions are considered with respect to several points, allowing confluence of any of them. Cauchy-type formulas are given for coefficients and remainders in the expansions, and the regions of convergence are…
The infinite set of coupled integral nonlinear equations for correlation functions in the case of classical canonical ensemble is considered. Some kind of graph expansions of correlation functions in the density parameter are constructed.…
Machine learning interatomic potentials are revolutionizing large-scale, accurate atomistic modelling in material science and chemistry. Many potentials use atomic cluster expansion or equivariant message passing frameworks. Such frameworks…
We develop the cluster expansion for the multidimensional multiscaled contours defined by three of us. These contours are suitable for long-range Ising models with interaction $J_{xy}=J(|x-y|)= J/|x-y|^\alpha$, $J>0$, and $\alpha>d$. As an…