Related papers: Sum rule for the pair correlation function
We use the Bogoliubov theory of Bose-Einstein condensation to study the properties of dipolar particles (atoms or molecules) confined in a uniform two-dimensional geometry at zero temperature. We find equilibrium solutions to the dipolar…
We use the extension of scaled particle theory (ESPT) presented in the accompanying paper [Stillinger et al. J. Chem. Phys. xxx, xxx (2007)] to calculate numerically pair correlation function of the hard sphere fluid over the density range…
We show that short-range pair correlations in a strongly interacting Fermi gas follow a simple universal law described by Tan's relations. This is achieved through measurements of the static structure factor which displays a universal…
We present the first theoretical approach to the angular-average of the two-body correlation function $\tilde g(r)$ for simple solids. It is based on three sum rules for $\tilde g(r)$: the compressibility and virial equations and the…
We derive a general relation between correlators of density of states fluctuations and density response functions. It applies equally to quantum chaotic systems of pure symmetry (unitary, orthogonal, and symplectic) as well as to the…
Based on an equations--of--motion approach for time--dependent pair correlations in strongly interacting Fermi liquids, we have developed a theory for describing the excitation spectrum of these systems. Compared to the known ``correlated''…
The strongly attractive Fermi gas in the BCS-BEC crossover is efficiently described in terms of coupled fermions and fermion pairs, or molecules. We compute the spectral functions of both fermions and pairs in the normal state near the…
We show that the long-distance behavior of the two-body density correlation functions and the Cooper-pair probability density of a balanced mixture of a two-component Fermi gas at $T = 0$, is universal along the BEC-BCS crossover. Our…
It is shown how the universal correlation function of Brezin and Zee, and Beenakker, for random matrix ensembles of Wigner-Dyson type with density support on a finite interval can be derived using a linear response argument and macroscopic…
For a freely evolving granular fluid, the buildup of spatial correlations in density and flow field is described using fluctuating hydrodynamics. The theory for incompressible flows is extended to the general, compressible case, including…
Analytical expressions are given for the static structure factor S(k) and the pair correlation function g(r) for uniform ideal Bose-Einstein and Fermi-Dirac gases for all temperatures. In the vicinity of Bose Einstein condensation (BEC)…
Approximate expressions for correlation functions in binary inhomogeneous mixtures are derived in a framework of the mesoscopic theory [Ciach A., Mol. Phys., 2011, {\textbf{109}}, 1101]. Fluctuation contribution is taken into account in a…
A generalized Friedel sum rule is derived for a quantum dot with internal orbital and spin degrees of freedom. The result is valid when all many-body correlations are taken into account and it links the phase shift of the scattered electron…
We review the linear response theory in the horizontal quantum liquids framework spanning from Coulomb liquids to Atomic gases. There are several well known references about this subject, like the onset of the Kramers-Kronig relations and…
Sum rules -- relating the static quark potential V(R) to the spatial distribution of the action and energy in the colour fields of flux-tubes -- are applied in three ways: 1) To extract generalised beta-functions: 2) As a consistency check…
The derivation of mean-field limits for quantum systems at zero temperature has attracted many researchers in the last decades. Recent developments are the consideration of pair correlations in the effective description, which lead to a…
We calculate the pair correlation function of an interacting Bose gas in a harmonic trap directly via Path Integral Quantum Monte Carlo simulation for various temperatures and compare the numerical result with simple approximative…
Compressible isothermal turbulence is analyzed under the assumption of homogeneity and in the asymptotic limit of a high Reynolds number. An exact relation is derived for some two-point correlation functions which reveals a fundamental…
A generalized Bogoliubov model of the Bose gas in the ground state is proposed which properly takes into account both the long-range and short-range spatial boson correlations. It concerns equilibrium characteristics and operates with…
We apply the flow equation method for studying the fermion systems where pairing interactions can either trigger the BCS instability with the symmetry breaking manifested by the off-diagonal order parameter or lead to the gaped single…