@article{Kelbg:Annalen:1963, author = {Kelbg, G.}, journal = {Annalen der Physik}, number = {3-4}, pages = {219-224}, title = {Theorie des Quanten-Plasmas}, volume = {467}, year = {1963}, abstract = {Abstract Es wird die quantenstatistische Zustandssumme eines N-Teilchensystems im Falle weitreichender zwischenmolekularer Wechselwirkungen berechnet. Das Verfahren ist anwendbar, wenn die Potentiale Fourier-Transformierte besitzen. Durch Einführung effektiver Potentiale, die von der Temperatur und dem Planckschen Wirkungsquantum abhängen, wird es möglich, bekannte klassische Gleichungen heranzuziehen und Formeln für die freie Energie und die radiale Verteilungsfunktion aufzustellen. Im Falle eines Plasmas tritt an die Stelle des Coulomb-Potentials eine in der Nähe des Nullpunktes davon abweichende nichtsinguläre Potentialfunktion, deren Betrag im Nullpunkt durch den reziproken Wert der thermischen Wellenlänge bestimmt wird.}, doiurl = {https://doi.org/10.1002/andp.19634670308}, } @article{Filinov:PRE:2004, author = {Filinov, A. V. and Golubnychiy, V. O. and Bonitz, M. and Ebeling, W. and Dufty, J. W.}, journal = {Phys. Rev. E}, month = {Oct}, number = {4}, pages = {046411}, publisher = {American Physical Society}, title = {Temperature-dependent quantum pair potentials and their application to dense partially ionized hydrogen plasmas}, volume = {70}, year = {2004}, doiurl = {10.1103/PhysRevE.70.046411}, url = {https://link.aps.org/doi/10.1103/PhysRevE.70.046411}, } @article{Filinov:IOP:2001, author = {V S Filinov and M Bonitz and W Ebeling and V E Fortov}, journal = {Plasma Physics and Controlled Fusion}, month = {may}, number = {6}, pages = {743--759}, publisher = {{IOP} Publishing}, title = {Thermodynamics of hot dense H-plasmas: path integral Monte Carlo simulations and analytical approximations}, volume = {43}, year = {2001}, abstract = {This work is devoted to the thermodynamics of high-temperature dense hydrogen plasmas in the pressure region between 10-1 and 102 Mbar. In particular, we present for this region results of extensive calculations based on a recently developed path integral Monte Carlo scheme (direct PIMC). This method allows for a correct treatment of the thermodynamic properties of hot dense Coulomb systems. Calculations were performed in a broad region of the non-ideality parameter Γ≲3 and degeneracy parameter neΛ3≲10. We give a comparison with a few available results from other path integral calculations (restricted PIMC) and with analytical calculations based on Padé approximations for strongly ionized plasmas. Good agreement between the results obtained from the three independent methods is found.}, doiurl = {10.1088/0741-3335/43/6/301}, url = {https://doi.org/10.1088/0741-3335/43/6/301}, } @article{Fraser:PRB:1996, author = {Fraser, Louisa M. and Foulkes, W. M. C. and Rajagopal, G. and Needs, R. J. and Kenny, S. D. and Williamson, A. J.}, journal = {Phys. Rev. B}, month = {Jan}, number = {4}, pages = {1814--1832}, publisher = {American Physical Society}, title = {Finite-size effects and Coulomb interactions in quantum Monte Carlo calculations for homogeneous systems with periodic boundary conditions}, volume = {53}, year = {1996}, doiurl = {10.1103/PhysRevB.53.1814}, url = {https://link.aps.org/doi/10.1103/PhysRevB.53.1814}, } @article{DORNHEIM:PhysRep:2018, author = {Tobias Dornheim and Simon Groth and Michael Bonitz}, journal = {Physics Reports}, pages = {1-86}, title = {The uniform electron gas at warm dense matter conditions}, volume = {744}, year = {2018}, abstract = {Motivated by the current high interest in the field of warm dense matter research, in this article we review the uniform electron gas (UEG) at finite temperature and over a broad density range relevant for warm dense matter applications. We provide an exhaustive overview of different simulation techniques, focusing on recent developments in the dielectric formalism (linear response theory) and quantum Monte Carlo (QMC) methods. Our primary focus is on two novel QMC methods that have recently allowed us to achieve breakthroughs in the thermodynamics of the warm dense electron gas: Permutation blocking path integral MC (PB-PIMC) and configuration path integral MC (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, on the basis of these data — the central thermodynamic quantity that provides a complete description of the UEG and is of crucial importance as input for the simulation of real warm dense matter applications, e.g., via thermal density functional theory. A second major aspect of this review is the use of our ab initio simulation results to 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 (both in the static and quantum versions), Vashishta–Singwi and the recent Tanaka scheme for the local field correction. Thus, for the first time, thorough benchmarks of the accuracy 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. In the final part of this paper, we outline a way how to rigorously extend our QMC studies to the inhomogeneous electron gas. We present first ab initio data for the static density response and for the static local field correction.}, doiurl = {https://doi.org/10.1016/j.physrep.2018.04.001}, issn = {0370-1573}, url = {https://www.sciencedirect.com/science/article/pii/ S0370157318300516}, } @misc{Mathematica, author = {Wolfram Research{,} Inc.}, note = {Champaign, IL, 2021}, title = {Mathematica, {V}ersion 12.3.1}, } @book{Feynman:1972:SMS, address = {}, author = {Richard P. Feynman}, note = {Notes taken by R. Kikuchi and H. A. Feiveson. Edited by Jacob Shaham}, pages = {xii + 354}, publisher = {}, series = {Frontiers in physics}, title = {Statistical mechanics: a set of lectures by {R. P. Feynman}}, year = {1972}, isbn = {0-8053-2508-5, 0-8053-2509-3 (paperback)}, } @book{Kleinert:book:2009, author = {Kleinert, Hagen}, publisher = {World scientific}, title = {Path integrals in quantum mechanics, statistics, polymer physics, and financial markets}, year = {2009}, }