Isomorph theory is employed in order to establish a mapping between the bridge function of Coulomb and Yukawa one-component plasmas. Within an exact invariance ansatz for the bridge functions and by capitalizing on the availability of simulation-extracted Coulomb bridge functions, an analytical Yukawa bridge function is derived which is inserted into the integral theory framework. In spite of its simplicity and computational speed, the proposed integral approach exhibits an excellent agreement with computer simulations of dense Yukawa liquids without invoking adjustable parameters. 

In numerous realizations of complex plasmas, dust-dust interactions are characterized by two screening lengths and are thus better described by a combination of Yukawa potentials. The present work investigates the static correlations and the thermodynamics of repulsive dense bi-Yukawa fluids based on the fact that such strongly coupled systems exhibit isomorph invariance. The strong virial-potential energy correlations are demonstrated with the aid of molecular dynamics simulations, an accurate analytical expression for the isomorph family of curves is obtained, and an empirical expression for the fluid-solid phase-coexistence line is proposed. The isomorph-based empirically modified hypernetted-chain approach, grounded on the ansatz of isomorph invariant bridge functions, is then extended to such systems and the resulting structural properties show an excellent agreement with the results of computer simulations. A simple and accurate closed-form expression is obtained for the excess internal energy of dense bi-Yukawa fluids by capitalizing on the compact parameterization offered by the Rosenfeld-Tarazona decomposition in combination with the Rosenfeld scaling, which opens up the energy route to thermodynamics.

Different advanced bridge function closures are utilized to investigate the structural and thermodynamic properties of dense Yukawa one-component plasma liquids within the framework of integral equation theory. The isomorph-based empirically modified hypernetted-chain, the variational modified hypernetted-chain, the Rogers-Young, and the Ballone-Pastore-Gall-Gazzillo approaches are compared at the level of thermodynamic properties, radial distribution functions, and bridge functions. The comparison, based on accuracy and computational speed, concludes that the two modified hypernetted-chain approaches are superior and singles out the isomorph-based variant as the most promising alternative to computer simulations of structural properties of dense Yukawa liquids. The possibility of further improvement through artificial crossover to exact asymptotic limits is studied. 

The mode coupling theory of supercooled liquids is combined with advanced closures to the integral equation theory of liquids in order to estimate the glass transition line of Yukawa one-component plasmas from the unscreened Coulomb limit up to the strong screening regime. The present predictions constitute a major improvement over the current literature predictions. The calculations confirm the validity of an existing analytical parameterization of the glass transition line. It is verified that the glass transition line is an approximate isomorphic curve and the value of the corresponding reduced excess entropy is estimated. Capitalizing on the isomorphic nature of the glass transition line, two structural vitrification indicators are identified that allow a rough estimate of the glass transition point only through simple curve metrics of the static properties of supercooled liquids. The vitrification indicators are demonstrated to be quasi-universal by an investigation of hard sphere and inverse power law supercooled liquids. The straightforward extension of the present results to bi-Yukawa systems is also discussed.

In moderately coupled Yukawa fluids, longitudinal mode dispersion is determined by the competition between kinetic and potential effects. In a recent paper [S. Khrapak and L. Couedel, Phys. Rev. E 102, 033207 (2020)], a semi-phenomenological dispersion relation was constructed by the ad hoc addition of the Bohm-Gross kinetic term to the generalized instantaneous excess bulk modulus, which showed very good agreement with simulations. In this paper, a nearly identical dispersion relation is derived in a rigorous manner based on a dielectric formulation with static local field corrections. At moderate coupling, this formalism is revealed to be more accurate than other successful theoretical approaches.

The thermodynamic and structural properties of two dimensional dense Yukawa liquids are studied with molecular dynamics simulations. The "exact" thermodynamic properties are simultaneously employed in an advanced scheme for the determination of an equation of state that shows an unprecedented level of accuracy for the internal energy, pressure and isothermal compressibility. The "exact" structural properties are utilized to formulate a novel empirical correction to the hypernetted-chain approach that leads to a very high accuracy level in terms of static correlations and thermodynamics.

It has been recently conjectured that bridge functions remain nearly invariant along phase diagram lines of constant excess entropy for the broad class of R-simple liquids. To test this hypothesis, the bridge functions of Yukawa systems are computed outside the correlation void with the Ornstein-Zernike inversion method employing structural input from ultra-accurate molecular dynamics simulations and inside the correlation void with the cavity distribution method employing structural input from ultra-long specially designed molecular dynamics simulations featuring a tagged particle pair. Yukawa bridge functions are revealed to be isomorph invariant to a very high degree. The observed invariance is not exact, however, since isomorphic deviations exceed the overall uncertainties.

In a recent paper, Lucco Castello et al. (arXiv:2107.03537) provided an accurate parameterization of classical one-component plasma bridge functions that was embedded in a novel dielectric scheme for strongly coupled electron liquids. Here, this approach is rigorously formulated, its set of equations is formally derived, and its numerical algorithm is scrutinized. A systematic comparison with available and new path integral Monte Carlo simulations reveals a rather unprecedented agreement especially in terms of the interaction energy and the long wavelength limit of the static local field correction.