Related papers: The density gradient expansion of correlation func…
We develop strong-coupling series expansion methods to study two-particle spectra of quantum lattice models. At the heart of the method lies the calculation of an effective Hamiltonian in the two-particle subspace. We explicitly consider an…
The quantum-statistical cluster expansion method of Lee and Yang is extended to investigate off-diagonal long-range order (ODLRO) in one- and multi-component mixtures of bosons or fermions. Our formulation is applicable to both a uniform…
We compute the large scale (macroscopic) correlations in ensembles of normal random matrices with an arbitrary measure and in ensembles of general non-Hermition matrices with a class of non-Gaussian measures. In both cases the eigenvalues…
The Boltzmann kinetic equation is considered to compute the transport coefficients associated with the mass flux of intruders in a granular gas. Intruders and granular gas are immersed in a gas of elastic hard spheres (molecular gas). We…
Accurate treatment of the electronic correlation in inhomogeneous electronic systems, combined with the ability to capture the correlation energy of the homogeneous electron gas, allows to reach high predictive power in the application of…
An existence result is proved for a nonlinear diffusion problem of phase-field type, consisting of a parabolic system of two partial differential equations, complemented by Neumann homogeneous boundary conditions and initial conditions.…
One possible way to investigate the nature of the primordial power spectrum fluctuations is by investigating the statistical properties of the local maximum in the density fluctuation fields. In this work we present a study of the mean…
The one-dimensional coagulation-diffusion process describes the strongly fluctuating dynamics of particles, freely hopping between the nearest-neighbour sites of a chain such that one of them disappears with probability 1 if two particles…
We present a new a-priori estimate for discrete coagulation-fragmentation systems with size-dependent diffusion within a bounded, regular domain confined by homogeneous Neumann boundary conditions. Following from a duality argument, this…
We study the long-time behaviour of the growth-fragmentation equation, a nonlocal linear evolution equation describing a wide range of phenomena in structured population dynamics. We show the existence of a spectral gap under conditions…
Semilocal exchange-correlation functionals are the most accurate, realistic and widely used ones to describe the complex many-electron effects of two-dimensional quantum systems. Beyond local density approximation, the generalized gradient…
In this paper, we first prove that the existence of a solution of SDEs under the assumptions that the drift coefficient is of linear growth and path--dependent, and diffusion coefficient is bounded, uniformly elliptic and H\"older…
We propose a new estimation procedure of the conditional density for independent and identically distributed data. Our procedure aims at using the data to select a function among arbitrary (at most countable) collections of candidates. By…
Polymer self-consistent field theory techniques are used to derive quantum density functional theory without the use of the theorems of density functional theory. Instead, a free energy is obtained from a partition function that is…
Gradient algorithms are classical in adaptive control and parameter estimation. For instantaneous quadratic cost functions they lead to a linear time-varying dynamic system that converges exponentially under persistence of excitation…
We continue the development of transfer operator techniques for expanding maps on a lattice coupled by general interaction functions. We obtain a spectral gap for an appropriately defined transfer operator, and, as corollaries, the…
Finite volume methods for problems involving second order operators with full diffusion matrix can be used thanks to the definition of a discrete gradient for piecewise constant functions on unstructured meshes satisfying an orthogonality…
We develop a new computational framework to solve the partial differential equations (PDEs) governing the flow of the joint probability density functions (PDFs) in continuous-time stochastic nonlinear systems. The need for computing the…
We consider density functionals for exchange and correlation energies in two-dimensional systems. The functionals are constructed by making use of exact constraints for the angular averages of the corresponding exchange and correlation…
The semilocal meta generalized gradient approximation (MGGA) for the exchange-correlation functional of Kohn-Sham (KS) density functional theory can yield accurate ground-state energies simultaneously for atoms, molecules, surfaces, and…