Classical bridge functions in classical and quantum plasma liquids

Bridge functions, the missing link in the exact description of strong correlations, are indirectly extracted from specially designed molecular dynamics simulations of classical one-component plasma liquids and accurately parameterized. Their incorporation into an advanced integral equation theory description of Yukawa one-component plasma liquids and a novel dielectric formalism scheme for quantum one-component plasma liquids leads to an unprecedented agreement with available molecular dynamics simulations and new ab initio path integral Monte Carlo simulations, respectively.Comment: 6 pages, 4 figures, 2 table

Quantum version of the integral equation theory based dielectric scheme for strongly coupled electron liquids

A novel dielectric scheme is proposed for strongly coupled electron liquids that handles quantum mechanical effects beyond the random phase approximation level and treats electronic correlations within the integral equation theory of classical liquids. The self-consistent scheme features a complicated dynamic local field correction functional and its formulation is guided by ab initio path integral Monte Carlo simulations. Remarkably, our scheme is capable to provide unprecedently accurate results for the static structure factor with the exception of the Wigner crystallization vicinity, despite the absence of adjustable or empirical parameters.Comment: 8 pages, 3 figure

Testing the isomorph invariance of the bridge functions of Yukawa one-component plasmas

It has been conjectured that bridge functions remain nearly invariant along phase diagram lines of constant excess entropy for the class of R-simple liquids. In the companion paper, this hypothesis has been confirmed for Yukawa bridge functions outside the correlation void. In order to complete the testing of the invariance ansatz, Yukawa bridge functions are here computed inside the correlation void with the cavity distribution method and input from ultra-long molecular dynamics simulations featuring a tagged particle pair. A general methodology is developed for the design of the tagged pair interaction potential that leads to the acquisition of uniform statistics. An extrapolation technique is developed to determine the bridge function value at zero separation. The effect of different sources of errors is quantified. Yukawa bridge functions are demonstrated to be nearly isomorph invariant also in the short range. Generalization to all R-simple systems and practical implications are discussed.Comment: 19 pages, 10 figures, 3 tables, supplementary materia

Testing the isomorph invariance of the bridge functions of Yukawa one-component plasmas. I. Intermediate and long range

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 and structural input from ultra-accurate molecular dynamics simulations. The effect of statistical, grid, finite-size, tail and isomorphic errors is quantified. Uncertainty propagation analysis is complemented with a detailed investigation of the sensitivity of the bridge function to periodic and aperiodic multiplicative perturbations in the radial distribution function. In the long and intermediate range, bridge functions are demonstrated to be approximately isomorph invariant.Comment: 22 pages; 12 figure

Isomorph invariance and thermodynamics of repulsive dense bi-Yukawa one-component plasmas

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.Comment: 11 pages, 6 figure

Bridge functions in strongly coupled plasmas : theory, simulations and applications

Strongly coupled or non-ideal plasmas are multi-component charged systems in which at least one species possesses an average interaction energy that is comparable or larger than its thermal energy. Non-ideal plasmas are naturally occurring in dense astrophysical objects (e.g. giant planet interiors) but also engineered in the laboratory (e.g. plasma discharges seeded with solid particulates). They are typically encountered in the liquid state, whose theoretical description is particularly challenging due to the lack of small parameters.  This thesis is focused on the development of a  novel theoretical approach for the accurate calculation of the structural and thermodynamic properties of plasma liquids. Apart from their inherent significance, these properties also constitute necessary input to advanced theories of dynamical correlations, collective excitations and transport coefficients. The theoretical approach is based on the integral equation theory framework, whose central quantity is the bridge function; an abstract object of diagrammatic analysis that is impossible to calculate or even approximate through virial-type expansions.  Here the bridge function is accurately determined by combining elements of the isomorph theory of R-simple liquids with indirect extractions from computer simulations. The unprecedented level of accuracy in both the structural and thermodynamic properties and the very low computational cost, render the approach the most efficient alternative to computer simulations of classical and quantum plasma liquids. Applications to collective modes and metastable properties are also discussed.Starkt kopplade eller icke-ideala plasma är flerkomponent system av laddade partiklar där minst ett partikelslag har en genomsnittlig interaktionsenergi som är jämförbar eller större än dess termiska energi. Icke-idealiska plasma förekommer naturligt i täta astrofysiska objekt (t.ex. jätteplaners interiörer) men är också konstruerade i laboratoriet (t.ex.  plasmaurladdningar med fasta partiklar). De påträffas vanligtvis i flytande tillstånd, vars teoretiska beskrivning är särskilt utmanande då det saknas små parametrar som kan användas för approximation.Denna avhandling är fokuserad på utvecklingen av en ny teoretisk metod för noggrann beräkning av plasmavätskors strukturella och termodynamiska egenskaper. Förutom deras inneboende betydelse utgör dessa egenskaper också nödvändig input till teorier om dynamiska korrelationer, kollektiva excitationer och transportkoefficienter. Det teoretiska tillvägagångssättet är baserat på det integralekvationsteoretiska ramverket, vars centrala kvantitet är bryggfunktionen; ett abstrakt objekt för diagrammatisk analys som är omöjligt att beräkna eller ens approximera genom expansioner av virialtyp. Här bestäms bryggfunktionen noggrant genom att kombinera element från isomorfteorin för R-enkla vätskor med indirekta extraktioner från datorsimuleringar. Den oöverträffade nivån av noggrannhet i både de strukturella och termodynamiska egenskaperna och den mycket låga beräkningskostnaden, gör metoden till det mest effektiva alternativet till datorsimuleringar av klassiska och kvantplasmavätskor. Tillämpningar på vågor och metastabila egenskaper diskuteras också.QC 20211117</p

Bridge functions in strongly coupled plasmas : theory, simulations and applications

Strongly coupled or non-ideal plasmas are multi-component charged systems in which at least one species possesses an average interaction energy that is comparable or larger than its thermal energy. Non-ideal plasmas are naturally occurring in dense astrophysical objects (e.g. giant planet interiors) but also engineered in the laboratory (e.g. plasma discharges seeded with solid particulates). They are typically encountered in the liquid state, whose theoretical description is particularly challenging due to the lack of small parameters.  This thesis is focused on the development of a  novel theoretical approach for the accurate calculation of the structural and thermodynamic properties of plasma liquids. Apart from their inherent significance, these properties also constitute necessary input to advanced theories of dynamical correlations, collective excitations and transport coefficients. The theoretical approach is based on the integral equation theory framework, whose central quantity is the bridge function; an abstract object of diagrammatic analysis that is impossible to calculate or even approximate through virial-type expansions.  Here the bridge function is accurately determined by combining elements of the isomorph theory of R-simple liquids with indirect extractions from computer simulations. The unprecedented level of accuracy in both the structural and thermodynamic properties and the very low computational cost, render the approach the most efficient alternative to computer simulations of classical and quantum plasma liquids. Applications to collective modes and metastable properties are also discussed.Starkt kopplade eller icke-ideala plasma är flerkomponent system av laddade partiklar där minst ett partikelslag har en genomsnittlig interaktionsenergi som är jämförbar eller större än dess termiska energi. Icke-idealiska plasma förekommer naturligt i täta astrofysiska objekt (t.ex. jätteplaners interiörer) men är också konstruerade i laboratoriet (t.ex.  plasmaurladdningar med fasta partiklar). De påträffas vanligtvis i flytande tillstånd, vars teoretiska beskrivning är särskilt utmanande då det saknas små parametrar som kan användas för approximation.Denna avhandling är fokuserad på utvecklingen av en ny teoretisk metod för noggrann beräkning av plasmavätskors strukturella och termodynamiska egenskaper. Förutom deras inneboende betydelse utgör dessa egenskaper också nödvändig input till teorier om dynamiska korrelationer, kollektiva excitationer och transportkoefficienter. Det teoretiska tillvägagångssättet är baserat på det integralekvationsteoretiska ramverket, vars centrala kvantitet är bryggfunktionen; ett abstrakt objekt för diagrammatisk analys som är omöjligt att beräkna eller ens approximera genom expansioner av virialtyp. Här bestäms bryggfunktionen noggrant genom att kombinera element från isomorfteorin för R-enkla vätskor med indirekta extraktioner från datorsimuleringar. Den oöverträffade nivån av noggrannhet i både de strukturella och termodynamiska egenskaperna och den mycket låga beräkningskostnaden, gör metoden till det mest effektiva alternativet till datorsimuleringar av klassiska och kvantplasmavätskor. Tillämpningar på vågor och metastabila egenskaper diskuteras också.QC 20211117</p