Decay of correlations in fluids: The one-component plasma from Debye-Hückel to the asymptotic-high-density limit

Abstract

The decay of structural correlations in the classical one-component plasma is analyzed by calculating the poles of the Fourier transform of the total ͑pairwise͒ correlation function h(r) for two integral equation theories, the soft mean spherical approximation and the hypernetted chain ͑HNC͒. We show that for all except the largest values of the plasma coupling constant ⌫, the leading-order pole contribution provides an accurate description of h(r) at intermediate range, as well as the ultimate asymptotic decay. The crossover from monotonic decay at weak coupling to exponentially damped oscillatory decay at strong coupling is shown to arise from the same mechanism as that which occurs for charge correlations in binary ionic fluids. We calculate the values of ⌫ at which the crossover occurs in the two theories. The role of higher-order poles and ͑within the HNC͒ other singularities in determining the intermediate range behavior of h(r) for strong coupling is discussed. We investigate the properties of the solutions of the integral equations in the strong coupling, ⌫ →ϱ, asymptotic high-density limit ͑AHDL͒. Padé approximants are employed in order to test the validity of the scaling laws proposed for the potential energy, direct correlation function, and for the poles and their contributions to h(r) in the AHDL. Our numerical results provide strong support for the validity of the theoretical predictions concerning the AHDL.

Pair-correlation functions and phase separation in a two-component point Yukawa fluid

“…In general, the relevant integrals converge only for complex q such that I͓q͔ Շ 2␣ 0 , where ␣ 0 is the imaginary part of the leading order pole. 17 It follows that only a few poles can be calculated; the remaining poles are situated outside this region of convergence. Fortunately the poles relevant for determining the basic features of the decay of correlations can be obtained.…”

Melting of the vortex lattice in high−Tcsuperconductors

“…A variety of analytical and numerical methods [22] have indicated that liquid (gas) phase of the classical one component Coulomb plasma also exists as a metastable state down to T = 0 with energy gradually approaching that of the Madelung solid and the excitation energy diminishing. We speculate that the same phenomenon would appear to happen in any system of particles interacting via long range repulsive forces.…”

The decay of pair correlations in quantum hard-sphere fluids

“…39 Such a fixing of R Z , which from the numerical standpoint forces c(rуR Z )ϭ0, is carried out via a leastsquares minimization of an objective function F ϭF(Q,QЈ), which yields one or more than one R Z values. 13,15,16 Note that the interesting case of Yukawa attractions beyond the hard core, where an exponential decay of c(r) occurs in the MSA classical case, 55 falls completely within the foregoing issue. 29,33 Note that the foregoing assumption ͑i͒ requires careful consideration.…”

“…15,16 These divergences may be related to both the existence of attractions and the theoretical forms of the c(r) tails ͑e.g., HNC, MSA͒, and they can be characterized by comparing the imaginary components y n of the poles k Ϯn with physically relevant inverse distance parameters. If, on the contrary, y 1 Ͻy 0 , the pair k Ϯ1 will dominate and exponentially damped oscillatory decay will result.…”