Related papers: On Virial Expansion in Hard Sphere Model
Quantum virial expansion provides an ideal tool to investigate the high-temperature properties of a strongly correlated Fermi gas. Here, we construct the virial expansion in the presence of spin population imbalance. Up to the third order,…
Using a coarse temporal lattice approximation, we calculate the first few terms of the virial expansion of a three-species fermion system with a three-body contact interaction in $d$ spatial dimensions, both in homogeneous space as well as…
We study pressurised self-avoiding ring polymers in two dimensions using Monte Carlo simulations, scaling arguments and Flory-type theories, through models which generalise the model of Leibler, Singh and Fisher [Phys. Rev. Lett. Vol. 59,…
We formulate a straightforward scheme of statistical mechanics for inhomogeneous systems that includes the virial series in powers of the activity for the grand free energy and density distributions. There, cluster integrals formulated for…
The dynamics of a stiff filament (made by connecting beads) embedded in size-polydisperse hard sphere fluid is investigated by means of molecular dynamics simulations with focus on how the degree of size-polydispersity, characterized by…
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…
Experiments show that all the derivatives of the thermo-physical variables are nearly constant. The constant value of the derivatives indicates linear relationship between the variables. Neither the volume coefficient of thermal expansion…
The partition function and the one- and two-body distribution functions are evaluated for two hard spheres with different sizes constrained into a spherical pore. The equivalent problem for hard disks is addressed too. We establish a…
We explore quantitative descriptors that herald when a many-particle system in $d$-dimensional Euclidean space $\mathbb{R}^d$ approaches a hyperuniform state as a function of the relevant control parameter. We establish quantitative…
A model for the radial distribution function $g(r)$ of a square-well fluid of variable width previously proposed [S. B. Yuste and A. Santos, J. Chem. Phys. {\bf 101}, 2355 (1994)] is revisited and simplified. The model provides an explicit…
We prove a novel inversion theorem for functionals given as power series in infinite-dimensional spaces and apply it to the inversion of the density-activity relation for inhomogeneous systems. This provides a rigorous framework to prove…
We determine the second, third, and fourth virial coefficients appearing in the density expansion of the osmotic pressure of a monodisperse polymer solution in good-solvent conditions. Using the expected large-concentration behavior, we…
The penetrable-sphere model has been introduced in the literature to describe the peculiar thermodynamic behavior of some colloidal systems. In this model the interaction potential is $\phi(r)=\epsilon>0$ if the two spheres are overlapped…
Accurate descriptions of reference systems are a central task in liquid-state theories for the study of more complex systems. Using scaled particle theory (SPT), we derive a fully analytical description of the thermodynamic properties of a…
We characterize the high-temperature thermodynamics of rotating bosons and fermions in two- (2D) and three-dimensional (3D) isotropic harmonic trapping potentials. We begin by calculating analytically the conventional virial coefficients…
We analyze numerically the critical properties of a two-dimensional discretized random surface with extrinsic curvature embedded in a three-dimensional space. The use of the toroidal topology enables us to enforce the non-zero external…
A new method of estimating high-order virial coefficients for fluids composed of equal three-dimensional rigid spheres is proposed. The predicted $B_{11}$ and $B_{12}$ values are in good agreement with reliable estimates previously…
We consider a mixture of non-overlapping rods of different lengths $\ell_k$ moving in $\mathbb{R}$ or $\mathbb{Z}$. Our main result are necessary and sufficient convergence criteria for the expansion of the pressure in terms of the…
In this work I derive analytic expressions for the curvature dependent fluid-substrate surface tension of a hard sphere fluid on a hard curved wall. In a first step, the curvature thermodynamic properties are found as truncated power series…
On the example of a lattice-gas model, a convincing confirmation is obtained for the direct relationship between the condensation phenomenon and divergent behavior of the virial expansions for pressure and density in powers of activity. The…