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Filinov VS, Levashov PR, Larkin AS. Phase-space path-integral representation of the quantum density of states: Monte Carlo simulation of strongly correlated soft-sphere fermions. Phys Rev E 2024; 109:024137. [PMID: 38491615 DOI: 10.1103/physreve.109.024137] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/31/2023] [Accepted: 01/30/2024] [Indexed: 03/18/2024]
Abstract
The Wigner formulation of quantum mechanics is used to derive a path-integral representation of the quantum density of states (DOS) of strongly correlated fermions in the canonical ensemble. A path-integral Monte Carlo approach for the simulation of DOS and other thermodynamic functions is suggested. The derived Wigner function in the phase space resembles the Maxwell-Boltzmann distribution but allows for quantum effects. We consider a three-dimensional quantum system of strongly correlated soft-sphere fermions at different densities and temperatures. The calculated properties include the DOS, momentum distribution functions, spin-resolved radial distribution functions, potentials of mean force, and related energy levels obtained from the Bohr-Sommerfeld condition. We observe sharp peaks on DOS and momentum distribution curves, which are explained by the appearance of fermionic bound states.
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Affiliation(s)
- V S Filinov
- Joint Institute for High Temperatures RAS, Izhorskaya 13 Building 2, Moscow 125412, Russia
| | - P R Levashov
- Joint Institute for High Temperatures RAS, Izhorskaya 13 Building 2, Moscow 125412, Russia
| | - A S Larkin
- Joint Institute for High Temperatures RAS, Izhorskaya 13 Building 2, Moscow 125412, Russia
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Demyanov GS, Fokin VB, Knyazev DV, Minakov DV, Paramonov MA, Levashov PR. How to read optical properties of matter via the Kubo-Greenwood approach. Phys Rev E 2023; 108:L053301. [PMID: 38115528 DOI: 10.1103/physreve.108.l053301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/17/2023] [Accepted: 11/03/2023] [Indexed: 12/21/2023]
Abstract
Substances with a complex electronic structure exhibit non-Drude optical properties that are challenging to interpret experimentally and theoretically. In our recent paper [Phys. Rev. E 105, 035307 (2022)2470-004510.1103/PhysRevE.105.035307], we offered a computational method based on the continuous Kubo-Greenwood formula, which expresses dynamic conductivity as an integral over the electron spectrum. In this Letter, we propose a methodology to analyze the complex conductivity using liquid Zr as an example to explain its nontrivial behavior. To achieve this, we apply the continuous Kubo-Greenwood formula and extend it to include the imaginary part of the complex conductivity into the analysis. Our method is suitable for a wide range of substances, providing an opportunity to explain optical properties from ab initio calculations of any difficulty.
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Affiliation(s)
- G S Demyanov
- Joint Institute for High Temperatures, Izhorskaya 13 Building 2, Moscow 125412, Russia
| | - V B Fokin
- Joint Institute for High Temperatures, Izhorskaya 13 Building 2, Moscow 125412, Russia
| | - D V Knyazev
- Joint Institute for High Temperatures, Izhorskaya 13 Building 2, Moscow 125412, Russia
| | - D V Minakov
- Joint Institute for High Temperatures, Izhorskaya 13 Building 2, Moscow 125412, Russia
| | - M A Paramonov
- Joint Institute for High Temperatures, Izhorskaya 13 Building 2, Moscow 125412, Russia
| | - P R Levashov
- Joint Institute for High Temperatures, Izhorskaya 13 Building 2, Moscow 125412, Russia
- Moscow Institute of Physics and Technology, Institutskiy Pereulok 9, Dolgoprudny, Moscow Region 141701, Russia
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Filinov VS, Syrovatka RA, Levashov PR. Exchange-correlation bound states of the triplet soft-sphere fermions by path-integral Monte Carlo simulations. Phys Rev E 2023; 108:024136. [PMID: 37723742 DOI: 10.1103/physreve.108.024136] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/24/2022] [Accepted: 08/01/2023] [Indexed: 09/20/2023]
Abstract
Path-integral Monte Carlo simulations in the Wigner approach to quantum mechanics has been applied to calculate momentum and spin-resolved radial distribution functions of the strongly correlated soft-sphere quantum fermions. The obtained spin-resolved radial distribution functions demonstrate arising triplet clusters of fermions, that is the consequence of the interference of exchange and interparticle interactions. The semiclassical analysis in the framework of the Bohr-Sommerfeld quantization condition, applied to the potential of the mean force corresponding to the same-spin radial distribution functions, allows to detect exchange-correlation bound states in triplet clusters and to estimate corresponding averaged energy levels. The obtained momentum distribution functions demonstrate the narrow sharp separated peaks corresponding to bound states and disturbing the Maxwellian distribution.
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Affiliation(s)
- V S Filinov
- Joint Institute for High Temperatures of the Russian Academy of Sciences, Izhorskaya 13, Bldg 2, Moscow 127412, Russia
| | - R A Syrovatka
- Joint Institute for High Temperatures of the Russian Academy of Sciences, Izhorskaya 13, Bldg 2, Moscow 127412, Russia
| | - P R Levashov
- Joint Institute for High Temperatures of the Russian Academy of Sciences, Izhorskaya 13, Bldg 2, Moscow 127412, Russia
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Filinov VS, Syrovatka RS, Levashov PR. Solution of the ‘sign problem’ in the path integral Monte Carlo simulations of strongly correlated Fermi systems: thermodynamic properties of helium-3. Mol Phys 2022. [DOI: 10.1080/00268976.2022.2102549] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/16/2022]
Affiliation(s)
- V. S. Filinov
- Joint Institute for High Temperatures, Russian Academy of Sciences, Moscow, Russia
| | - R. S. Syrovatka
- Joint Institute for High Temperatures, Russian Academy of Sciences, Moscow, Russia
| | - P. R. Levashov
- Joint Institute for High Temperatures, Russian Academy of Sciences, Moscow, Russia
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Demyanov GS, Levashov PR. One-component plasma of a million particles via angular-averaged Ewald potential: A Monte Carlo study. Phys Rev E 2022; 106:015204. [PMID: 35974543 DOI: 10.1103/physreve.106.015204] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/03/2022] [Accepted: 06/30/2022] [Indexed: 06/15/2023]
Abstract
In this work we derive a correct expression for the one-component plasma (OCP) energy via the angular-averaged Ewald potential (AAEP). Unlike Yakub and Ronchi [J. Low Temp. Phys. 139, 633 (2005)0022-229110.1007/s10909-005-5451-5], who had tried to obtain the same energy expression from a two-component plasma model, we used the original Ewald potential for an OCP. A constant in the AAEP was determined using the cluster expansion in the limit of weak coupling. The potential has a simple form suitable for effective numerical simulations. To demonstrate the advantages of the AAEP, we performed a number of Monte Carlo simulations for an OCP with up to a million particles in a wide range of the coupling parameter. Our computations turned out at least two orders of magnitude more effective than those with a traditional Ewald potential. A unified approach is offered for the determination of the thermodynamic limit in the whole investigated range. Our results are in good agreement with both theoretical data for a weakly coupled OCP and previous numerical simulations. We hope that the AAEP will be useful in path integral Monte Carlo simulations of the uniform electron gas.
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Affiliation(s)
- G S Demyanov
- Joint Institute for High Temperatures, Izhorskaya 13 Bldg 2, Moscow 125412, Russia and Moscow Institute of Physics and Technology, Institutskiy Pereulok 9, Dolgoprudny, Moscow Region, 141701, Russia
| | - P R Levashov
- Joint Institute for High Temperatures, Izhorskaya 13 Bldg 2, Moscow 125412, Russia and Moscow Institute of Physics and Technology, Institutskiy Pereulok 9, Dolgoprudny, Moscow Region, 141701, Russia
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Demyanov GS, Knyazev DV, Levashov PR. Continuous Kubo-Greenwood formula: Theory and numerical implementation. Phys Rev E 2022; 105:035307. [PMID: 35428130 DOI: 10.1103/physreve.105.035307] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/28/2021] [Accepted: 03/02/2022] [Indexed: 06/14/2023]
Abstract
In this paper, we present the so-called continuous Kubo-Greenwood formula intended for the numerical calculation of the dynamic Onsager coefficients and, in particular, the real part of dynamic electrical conductivity. In contrast to the usual Kubo-Greenwood formula, which contains the summation over a discrete set of transitions between electron energy levels, the continuous one is formulated as an integral over the whole energy range. This integral includes the continuous functions: the smoothed squares of matrix elements, D(ɛ,ɛ+ℏω), the densities of state, g(ɛ)g(ɛ+ℏω), and the difference of the Fermi weights, [f(ɛ)-f(ɛ+ℏω)]/(ℏω). The function D(ɛ,ɛ+ℏω) is obtained via the specially developed smoothing procedure. From the theoretical point of view, the continuous formula is an alternative to the usual one. Both can be used to calculate matter properties and produce close results. However, the continuous formula includes the smooth functions that can be plotted and examined. Thus, we can analyze the contributions of various parts of the electron spectrum to the obtained properties. The possibility of such analysis is the main advantage of the continuous formula. The continuous Kubo-Greenwood formula is implemented in the parallel code cubogram. Using the code we demonstrate the influence of technical parameters on the simulation results for liquid aluminum. We also analyze various methods of matrix elements computation and their effect on dynamic electrical conductivity.
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Affiliation(s)
- G S Demyanov
- Joint Institute for High Temperatures, Izhorskaya 13 Building 2, Moscow 125412, Russia and Moscow Institute of Physics and Technology, Institutskiy Pereulok 9, Dolgoprudny, Moscow Region 141700, Russia
| | - D V Knyazev
- Joint Institute for High Temperatures, Izhorskaya 13 Building 2, Moscow 125412, Russia and Moscow Institute of Physics and Technology, Institutskiy Pereulok 9, Dolgoprudny, Moscow Region 141700, Russia
| | - P R Levashov
- Joint Institute for High Temperatures, Izhorskaya 13 Building 2, Moscow 125412, Russia and Moscow Institute of Physics and Technology, Institutskiy Pereulok 9, Dolgoprudny, Moscow Region 141700, Russia
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Filinov VS, Larkin AS, Levashov PR. Uniform electron gas at finite temperature by fermionic-path-integral Monte Carlo simulations. Phys Rev E 2020; 102:033203. [PMID: 33075865 DOI: 10.1103/physreve.102.033203] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/29/2020] [Accepted: 08/11/2020] [Indexed: 11/07/2022]
Abstract
In this paper we study thermodynamic properties of uniform electron gas (UEG) over wide density and temperature range, using the improved fermionic-path-integral Monte Carlo (FPIMC) method. This method demonstrates a significant reduction of the "fermionic sign problem," which takes place in standard path-integral Monte Carlo simulations of degenerate fermionic systems. We introduce three basic improvements. The first one is the improved treatment of exchange interaction, achieved by the proper change of variables in the path-integral measure. The second improvement is the inclusion of long-range Coulomb effects into an angle-averaged effective potential, as proposed by Yakub and Ronchi [J. Chem. Phys. 119, 11556 (2003)JCPSA60021-960610.1063/1.1624364]. The third improvement is the angle-averaging of an exchange determinant, describing the fermionic exchange interaction not only between particles in the main Monte Carlo cell, but also with electrons in the nearest periodic images. The FPIMC shows very good agreement with analytical data for ideal Fermi gas. For strongly coupled UEG under warm dense matter conditions we compare our total and exchange-correlation energy results with other Monte Carlo approaches.
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Affiliation(s)
- V S Filinov
- Joint Institute for High Temperatures, Russian Academy of Sciences, Izhorskaya 13 Bldg 2, Moscow 125412, Russia
| | - A S Larkin
- Joint Institute for High Temperatures, Russian Academy of Sciences, Izhorskaya 13 Bldg 2, Moscow 125412, Russia
| | - P R Levashov
- Joint Institute for High Temperatures, Russian Academy of Sciences, Izhorskaya 13 Bldg 2, Moscow 125412, Russia.,Moscow Institute of Physics and Technology, 9 Institutskiy per., Dolgoprudny, Moscow Region, 141700, Russia
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Dozhdikov VS, Basharin AY, Levashov PR, Minakov DV. Atomistic simulations of the equation of state and hybridization of liquid carbon at a temperature of 6000 K in the pressure range of 1-25 GPa. J Chem Phys 2017; 147:214302. [PMID: 29221406 DOI: 10.1063/1.4999070] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The equation of state and the structure of liquid carbon are studied by molecular simulation. Both classical and quantum molecular dynamics (QMD) are used to calculate the equation of state and the distribution of chemical bonds at 6000 K in the pressure range 1-25 GPa. Our calculations and results of other authors show that liquid carbon has a fairly low density on the order of 1.2-1.35 g/cm3 at pressures about 1 GPa. Owing to the coordination number analysis, this fact can be attributed to the high content of sp1-bonded atoms (more than 50% according to our ab initio computations). Six empirical potentials have been tested in order to describe the density dependence of pressure and structure at 6000 K. As a result, only one potential, ReaxFF/lg, was able to reproduce the QMD simulations for both the equation of state and the fraction of sp1, sp2, sp3-bonded atoms.
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Affiliation(s)
- V S Dozhdikov
- Joint Institute for High Temperatures RAS, Izhorskaya 13 Bldg 2, Moscow 125412, Russia
| | - A Yu Basharin
- Joint Institute for High Temperatures RAS, Izhorskaya 13 Bldg 2, Moscow 125412, Russia
| | - P R Levashov
- Joint Institute for High Temperatures RAS, Izhorskaya 13 Bldg 2, Moscow 125412, Russia
| | - D V Minakov
- Joint Institute for High Temperatures RAS, Izhorskaya 13 Bldg 2, Moscow 125412, Russia
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Dozhdikov VS, Basharin AY, Levashov PR. Two-phase simulation of the crystalline silicon melting line at pressures from –1 to 3 GPa. J Chem Phys 2012; 137:054502. [PMID: 22894359 DOI: 10.1063/1.4739085] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- V S Dozhdikov
- Joint Institute for High Temperatures RAS, Izhorskaya 13 bldg. 2, Moscow 125412, Russia
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Levashov PR, Sin'ko GV, Smirnov NA, Minakov DV, Shemyakin OP, Khishchenko KV. Pseudopotential and full-electron DFT calculations of thermodynamic properties of electrons in metals and semiempirical equations of state. J Phys Condens Matter 2010; 22:505501. [PMID: 21406798 DOI: 10.1088/0953-8984/22/50/505501] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
In the present work, we compare the thermal contribution of electrons to thermodynamic functions of metals in different models at high densities and electron temperatures. One of the theoretical approaches, the full-potential linear-muffin-tin-orbital method, treats all electrons in the framework of density functional theory (DFT). The other approach, VASP, uses projector-augmented-wave pseudopotentials for the core electrons and considers the valent electrons also in the context of DFT. We analyze the limitations of the pseudopotential approach and compare the DFT results with a finite-temperature Thomas-Fermi model and two semiempirical equations of state.
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Affiliation(s)
- P R Levashov
- Joint Institute for High Temperatures, Russian Academy of Sciences, Moscow, Russia
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Povarnitsyn ME, Itina TE, Khishchenko KV, Levashov PR. Suppression of ablation in femtosecond double-pulse experiments. Phys Rev Lett 2009; 103:195002. [PMID: 20365933 DOI: 10.1103/physrevlett.103.195002] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/16/2009] [Indexed: 05/29/2023]
Abstract
We report the physical reasons of a curious decrease in the crater depth observed for long delays in experiments with two successive femtosecond pulses. Detailed hydrodynamic modeling demonstrates that the ablation mechanism is dumped when the delay between the pulses exceeds the electron-ion relaxation time. In this case, the interaction of the second laser pulse with the expanding target material leads to the formation of the second shock wave suppressing the rarefaction wave created by the first pulse. The evidence of this effect follows from the pressure and density profiles obtained at different delays after the first laser pulse.
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Affiliation(s)
- M E Povarnitsyn
- Joint Institute for High Temperatures RAS, Izhorskaya 13 Building 2, Moscow, 125412, Russia
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Levashov PR, Filinov VS, Bonitz M, Fortov VE. Path integral Monte Carlo calculations of helium and hydrogen–helium plasma thermodynamics and of the deuterium shock Hugoniot. ACTA ACUST UNITED AC 2006. [DOI: 10.1088/0305-4470/39/17/s20] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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Bonitz M, Filinov VS, Fortov VE, Levashov PR, Fehske H. Crystallization in two-component Coulomb systems. Phys Rev Lett 2005; 95:235006. [PMID: 16384315 DOI: 10.1103/physrevlett.95.235006] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/21/2005] [Indexed: 05/05/2023]
Abstract
The analysis of Coulomb crystallization is extended from one-component to two-component plasmas. Critical parameters for the existence of Coulomb crystals are derived for both classical and quantum crystals. In the latter case, a critical mass ratio of the two charged components is found, which is of the order of 80. Thus, holes in semiconductors with sufficiently flat valence bands are predicted to spontaneously order into a regular lattice. Such hole crystals are intimately related to ion Coulomb crystals in white dwarf and neutron stars as well as to ion crystals produced in the laboratory. A unified phase diagram of two-component Coulomb crystals is presented and is verified by first-principles computer simulations.
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Affiliation(s)
- M Bonitz
- Institut für Theoretische Physik und Astrophysik, Christian-Albrechts-Universität zu Kiel, Leibnizstrasse 15, 24098 Kiel, Germany
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Bezkrovniy V, Filinov VS, Kremp D, Bonitz M, Schlanges M, Kraeft WD, Levashov PR, Fortov VE. Monte Carlo results for the hydrogen Hugoniot. Phys Rev E Stat Nonlin Soft Matter Phys 2004; 70:057401. [PMID: 15600800 DOI: 10.1103/physreve.70.057401] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/26/2004] [Indexed: 05/24/2023]
Abstract
We propose a theoretical Hugoniot relation obtained by combining results for the equation of state from the direct path integral Monte Carlo technique (DPIMC) and those from reaction ensemble Monte Carlo (REMC) simulations. The main idea of this proposal is based on the fact that the DPMIC technique provides first-principle results for a wide range of densities and temperatures including the region of partially ionized plasmas. On the other hand, for lower temperatures where the formation of molecules becomes dominant, DPIMC simulations become cumbersome and inefficient. For this region it is possible to use accurate REMC simulations where bound states (molecules) are treated on the Born-Oppenheimer level. The remaining interaction is then reduced to the scattering between neutral particles which is reliably treated classically by applying effective potentials. The resulting Hugoniot is located between the experimental values of Knudson et al. [Phys. Rev. Lett. 87, 225501 (2001)] and Collins et al. [Science 281, 1178 (1998)].
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Affiliation(s)
- V Bezkrovniy
- Institut für Physik, Ernst-Moritz-Arndt-Universität Greifswald, Domstrasse 10a, D-17487, Greifswald, Germany
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