Towards a quantum fluid theory of correlated many-fermion systems from first principles

Zhandos Moldabekov,Gianluca Gregori,Michael Bonitz,Attila Cangi,Frank Graziani,Tobias Dornheim

doi:10.21468/scipostphys.12.2.062

Abstract

Correlated many-fermion systems emerge in a broad range of phenomena in warm dense matter, plasmonics, and ultracold atoms. Quantum hydrodynamics (QHD) complements first-principles methods for many-fermion systems at larger scales. We illustrate the failure of the standard Bohm potential central to QHD for strong perturbations when the density perturbation is larger than about 10^{-3}10−3 of the mean density. We then extend QHD to this regime via the many-fermion Bohm potential from first-principles. This may lead to more accurate QHD simulations beyond their common application domain in the presence of strong perturbations at scales unattainable with first-principles methods.

Highlights

We illustrate the failure of the standard Bohm potential central to Quantum hydrodynamics (QHD) for strong perturbations when the density perturbation is larger than about 10−3 of the mean density
As the central result of this work we demonstrate the relevance of the many-fermion Bohm potential for the QHD equations (5) and (6), whereas in all prior works the standard Bohm potential was used
While approximations to the pressure and viscous stress-tensor influence the accuracy of the QHD equations, we focus on the manyfermion Bohm potential

Summary

Introduction

Correlated quantum many-fermion systems are currently in the focus of several fields ranging from high-energy-density physics [1] to ultracold fermionic atoms [2] and correlated materials [3]. There is a high need for complementary methods that extend the domain of simulations to length and time scales relevant for experiments, even at the price of reduced accuracy One such method is quantum hydrodynamics (QHD). While standard QHD has proven useful, we question the validity of the standard Bohm potential when strong density perturbations are present These emerge, for example, in strongly perturbed WDM [26] and quantum plasmas [27, 28]. Throughout the manuscript, we consider the practically important example of the harmonically perturbed, interacting electron gas at finite temperature which is a challenging many-fermion system and is a relevant for modeling high-energy density experiments conducted at coherent light sources and pulsed power facilities around the globe. Utilizing the many-fermion Bohm potential in QHD is motivated by the fact that it is derived from the exact quantum dynamics of electrons within time-dependent DFT [6] which provides the crucial link between QHD and interacting many-fermion systems

Theory

Results

Conclusions and Outlook

A KS-DFT simulation details

B QMC simulation details

C KS-DFT results for the many-fermion Bohm potential