RELAXATION TIMES FOR A HARD-SPHERE GAS

Collisional statistics of the hard-sphere gas.

We investigate the probability distribution functions of the free flight time and of the number of collisions in a hard-sphere gas at equilibrium. At variance with naive expectation, the latter quantity does not follow Poissonian statistics, even in the dilute limit, which is the focus of the present analysis. The corresponding deviations are addressed both numerically and analytically. In writ...

Hard-sphere-like dynamics in a non-hard-sphere liquid.

The collective dynamics of liquid gallium close to the melting point has been studied using inelastic x-ray scattering to probe length scales smaller than the size of the first coordination shell. Although the structural properties of this partially covalent liquid strongly deviate from a simple hard-sphere model, the dynamics, as reflected in the quasielastic scattering, are beautifully descri...

Universality in the Three-Dimensional Hard- Sphere Lattice Gas

We perform Monte Carlo simulations of the hard-sphere lattice gas on the body-centred cubic lattice with nearest neighbour exclusion. We get the critical exponents, β/ν = 0.311(8) and γ/ν = 2.38(2), where β, γ, and ν are the critical exponents of the staggered density, the staggered compressibility, and the correlation length, respectively. The values of the hard-sphere lattice gas on the simpl...

The Onset of Chaos in the Quantum Hard-Sphere Gas

We show that the condition for the appearance of quantum chaos (Wigner-Dyson distribution of energy eigenvalues, gaussian-random energy eigenfunctions) in a dilute gas of many hard spheres is λ ≪ l, where λ is the wavelength of a typical particle and l is the mean free path between collisions. For fermions with Fermi wavelength λF ≪ l, this implies that all energy eigenstates, including the gro...

Phase Transition for a Hard Sphere System