Related papers: Radial Distribution Function in a Two Dimensional …
The density of states for a particle moving in a random potential with a Gaussian correlator is calculated exactly using the functional integral technique. It is achieved by expressing the functional degrees of freedom in terms of the…
We investigate the relationship between the functional renormalization group (RG) and the dual holography framework in the path integral formulation, highlighting how each can be understood as a manifestation of the other. Rather than…
Recent simulation studies have drawn attention to the shoulder which forms in the second peak of the radial distribution function of hard-spheres at densities close to freezing and which is associated with local crystalline ordering in the…
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 present a general scheme based on nonlinear response theory to calculate the expansion of correlation functions such as the pair-correlation function or the exchange-correlation hole of an inhomogeneous many-particle system in terms of…
When a fluid is subject to an external field, as is the case near an interface or under spatial confinement, then the density becomes spatially inhomogeneous. Although the one-body density provides much useful information, a higher level of…
We study the steady-state distribution function of a run-and-tumble particle evolving around a repulsive hard spherical obstacle. We show that the well-documented activity-induced attraction translates into a delta peak accumulation at the…
Quantum mechanical scalar particle with polarizability is considered in the presence of the Coulomb field. Separation of variables is performed with the use of Wigner $D$-functions, the radial system of 15 equations is reduced to a single…
We show different expressions of distribution functions (DFs) which depend only on the two classical integrals of the energy and the magnitude of the angular momentum with respect to the axis of symmetry for stellar systems with known…
A formalism is presented for analytically obtaining the probability density function, (P_{n}(s)), for the random distance (s) between two random points in an (n)-dimensional spherical object of radius (R). Our formalism allows (P_{n}(s)) to…
The celebrated work of Onsager on hard particle systems, based on the truncated second order virial expansion, is valid at relatively low volume fractions for large aspect ratio particles. While it predicts the isotropic-nematic phase…
We derive the Ornstein-Zernike equation for molecular crystals of axially symmetric particles and apply the Percus-Yevick approximation to this system. The one-particle orientational distribution function has a nontrivial dependence on the…
We derive from first principles (without resorting to the replica trick) a density functional theory for fluids in quenched disordered matrices (QA-DFT). We show that the disorder-averaged free energy of the fluid is a functional of the…
Current-density-functional theory is used to calculate ionization energies of current-carrying atomic states. A perturbative approximation to full current-density-functional theory is implemented for the first time, and found to be…
Understanding the statistical behavior of the heat in stochastic systems gives us insight about the thermodynamics of such systems. Using the recently proposed Relativistic Stochastic Thermodynamics, we investigate the statistics of the…
By the continuous mapping theorem, if a sequence of $d$-dimensional random vectors $(\mathbf{W}_n)_{n\geq1}$ converges in distribution to a multivariate normal random variable $\Sigma^{1/2}\mathbf{Z}$, then the sequence of random variables…
It is necessary for the statistical description of collective effects in liquids to set that or other approximation between direct and pair correlation functions which describe a neighboring order. The analytical solution of the generalized…
We develop an Ornstein--Zernike theory for the two-dimensional random-cluster model with $1 \leq q <4$ that also applies in its near-critical regime. In particular, we prove an asymptotic formula for the two-point function which holds…
We apply reduced density-matrix functional theory to the parabolically confined quantum Hall droplet in the spin-frozen strong magnetic field regime. One-body reduced density matrix functional method performs remarkably well in obtaining…
Density-potential functional theory (DPFT) is an alternative formulation of orbital-free density functional theory that may be suitable for modeling the electronic structure of large systems. To date, DPFT has been applied mainly to quantum…