Related papers: Clustering Bounds on N-Point Correlations for Unbo…
We develop a numerical linked cluster expansion (NLCE) method that can be applied directly to inhomogeneous systems, for example Hamiltonians with disorder and dynamics initiated from inhomogeneous initial states. We demonstrate the method…
A univariate clustering criterion for stationary processes satisfying a $\beta$-mixing condition is proposed extending the work of \cite{KB2} to the dependent setup. The approach is characterized by an alternative sample criterion function…
We develop a unified approach to the problem of clustering in the three different fields of applications, as indicated in the title the paper. The approach is based on Khintchine's probabilistic method that grew out of the Darwin-Fawler…
We show that numerical linked cluster expansions (NLCEs) based on sufficiently large building blocks allow one to obtain accurate low-temperature results for the thermodynamic properties of spin lattice models with continuous disorder…
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…
This paper delves into a fundamental aspect of quantum statistical mechanics -- the absence of thermal phase transitions in one-dimensional (1D) systems. Originating from Ising's analysis of the 1D spin chain, this concept has been pivotal…
We calculate thermodynamic properties of soft-core lattice bosons with on-site $n$-body interactions using up to twelfth and tenth order strong coupling expansion in one and two dimensional cubic lattices at zero temperature. Using linked…
We apply the coupled cluster method (CCM) to the Hamiltonian version of the latticised O(4) non-linear sigma model. The method, which was initially developed for the accurate description of quantum many-body systems, gives rise to two…
Nuclear systems are treated within a quantum statistical approach. Correlations and cluster formation are relevant for the properties of warm dense matter, but the description is challenging and different approximations are discussed. The…
A coupled-cluster approach for systems of $N$ bosons in external traps is developed. In the coupled-cluster approach the exact many-body wavefunction is obtained by applying an exponential operator $\exp{T}$ to the ground configuration…
We consider the sampling of the coupled cluster expansion within stochastic coupled cluster theory. Observing the limitations of previous approaches due to the inherently non-linear behaviour of a coupled cluster wavefunction representation…
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…
The Lieb-Robinson bound shows that the speed of propagating information in a nonrelativistic quantum lattice system is bounded by a finite velocity, which entails the clustering of correlations. In this paper, we extend the Lieb-Robinson…
In a series of two articles, we propose a comprehensive mathematical framework for Coupled-Cluster-type methods. In this second part, we analyze the nonlinear equations of the single-reference Coupled-Cluster method using topological degree…
Bosonic lattice systems with non-trivial interactions represent an intriguing platform to study exotic phases of matter. Here, we study the effects of extended correlated hopping processes in a system of bosons trapped in a lattice…
In [7], a cluster expansion method has been developed to study the fluctuations of the hard sphere dynamics around the Boltzmann equation. This method provides a precise control on the exponential moments of the empirical measure, from…
The determination of the resolution of cosmological N-body simulations, i.e., the range of scales in which quantities measured in them represent accurately the continuum limit, is an important open question. We address it here using…
The gravitational clustering of collisionless particles in an expanding universe is modelled using some simple physical ideas. I show that it is possible to understand the nonlinear clustering in terms of three well defined regimes: (1)…
We consider stochastic processes arising from dynamical systems by evaluating an observable function along the orbits of the system. The novelty is that we will consider observables achieving a global maximum value (possible infinite) at…
The one-dimensional contact process is analyzed by a cluster approximation. In this approach, the hierarchy of rate equations for the densities of finite length empty intervals are truncated under the assumption that adjacent intervals are…