# Structure and thermodynamics of classical & quantum plasma liquids

Docentlecture by Panagiotis Tolias, Division of Space and Plasma Physics, Department of Electrical Engineering

**Time: **
Wed 2021-12-15 10.00

**Location: **
Teknikringen 14, Floor 3, Room 304 (Jan-Olof Eklundh)

**Language: **
English

**Lecturer: **
Dr. Panagiotis Tolias

Strongly coupled plasmas are ubiquitous in the universe (giant planet interiors, brown dwarfs, outer neutron star crusts) and the laboratory (complex plasmas, ultra-cold neutral plasmas, fast laser heating of metals). They consist of classical point particles or fermions interacting via bare or screened Coulomb potentials. Pivotal to their understanding are three models; the classical, quantum and Yukawa one-component plasma (cOCP, qOCP, YOCP) which assume a strongly coupled charged component embedded in a rigid or polarizable uniform neutralizing background. The liquid state of such systems, although confined in a small portion of the phase diagram between the gas and crystal states, has proven to be the most theoretically elusive due to its lack of small parameters that forbid perturbative expansions. Integral equation theory of liquids constitutes the most appropriate framework for the accurate computation of structural and thermodynamic properties, given its ability to retain information at all orders. However, it requires a closure for the so-called bridge function; a rather enigmatic object of diagrammatic analysis, whose density expansion is slowly convergent and impossible to calculate as well as whose indirect extraction from simulations is quite formidable and relatively unexplored.

*In the first part of the lecture*, I will present a general methodology for the indirect extraction of bridge functions from molecular dynamics simulations, which requires input from standard canonical simulations and specially designed canonical simulations featuring tagged particle pairs. The methodology is applied to the cOCP, after some Coulomb interaction peculiarities are taken into account, ultimately leading to an accurate parametrization that is valid within the entire dense liquid region of the phase diagram. This leads to a near-exact solution of the structural and thermodynamic problem for the cOCP. *In the second part*, I will show that the bridge functions are constant along isentropic phase diagram lines for the broad class of R-simple liquids. Given the continuity between cOCP and YOCP states, this allows a one-to-one mapping of the cOCP to the YOCP bridge functions. Combined with integral equation theory, this amounts to the novel isomorph-based empirically modified hypernetted chain approach whose predictions have an unprecedented level of accuracy on par with that of simulations. *In the last part*, I will employ the cOCP bridge functions as input in a novel dielectric formalism scheme for the qOCP. A comparison with *ab initio *path integral Monte Carlo simulations targeting the paramagnetic electron liquid will again reveal an excellent agreement.