Related papers: Towards analytical approaches to the dynamical-clu…
We develop a non-perturbative method to derive the probability distribution $P(\delta_R)$ of the density contrast within spherical cells in the quasi-linear regime. Indeed, since this corresponds to a rare-event limit a steepest-descent…
In the limit of infinite spatial dimensions a thermodynamically consistent theory of the strongly correlated electron systems, which is valid for arbitrary value of the Coulombic interaction ($U<\infty$), is built. For the Hubbard model the…
We present a general method by which linear quantum Hamiltonian dynamics with exponentially many degrees of freedom is replaced by approximate classical nonlinear dynamics with the number of degrees of freedom (phase space dimensionality)…
Density functional theory (DFT) provides convenient electronic structure methods for the study of molecular systems and materials. Regular Kohn-Sham DFT calculations rely on unitary transformations to determine the ground-state electronic…
The liquid structure of a glass-forming binary alloy is studied using molecular dynamics simulations. The analysis combines common neighbour analysis with the geometrical approach of Frank and Kasper to establish that the supercooled liquid…
We review some recent progress on applications of Cluster Expansions. We focus on a system of classical particles living in a continuous medium and interacting via a stable and tempered pair potential. We review the cluster expansion in…
A method, called the adaptive cluster approximation (ACA), for single-impurity Anderson models is proposed. It is based on reduced density-matrix functional theory, where the one-particle reduced density matrix is used as the basic…
A well-established method to deal with highly correlated systems is based on the expansion of the Green's function in terms of spectral moments. In the context of the Composite Operator Method one approximation is proposed: a set of n…
A well-known cluster expansion, which leads to virial expansion for the free energy of low density systems, is modified in such a way that it becomes applicable to the description of condensed state of matter. To this end, the averaging of…
We begin by reviewing some probabilistic results about the Dirichlet Process and its close relatives, focussing on their implications for statistical modelling and analysis. We then introduce a class of simple mixture models in which…
This work discusses a two-step procedure, based on formal abstractions, to generate a finite-space stochastic dynamical model as an aggregation of the continuous temperature dynamics of a homogeneous population of Thermostatically…
It is essential that mesoscopic simulations of reactive systems reproduce the correct statistical distributions at thermodynamic equilibrium. By considering a compressible fluctuating hydrodynamics (FHD) simulation method of ideal gas…
We investigate different mean-field-like approximations for stochastic dynamics on graphs, within the framework of a cluster-variational approach. In analogy with its equilibrium counterpart, this approach allows one to give a unified view…
Velocity and density structure factors are measured over a hydrodynamic range of scales in a horizontal quasi-2d fluidized granular experiment, with packing fractions $\phi\in[10%,40%]$. The fluidization is realized by vertically vibrating…
We develop an effective nonhierarchical data clustering method using an analogy to the dynamic coarse graining of a stochastic system. Analyzing the eigensystem of an interitem transition matrix identifies fuzzy clusters corresponding to…
A recently introduced recurrence-relation ansatz applied to the Fermi-Hubbard model gives rise to a soluble model and here is used to calculate several thermodynamic observables. The constraint of unit density per site, density = 1, is…
Impact processes of nanoclusters subject to thermal fluctuations are investigated, theoretically. In the former half of the paper, we discuss the basis of quasi-static theory. In the latter part, we carry out the molecular dynamics…
We study clustering in a stochastic system of particles sliding down a fluctuating surface in one and two dimensions. In steady state, the density-density correlation function is a scaling function of separation and system size.This scaling…
Aggregation-diffusion equations are foundational tools for modelling biological aggregations. Their principal use is to link the collective movement mechanisms of organisms to their emergent space use patterns in a concrete mathematical…
The response of thermodynamic systems perturbed out of an equilibrium steady-state is described by the reciprocal and the fluctuation-dissipation relations. The so-called fluctuation theorems extended the study of fluctuations far beyond…