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Dornheim T, Moldabekov ZA, Vorberger J, Militzer B. Path integral Monte Carlo approach to the structural properties and collective excitations of liquid [Formula: see text] without fixed nodes. Sci Rep 2022; 12:708. [PMID: 35027602 PMCID: PMC8758733 DOI: 10.1038/s41598-021-04355-9] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/05/2021] [Accepted: 12/21/2021] [Indexed: 11/10/2022] Open
Abstract
Due to its nature as a strongly correlated quantum liquid, ultracold helium is characterized by the nontrivial interplay of different physical effects. Bosonic [Formula: see text] exhibits superfluidity and Bose-Einstein condensation. Its physical properties have been accurately determined on the basis of ab initio path integral Monte Carlo (PIMC) simulations. In contrast, the corresponding theoretical description of fermionic [Formula: see text] is severely hampered by the notorious fermion sign problem, and previous PIMC results have been derived by introducing the uncontrolled fixed-node approximation. In this work, we present extensive new PIMC simulations of normal liquid [Formula: see text] without any nodal constraints. This allows us to to unambiguously quantify the impact of Fermi statistics and to study the effects of temperature on different physical properties like the static structure factor [Formula: see text], the momentum distribution [Formula: see text], and the static density response function [Formula: see text]. In addition, the dynamic structure factor [Formula: see text] is rigorously reconstructed from imaginary-time PIMC data. From simulations of [Formula: see text], we derived the familiar phonon-maxon-roton dispersion function that is well-known for [Formula: see text] and has been reported previously for two-dimensional [Formula: see text] films (Nature 483:576-579 (2012)). The comparison of our new results for both [Formula: see text] and [Formula: see text] with neutron scattering measurements reveals an excellent agreement between theory and experiment.
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Affiliation(s)
- Tobias Dornheim
- Center for Advanced Systems Understanding (CASUS), 02826 Görlitz, Germany
- Helmholtz-Zentrum Dresden-Rossendorf (HZDR), 01328 Dresden, Germany
| | - Zhandos A. Moldabekov
- Center for Advanced Systems Understanding (CASUS), 02826 Görlitz, Germany
- Helmholtz-Zentrum Dresden-Rossendorf (HZDR), 01328 Dresden, Germany
| | - Jan Vorberger
- Helmholtz-Zentrum Dresden-Rossendorf (HZDR), 01328 Dresden, Germany
| | - Burkhard Militzer
- Department of Earth and Planetary Science, University of California, Berkeley, CA 94720 USA
- Department of Astronomy, University of California, Berkeley, CA 94720 USA
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Allers JP, Harvey JA, Garzon FH, Alam TM. Machine learning prediction of self-diffusion in Lennard-Jones fluids. J Chem Phys 2020; 153:034102. [DOI: 10.1063/5.0011512] [Citation(s) in RCA: 20] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/05/2023] Open
Affiliation(s)
- Joshua P. Allers
- Department of Organic Materials Science, Albuquerque, New Mexico 87185, USA
| | - Jacob A. Harvey
- Department of Geochemistry, Albuquerque, New Mexico 87185, USA
| | - Fernando H. Garzon
- Department of Power Sources Research and Development, Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
- Center of Micro-Engineered Materials, University of New Mexico, Albuquerque, New Mexico 87106, USA
| | - Todd M. Alam
- Department of Organic Materials Science, Albuquerque, New Mexico 87185, USA
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Affiliation(s)
- Frederike Jaeger
- Department of Physics, Imperial College London, London SW7 2AZ, United Kingdom
| | - Omar K. Matar
- Department of Chemical Engineering, Imperial College London, London SW7 2AZ, United Kingdom
| | - Erich A. Müller
- Department of Chemical Engineering, Imperial College London, London SW7 2AZ, United Kingdom
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Baidakov VG, Protsenko SP. Metastable Lennard-Jones fluids. III. Bulk viscosity. J Chem Phys 2014; 141:114503. [DOI: 10.1063/1.4895624] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Vladimir G. Baidakov
- Institute of Thermophysics, Ural Branch of the Russian Academy of Sciences, Amundsen Street 107a, 620016 Ekaterinburg, Russia
| | - Sergey P. Protsenko
- Institute of Thermophysics, Ural Branch of the Russian Academy of Sciences, Amundsen Street 107a, 620016 Ekaterinburg, Russia
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5
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Levashov VA, Morris JR, Egami T. The origin of viscosity as seen through atomic level stress correlation function. J Chem Phys 2013; 138:044507. [DOI: 10.1063/1.4789306] [Citation(s) in RCA: 35] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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6
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Levashov VA, Morris JR, Egami T. Viscosity, shear waves, and atomic-level stress-stress correlations. PHYSICAL REVIEW LETTERS 2011; 106:115703. [PMID: 21469880 DOI: 10.1103/physrevlett.106.115703] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/01/2010] [Revised: 02/01/2011] [Indexed: 05/30/2023]
Abstract
The Green-Kubo equation relates the macroscopic stress-stress correlation function to a liquid's viscosity. The concept of the atomic-level stresses allows the macroscopic stress-stress correlation function in the equation to be expressed in terms of the space-time correlations among the atomic-level stresses. Molecular dynamics studies show surprisingly long spatial extension of stress-stress correlations and also longitudinal and transverse waves propagating in liquids over ranges which could exceed the system size. The results reveal that the range of propagation of shear waves corresponds to the range of distances relevant for viscosity. Thus our results show that viscosity is a fundamentally nonlocal quantity. We also show that the periodic boundary conditions play a nontrivial role in molecular dynamics simulations, effectively masking the long-range nature of viscosity.
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Affiliation(s)
- V A Levashov
- Department of Physics and Astronomy, University of Tennessee, Knoxville, Tennessee 37996, USA
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Sengül S, González DJ, González LE. Structural and dynamical properties of liquid Mg. An orbital-free molecular dynamics study. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2009; 21:115106. [PMID: 21693911 DOI: 10.1088/0953-8984/21/11/115106] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
Several static and dynamic properties of liquid magnesium near melting have been evaluated by the orbital-free ab initio molecular dynamics method. The calculated static structure shows good agreement with recent experimental data, including an asymmetric second peak in the structure factor which has been linked to the existence of an important icosahedral short-range order in the liquid. As for the dynamic structure, we obtain collective density excitations with an associated dispersion relation which closely follows recent experimental results. Accurate estimates have also been obtained for several transport coefficients.
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Affiliation(s)
- S Sengül
- Physics Department, Trakya University, Edirne, Turkey
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8
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Juan-Coloa F, Osorio-González D, Rosendo-Francisco P, López-Lemus J. Structural and dynamic properties of liquid alkali metals: molecular dynamics. MOLECULAR SIMULATION 2007. [DOI: 10.1080/08927020701586928] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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9
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Pilgrim WC, Morkel C. State dependent particle dynamics in liquid alkali metals. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2006; 18:R585-R633. [PMID: 21690895 DOI: 10.1088/0953-8984/18/37/r01] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
This paper gives a survey of the particle dynamics in the liquid alkali metals observed with inelastic x-ray and neutron scattering experiments. Liquid rubidium and sodium are chosen as model fluids to represent the behaviour of this group of fluids. In the dense metallic monatomic melt the microscopic dynamics is characterized by collective excitations similar to those in the corresponding solids. The collective particle behaviour is appropriately described using a memory function formalism with two relaxation channels for the density correlation. A similar behaviour is found for the single particle motion where again two relaxation mechanisms are needed to accurately reproduce the experimental findings. Special emphasis is given to the density dependence of the particle dynamics. An interesting issue in liquid metals is the metal to non-metal transition, which is observed if the fluid is sufficiently expanded with increasing temperature and pressure. This causes distinct variations in the interparticle interactions, which feed back onto the motional behaviour. The associated variations in structure and dynamics are reflected in the shape of the scattering laws. The experimentally observed features are discussed and compared with simple models and with the results from computer simulations.
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Affiliation(s)
- W-C Pilgrim
- Department of Chemistry, Physical-Chemistry, Philipps-University of Marburg, D-35032 Marburg, Germany
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10
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Meier K, Laesecke A, Kabelac S. Transport coefficients of the Lennard-Jones model fluid. III. Bulk viscosity. J Chem Phys 2005; 122:14513. [PMID: 15638680 DOI: 10.1063/1.1828040] [Citation(s) in RCA: 68] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
In an extensive computer simulation study, the transport coefficients of the Lennard-Jones model fluid were determined with high accuracy from equilibrium molecular-dynamics simulations. In the frame of time-correlation function theory, the generalized Einstein relations were employed to evaluate the transport coefficients. This third of a series of four papers presents the results for the bulk viscosity. With comprehensive simulation data at over 350 state points, the temperature and density dependences of the bulk viscosity are characterized in this work over a wide range of fluid states. The bulk viscosity exhibits a large critical enhancement similar to that known for the thermal conductivity, but it extends much farther into the supercritical region and can be observed even at 4.5 times the critical temperature. An investigation of the pressure-fluctuation autocorrelation functions shows that the enhancement is caused by extremely slowly decaying pressure fluctuations.
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Affiliation(s)
- Karsten Meier
- Institut für Thermodynamik, Helmut-Schmidt-Universität-Universität der Bundeswehr Hamburg, Holstenhofweg 85, D-22043 Hamburg, Germany.
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Meier K, Laesecke A, Kabelac S. Transport coefficients of the Lennard-Jones model fluid. II Self-diffusion. J Chem Phys 2004; 121:9526-35. [PMID: 15538874 DOI: 10.1063/1.1786579] [Citation(s) in RCA: 94] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
In an extensive computer simulation study, the transport coefficients of the Lennard-Jones model fluid were determined with high accuracy from equilibrium molecular-dynamics simulations. In the frame of time-correlation function theory, the generalized Einstein relations were employed to evaluate the transport coefficients. This second of a series of four papers presents the results for the self-diffusion coefficient, and discusses and interprets the behavior of this transport coefficient in the fluid region of the phase diagram. The uncertainty of the self-diffusion data is estimated to be 1% in the gas region and 0.5% at high-density liquid states. With the very accurate data, even fine details in the shape of the self-diffusion isotherms are resolved, and the previously little-investigated behavior of the self-diffusion coefficient at low-density gaseous states is analyzed in detail. Finally, aspects of the mass transport mechanisms on the molecular scale are explored by an analysis of the velocity autocorrelation functions.
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Affiliation(s)
- Karsten Meier
- Institut für Thermodynamik, Helmut-Schmidt-Universität--Universität der Bundeswehr Hamburg, Holstenhofweg 85, D-22043 Hamburg, Germany.
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Meier K, Laesecke A, Kabelac S. Transport coefficients of the Lennard-Jones model fluid. I. Viscosity. J Chem Phys 2004; 121:3671-87. [PMID: 15303934 DOI: 10.1063/1.1770695] [Citation(s) in RCA: 126] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
In an extensive computer simulation study, the transport coefficients of the Lennard-Jones model fluid were determined with high accuracy from equilibrium molecular-dynamics simulations. In the frame of time-correlation function theory, the generalized Einstein relations were employed to evaluate the transport coefficients. This first of a series of four papers presents the results for the viscosity, and discusses and interprets the behavior of this transport coefficient in the fluid region of the phase diagram. Moreover, the kinetic-kinetic, kinetic-potential, and potential-potential viscosity contributions are resolved over the whole range of fluid states, and their characteristic dependence on temperature and density is described. Finally, an additional analysis of the shear-stress correlation functions reveals aspects of the momentum-transport mechanisms on the molecular scale.
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Affiliation(s)
- Karsten Meier
- Institut fur Thermodynamik, Helmut-Schmidt-Universitat-Universitat der Bundeswehr Hamburg, Holstenhofweg 85, D-22043 Hamburg, Germany
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Verdaguer A, Padro JA. Velocity cross-correlations and atomic momentum transfer in simple liquids with different potential cores. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 2000; 62:532-7. [PMID: 11088489 DOI: 10.1103/physreve.62.532] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/12/1999] [Indexed: 11/07/2022]
Abstract
Time correlation functions between the velocity of a tagged particle and velocities of particles within specified ranges of initial separations have been obtained by molecular dynamics simulation. These correlation functions have allowed us to analyze the momentum transfer between particles in different coordination shells. Two simple liquids at very different densities and two purely repulsive potentials with very different softnesses have been considered. The longitudinal correlations, which are the velocity cross-correlations along the initial direction defined by the centers of two given particles, have been calculated separately. It has been proven that these correlations should be attributed to particles both in front of and behind the central one. As with propagating longitudinal modes, they are strongly dependent on the softness of the potential core. Some characteristic features of the velocity correlation functions after the initial rise should be related to nonlongitudinal correlations. It has been shown that velocity cross-correlations between distinct particles cannot only be attributed to the direct interactions among particles, but also to the motions induced by the movement of a tagged particle on their neighbors.
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Affiliation(s)
- A Verdaguer
- Departament de Fisica Fonamental, Universitat de Barcelona, Diagonal 647, 08028 Barcelona, Spain
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Anento N, Padró JA, Canales M. Dynamic properties of simple liquids: Dependence on the softness of the potential core. J Chem Phys 1999. [DOI: 10.1063/1.480371] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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