arXiv subjects

Michael Bonitz

Publications and source records attributed to Michael Bonitz.

At least 55 records · Page 3Linked to original sources

arXiv2019

The Static Local Field Correction of the Warm Dense Electron Gas: An ab Initio Path Integral Monte Carlo Study and Machine Learning Representation

The study of matter at extreme densities and temperatures as they occur in astrophysical objects and state-of-the art experiments with high-intensity lasers is of high current interest for many applications. While no overarching theory for this regime exists, accurate data for the density response of correlated electrons to an external perturbation are of paramount importance. In this context, the key quantity is given by the local field correction (LFC), which provides a wave-vector resolved description of exchange-correlation effects. In this work, we present extensive new path integral Monte Carlo (PIMC) results for the static LFC of the uniform electron gas, which are subsequently used to train a fully connected deep neural network. This allows us to present a continuous representation of the LFC with respect to wave-vector, density, and temperature covering the entire warm dense matter regime. Both the PIMC data and neural-net results are available online. Moreover, we expect the presented combination of ab initio calculations with machine-learning methods to be a promising strategy for many applications.

physics.plasm-ph↗

arXiv2019

Path Integral Monte Carlo Simulation of Degenerate Electrons: Permutation-Cycle Properties

Being motivated by the surge of fermionic quantum Monte Carlo simulations at finite temperature, we present a detailed analysis of the permutation-cycle properties of path integral Monte Carlo (PIMC) simulations of degenerate electrons. Particular emphasis is put onto the uniform electron gas in the warm dense matter regime. We carry out PIMC simulations of up to $N=100$ electrons and investigate exchange-cycle frequencies, which are found not to follow any simple exponential law even in the case of ideal fermions due to the finite size of the simulation box. Moreover, we introduce a permutation-cycle correlation function, which allows us to analyse the joint probability to simultaneously find cycles of different lengths within a single configuration. Again, we find that finite-size effects predominate the observed behaviour. Finally, we briefly consider an inhomogeneous system, namely electrons in a $2D$ harmonic trap. We expect our results to be of interest for the further development of fermionic PIMC methods, in particular to alleviate the notorious fermion sign problem.

physics.comp-ph↗

arXiv2019

In memoriam Leonid V. Keldysh

Leonid Keldysh -- one of the most influential theoretical physicists of the 20th century -- passed away in November 2016. Keldysh is best known for the diagrammatic formulation of real-time (nonequilibrium) Green functions theory and for the theory of strong field ionization of atoms. Both theories profoundly changed large areas of theoretical physics and stimulated important experiments. Both these discoveries emerged almost simultaneously -- like Einstein, also Keldysh had his \textit{annus mirabilis} -- the year 1964. But the list of his theoretical developments is much broader and is briefly reviewed here.

physics.hist-ph↗

arXiv2018

Self-diffusion in two-dimensional quasi-magnetized rotating dusty plasmas

The self-diffusion phenomenon in a two-dimensional dusty plasma at extremely strong (effective) magnetic fields is studied experimentally and by means of molecular dynamics simulations. In the experiment the high magnetic field is introduced by rotating the particle cloud and observing the particle trajectories in a co-rotating frame, which allows reaching effective magnetic fields up to 3000 Tesla. The experimental results confirm the predictions of the simulations: (i) super-diffusive behavior is found at intermediate time-scales and (ii) the dependence of the self-diffusion coefficient on the magnetic field is well reproduced.

physics.plasm-ph↗

arXiv2018

The Uniform Electron Gas at Warm Dense Matter Conditions

We review the uniform electron gas (UEG) at finite temperature and over a broad density range relevant for warm dense matter (WDM) applications. We provide an overview of different simulation techniques, focusing on recent developments in the dielectric formalism and quantum Monte Carlo (QMC). Our primary focus is on two novel QMC methods: Permutation blocking path integral MC (PB-PIMC) and configuration PIMC (CPIMC). In fact, a combination of PB-PIMC and CPIMC has allowed for a highly accurate description of the warm dense UEG over a broad density-temperature range. We are able to effectively avoid the notorious fermion sign problem, without invoking uncontrolled approximations such as the fixed node approximation. Furthermore, a new finite-size correction scheme is presented that makes it possible to treat the UEG in the thermodynamic limit without loss of accuracy. In addition, we in detail discuss the construction of a parametrization of the exchange-correlation free energy that provides a complete description of the UEG and is of crucial importance as input for the simulation of real WDM applications. Further, we test previous theories, including restricted PIMC, finite-temperature Green functions, the classical mapping by Perrot and Dharma-wardana, and various dielectric methods such as the random phase approximation, or the Singwi-Tosi-Land-Sjölander, Vashishta-Singwi and the recent Tanaka scheme for the local field correction. Thus, for the first time, thorough benchmarks of important approximation schemes regarding various quantities such as different energies, in particular the exchange-correlation free energy, and the static structure factor, are possible. Finally, we outline a way how to rigorously extend our QMC studies to the inhomogeneous electron gas and present first ab initio data for the static density response and for the static local field correction.

physics.plasm-ph↗

arXiv2018

Doublon formation by ions impacting a strongly correlated finite lattice system

Strongly correlated systems of fermions have a number of exciting collective properties. Among them, the creation of a lattice that is occupied by doublons, i.e. two quantum particles with opposite spins, offers interesting electronic properties. In the past a variety of methods have been proposed to control doublon formation, both, spatially and temporally. Here, a novel mechanism is proposed and verified by exact diagonalization and nonequilibrium Green functions simulations---fermionic doublon creation by the impact of energetic ions. We report the formation of a nonequilibrium steady state with homogeneous doublon distribution. The effect should be observable in strongly correlated solids in contact with a high-pressure plasma and in fermionic atoms in optical lattices.

cond-mat.str-el↗

arXiv2017

\textit{Ab Initio} results for the Static Structure Factor of the Warm Dense Electron Gas

The uniform electron gas at finite temperature is of high current interest for warm dense matter research. The complicated interplay of quantum degeneracy and Coulomb coupling effects is fully contained in the pair distribution function or, equivalently, the static strucutre factor. By combining exact quantum Monte Carlo results for large wave vectors with the long-range behavior from the Singwi-Tosi-Land-Sjölander approximation, we are able to obtain highly accurate data for the static structure factor over the entire $k$-range. This allows us to gauge the accuracy of previous approximations and discuss their respective shortcomings. Further, our new data will serve as valuable input for the computation of other quantities.

physics.plasm-ph↗

arXiv2017

Configuration Path Integral Monte Carlo Approach to the Static Density Response of the Warm Dense Electron Gas

Precise knowledge of the static density response function (SDRF) of the uniform electron gas (UEG) serves as key input for numerous applications, most importantly for density functional theory beyond generalized gradient approximations. Here we extend the configuration path integral Monte Carlo (CPIMC) formalism that was previously applied to the spatially uniform electron gas to the case of an inhomogeneous electron gas by adding a spatially periodic external potential. This procedure has recently been successfully used in permutation blocking path integral Monte Carlo simulations (PB-PIMC) of the warm dense electron gas [Dornheim \textit{et al.}, Phys. Rev. E in press, arXiv:1706.00315], but this method is restricted to low and moderate densities. Implementing this procedure into CPIMC allows us to obtain exact finite temperature results for the SDRF of the electron gas at \textit{high to moderate densities} closing the gap left open by the PB-PIMC data. In this paper we demonstrate how the CPIMC formalism can be efficiently extended to the spatially inhomogeneous electron gas and present the first data points. Finally, we discuss finite size errors involved in the quantum Monte Carlo results for the SDRF in detail and present a solution how to remove them that is based on a generalization of ground state techniques.

cond-mat.str-el↗

arXiv2017

Permutation Blocking Path Integral Monte Carlo approach to the Static Density Response of the Warm Dense Electron Gas

The static density response of the uniform electron gas is of fundamental importance for numerous applications. Here, we employ the recently developed \textit{ab initio} permutation blocking path integral Monte Carlo (PB-PIMC) technique [T.~Dornheim \textit{et al.}, \textit{New J.~Phys.}~\textbf{17}, 073017 (2015)] to carry out extensive simulations of the harmonically perturbed electron gas at warm dense matter conditions. In particular, we investigate in detail the validity of linear response theory and demonstrate that PB-PIMC allows to obtain highly accurate results for the static density response function and, thus, the static local field correction. A comparison with dielectric approximations to our new \textit{ab initio} data reveals the need for an exact treatment of correlations. Finally, we consider a superposition of multiple perturbations and discuss the implications for the calculation of the static response function.

cond-mat.str-el↗

arXiv2017

Ab initio Exchange-Correlation Free Energy of the Uniform Electron Gas at Warm Dense Matter Conditions

In a recent Letter [T.~Dornheim \textit{et al.}, Phys. Rev. Lett. \textbf{117}, 156403 (2016)], we presented the first \textit{ab initio} quantum Monte-Carlo (QMC) results of the warm dense electron gas in the thermodynamic limit. However, a complete parametrization of the exchange-correlation free energy with respect to density, temperature, and spin polarization remained out of reach due to the absence of (i) accurate QMC results below $θ=k_\text{B}T/E_\text{F}=0.5$ and (ii) of QMC results for spin polarizations different from the paramagnetic case. Here we overcome both remaining limitations. By closing the gap to the ground state and by performing extensive QMC simulations for different spin polarizations, we are able to obtain the first complete \textit{ab initio} exchange-correlation free energy functional; the accuracy achieved is an unprecedented $\sim 0.3\%$. This also allows us to quantify the accuracy and systematic errors of various previous approximate functionals.

physics.plasm-ph↗

arXiv2017

Collision induced amplification of wakes in streaming plasmas

This work examines the formation of wake fields caused by ions streaming around a charged dust particle, using three-dimensional particle-in-cell (PIC) simulations with charge-neutral collisions included. The influence of an external driving electric field, which leads to a non-Maxwellian distribution of ions, is investigated in detail. The wake features formed for non-Maxwellian ions exhibit significant deviations from those observed within the model of a shifted Maxwellian distribution. The dependence of the peak amplitude and position of the wake potential upon the degree of collisionality is analyzed for a wide range of streaming velocities (Mach numbers). In contrast to a shifted Maxwellian distribution of ions, the drift-driven non-Maxwellian distribution exhibits an increase of the wake amplitude of the first attractive peak with increase in collisionality for high streaming velocities. At very low Mach numbers, collision-induced amplification is observed for Maxwellian as well as non-Maxwellian distributions.

physics.plasm-ph↗

arXiv2017

Advanced fluid modelling and PIC/MCC simulations of low-pressure ccrf discharges

Comparative studies of capacitively coupled radio-frequency discharges in helium and argon at pressures between 10 and 80 Pa are presented applying two different fluid modelling approaches as well as two independently developed particle-in-cell/Monte Carlo collision (PIC/MCC) codes. The focus is on the analysis of the range of applicability of a recently proposed fluid model including an improved drift-diffusion approximation for the electron component as well as its comparison with fluid modelling results using the classical drift-diffusion approximation and benchmark results obtained by PIC/MCC simulations. Main features of this time- and space-dependent fluid model are given. It is found that the novel approach shows generally quite good agreement with the macroscopic properties derived by the kinetic simulations and is largely able to characterize qualitatively and quantitatively the discharge behaviour even at conditions when the classical fluid modelling approach fails. Furthermore, the excellent agreement between the two PIC/MCC simulation codes using the velocity Verlet method for the integration of the equations of motion verifies their accuracy and applicability.

physics.plasm-ph↗

arXiv2016

Time Reversal Invariance of quantum kinetic equations: Nonequilibrium Green Functions Formalism

Time reversal symmetry is a fundamental property of many quantum mechanical systems. The relation between statistical physics and time reversal is subtle and not all statistical theories conserve this particular symmetry, most notably hydrodynamic equations and kinetic equations such as the Boltzmann equation. In this article it is shown analytically that quantum kinetic generalizations of the Boltzmann equation that are derived using the nonequilibrium Green functions formalism as well as all approximations that stem from $Φ$-derivable selfenergies are time reversal invariant.

cond-mat.str-el↗

arXiv2016

Free Energy of the Uniform Electron Gas: Testing Analytical Models against First Principle Results

The uniform electron gas is a key model system in the description of matter, including dense plasmas and solid state systems. However, the simultaneous occurence of quantum, correlation, and thermal effects makes the theoretical description challenging. For these reasons, over the last half century many analytical approaches have been developed the accuracy of which has remained unclear. We have recently obtained the first \textit{ab initio} data for the exchange correlation free energy of the uniform electron gas [T. Dornheim \textit{et al.}, Phys.~Rev.~Lett.~\textbf{117}, 156403 (2016)] which now provides the opportunity to assess the quality of the mentioned approaches and parametrizations. Particular emphasis is put on the warm dense matter regime, where we find significant discrepancies between the different approaches.

physics.plasm-ph↗

arXiv2016

\emph{Ab initio} Quantum Monte Carlo simulation of the warm dense electron gas

Warm dense matter is one of the most active frontiers in plasma physics due to its relevance for dense astrophysical objects as well as for novel laboratory experiments in which matter is being strongly compressed e.g. by high-power lasers. Its description is theoretically very challenging as it contains correlated quantum electrons at finite temperature---a system that cannot be accurately modeled by standard analytical or ground state approaches. Recently several breakthroughs have been achieved in the field of fermionic quantum Monte Carlo simulations. First, it was shown that exact simulations of a finite model system ($30 \dots 100$ electrons) is possible that avoid any simplifying approximations such as fixed nodes [Schoof {\em et al.}, Phys. Rev. Lett. {\bf 115}, 130402 (2015)]. Second, a novel way to accurately extrapolate these results to the thermodynamic limit was reported by Dornheim {\em et al.} [Phys. Rev. Lett. {\bf 117}, 156403 (2016)]. As a result, now thermodynamic results for the warm dense electron gas are available that have an unprecedented accuracy on the order of $0.1\%$. Here we present an overview on these results and discuss limitations and future directions.

physics.plasm-ph↗

arXiv2016

Stopping dynamics of ions passing through correlated honeycomb clusters

A combined nonequilibrium Green functions-Ehrenfest dynamics approach is developed that allows for a time-dependent study of the energy loss of a charged particle penetrating a strongly correlated system at zero and finite temperature. Numerical results are presented for finite inhomogeneous two-dimensional Fermi-Hubbard models, where the many-electron dynamics in the target are treated fully quantum mechanically and the motion of the projectile is treated classically. The simulations are based on the solution of the two-time Dyson (Keldysh-Kadanoff-Baym) equations using the second-order Born, third-order and T-matrix approximations of the self-energy. As application, we consider protons and helium nuclei with a kinetic energy between 1 and 500 keV/u passing through planar fragments of the two-dimensional honeycomb lattice and, in particular, examine the influence of electron-electron correlations on the energy exchange between projectile and electron system. We investigate the time dependence of the projectile's kinetic energy (stopping power), the electron density, the double occupancy and the photoemission spectrum. Finally, we show that, for a suitable choice of the Hubbard model parameters, the results for the stopping power are in fair agreement with ab-initio simulations for particle irradiation of single-layer graphene.

cond-mat.str-el↗

arXiv2016

{\em Ab initio} Quantum Monte Carlo simulation of the warm dense electron gas in the thermodynamic limit

We perform \emph{ab initio} quantum Monte Carlo (QMC) simulations of the warm dense uniform electron gas in the thermodynamic limit. By combining QMC data with linear response theory we are able to remove finite-size errors from the potential energy over the entire warm dense regime, overcoming the deficiencies of the existing finite-size corrections by Brown \emph{et al.}~[PRL \textbf{110}, 146405 (2013)]. Extensive new QMC results for up to $N=1000$ electrons enable us to compute the potential energy $V$ and the exchange-correlation free energy $F_{xc}$ of the macroscopic electron gas with an unprecedented accuracy of $|ΔV|/|V|, |ΔF_{xc}|/|F|_{xc} \sim 10^{-3}$. A comparison of our new data to the recent parametrization of $F_{xc}$ by Karasiev {\em et al.} [PRL {\bf 112}, 076403 (2014)] reveals significant deviations to the latter.

physics.plasm-ph↗

arXiv2016

Correlation effects in strong-field ionization of heteronuclear diatomic molecules

We develop a time-dependent theory to investigate electron dynamics and photoionization processes of diatomic molecules interacting with strong laser fields including electron-electron correlation effects. We combine the recently formulated time-dependent generalized-active-space configuration interaction theory [D. Hochstuhl and M. Bonitz, Phys. Rev. A 86, 053424 (2012); S. Bauch, et al., Phys. Rev. A 90, 062508 (2014)] with a prolate spheroidal basis set including localized orbitals and continuum states to describe the bound electrons and the outgoing photoelectron. As an example, we study the strong-field ionization of the two-center four-electron lithium hydride molecule in different intensity regimes. By using single-cycle pulses, two orientations of the asymmetric heteronuclear molecule are investigated: Li-H, with the electrical field pointing from H to Li, and the opposite case of H-Li. The preferred orientation for ionization is determined and we find a transition from H-Li, for low intensity, to Li-H, for high intensity. The influence of electron correlations is studied at different levels of approximation, and we find a significant change in the preferred orientation. For certain intensity regimes, even an interchange of the preferred configuration is observed, relative to the uncorrelated simulations. Further insight is provided by detailed comparisons of photoelectron angular distributions with and without correlation effects taken into account.

physics.chem-ph↗