Related papers: Deriving the Rosenfeld Functional from the Virial …
We show that the hierarchical model at finite volume has a symmetry group which can be decomposed into rotations and translations as the familiar Poincar\'e groups. Using these symmetries, we show that the intricate sums appearing in the…
3-loop diagrams of the ladder-type, which emerge for local quarkonic twist-2 operator matrix elements, are computed directly for general values of the Mellin variable $N$ using Appell-function representations and applying modern summation…
A loop series expansion for the partition function of a general statistical model on a graph is carried out. If the auxiliary probability distributions of the expansion are chosen to be a fixed point of the belief-propagation equation, the…
The concept of weighted asymmetries is revisited for semi-inclusive deep inelastic scattering. We consider the cross section in Fourier space, conjugate to the outgoing hadron's transverse momentum, where convolutions of transverse momentum…
Percolation clusters are random fractals whose geometrical and transport properties can be characterized with the help of probability distribution functions. Using renormalized field theory, we determine the asymptotic form of various of…
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)…
The area of fractional calculus has made its way into various pure and applied scientific fields, as evidenced by its integration into numerous disciplines. An increasing number of researchers are exploring various approaches to…
The free energy of the Ginzburg-Landau theory satisfies a nonlinear functional differential equation which is turned into a recursion relation. The latter is solved graphically order by order in the loop expansion to find all connected…
Response calculations in density functional theory aim at computing the change in ground-state density induced by an external perturbation. At finite temperature these are usually performed by computing variations of orbitals, which involve…
We use density functional theory to describe the phase behaviors of rigid molecules. The construction of kernel function G(x, P, x, P) is discussed. Excluded-volume potential is calculated for two types of molecules with C_{2v} symmetry.…
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…
Motivated by applications to Bayesian inference for statistical models with orthogonal matrix parameters, we present $\textit{polar expansion},$ a general approach to Monte Carlo simulation from probability distributions on the Stiefel…
We present the second part of a paper series devoted to the study of the multi-loop effective potential evolution in $\varphi^4$-theory using the conformal symmetry. In this paper, we demonstrate that the conformal symmetry can still be…
We turn the long time puzzle of the free volume, known for its highly irregular form, into exact analytical formulae and develop statistical mechanics of the hard disk model. The free volume is exactly expressed in terms of the intersection…
Inertial particle data from three-dimensional direct numerical simulations of particle-laden homogeneous isotropic turbulence at high Reynolds number are analyzed using Voronoi tessellation of the particle positions, considering different…
We evaluate one-loop partition functions of higher-spin fields in thermal flat space with angular potentials; this computation is performed in arbitrary space-time dimension, and the result is a simple combination of Poincar\'e characters.…
Loop calculations involve the evaluation of divergent integrals. Usually [1] one computes them in a number of dimensions different than four where the integral is convergent and then one performs the analytical continuation and considers…
The relationship between the exact kinetic energy density in a quantum system in the frame of Density Functional Theory and the semiclassical functional expression for the same quantity is investigated. The analysis is performed with Monte…
We study algebraic aspects of Kontsevich integrals as generating functions for intersection theory over moduli space and review the derivation of Virasoro and KdV constraints. 1. Intersection numbers 2. The Kontsevich integral 2.1. The main…
A recently proposed method of calculating scalar two-loop propagator and vertex functions with massive particles is illustrated with simple examples. A double integral representation is derived with the example of a propagator function. An…