Theory of the quantum breathing mode in harmonic traps and its use as a diagnostic tool

Fermionic physics from ab initio path integral Monte Carlo simulations of fictitious identical particles

The ab initio path integral Monte Carlo (PIMC) method is one of the most successful methods in statistical physics, quantum chemistry and related fields, but its application to quantum degenerate Fermi systems is severely hampered by an exponential computational bottleneck: the notorious fermion sign problem. Very recently, Xiong and Xiong [J. Chem. Phys. 157, 094112 (2022)] have suggested to partially circumvent the sign problem by carrying out simulations of fictitious systems guided by an interpolating continuous variable ξ ∈ [-1, 1], with the physical Fermi- and Bose-statistics corresponding to ξ = -1 and ξ = 1. It has been proposed that information about the fermionic limit might be obtained by calculations within the bosonic sector ξ > 0 combined with an extrapolation throughout the fermionic sector ξ < 0, essentially bypassing the sign problem. Here, we show how the inclusion of the artificial parameter ξ can be interpreted as an effective penalty on the formation of permutation cycles in the PIMC simulation. We demonstrate that the proposed extrapolation method breaks down for moderate to high quantum degeneracy. Instead, the method constitutes a valuable tool for the description of large Fermi-systems of weak quantum degeneracy. This is demonstrated for electrons in a 2D harmonic trap and for the uniform electron gas (UEG), where we find excellent agreement (∼0.5%) with exact configuration PIMC results in the high-density regime while attaining a speed-up exceeding 11 orders of magnitude. Finally, we extend the idea beyond the energy and analyze the radial density distribution (2D trap), as well as the static structure factor and imaginary-time density-density correlation function (UEG).

Finite-temperature quantum effects on confined charges

A quantum system of N Coulomb charges confined within a harmonic trap is considered over a wide range of densities and temperatures. A recently described construction of an equivalent classical system is applied in order to exploit the rather complete classical description of harmonic confinement via liquid-state theory. Here, the effects of quantum mechanics on that representation are described with attention focused on the origin and nature of shell structure. The analysis extends from the classical strong Coulomb coupling conditions of dusty plasmas to the opposite limit of low temperatures and large densities characteristic of "warm, dense matter."

Dynamics of strongly correlated and strongly inhomogeneous plasmas

Kinetic and fluid equations are derived for the dynamics of classical inhomogeneous trapped plasmas in the strong coupling regime. The starting point is an extended Singwi-Tosi-Land-Sjölander (STLS) ansatz for the dynamic correlation function, which is allowed to depend on time and both particle coordinates separately. The time evolution of the correlation function is determined from the second equation of the Bogolyubov-Born-Green-Kirkwood-Yvon hierarchy. We study the equations in the linear limit and derive a nonlocal equation for the fluid displacement field. Comparisons to first-principles molecular dynamics simulations reveal an excellent quality of our approach thereby overcoming the limitations of the broadly used STLS scheme.