Abstract
In the framework of the concept of time correlation functions, we develop a self-consistent relaxation theory of the transverse collective particle dynamics in liquids. The theory agrees with well-known results in both the short-wave (free-particle dynamics) and the long-wave (hydrodynamic) limits. We obtain a general expression for the spectral density \(C_{ \mathrm{T} }(k,\omega)\) of the transverse particle current realized in a range of wave numbers \(k\). In the domain of microscopic spatial scales comparable to the action range of effective forces of interparticle interaction, the theory reproduces a transition from a regime with typical equilibrium liquid dynamics to a regime with collective particle dynamics where properties similar to solid-state properties appear: effective shear stiffness and transverse (shear) acoustic waves. In the framework of the corresponding approximations, we obtain expressions for the spectral density of transverse particle current for all characteristic regimes in equilibrium collective dynamics. We obtain expressions for the dispersion law for transverse (shear) acoustic waves and also relations for the kinematic shear viscosity \(\nu\), the transverse speed of sound \(v^{( \mathrm{T} )}\), and the corresponding sound damping coefficient \(\Gamma^{( \mathrm{T} )}\). We compare the theoretical results with the results of atomistic dynamics simulations of liquid lithium near the melting point.
Similar content being viewed by others
References
J. Frenkel, Kinetic Theory of Liquids, Clarendon Press, Oxford (1946).
A. M. Prokhorov et al., eds., Encyclopedic Dictionary of Physics [in Russian], Sovet. Entsiklopediya, Moscow (1983).
A. M. Prokhorov et al., eds., Encyclopedia of Physics [in Russian], Vol. 2, Bol’shaya Rossiiskaya Entsiklopediya, Moscow (1998).
K. Trachenko and V. V. Brazhkin, “Collective modes and thermodynamics of the liquid state,” Rep. Prog. Phys., 79, 016502 (2016); arXiv:1512.06592v1 [cond-mat.soft] (2015).
E. E. Tareyeva, Yu. D. Fomin, E. N. Tsyok, and V. N. Ryzhov, “Supercritical anomalies and the Widom line for the isostructural phase transition in solids,” Theor. Math. Phys., 194, 148–156 (2018).
A. V. Granato, “The shear modulus of liquids,” J. Phys. IV France, 06, C8-1–C8-9 (1996).
D. Levesque, L. Verlet, and J. Kürkijarvi, “Computer ‘experiments’ on classical fluids: IV. Transport properties and time-correlation functions of the Lennard-Jones liquid near its triple point,” Phys. Rev. A, 7, 1690–1700 (1973).
L. Sjögren, “Kinetic theory of classical liquids: III. Numerical results on the transverse current correlation in liquid argon,” Ann. Phys., 110, 173–179 (1978).
Z. Donkó, G. J. Kalman, and P. Hartmann, “Dynamical correlations and collective excitations of Yukawa liquids,” J. Phys.: Condens. Matter, 20, 413101 (2008).
S. A. Khrapak, A. G. Khrapak, N. P. Kryuchkov, and S. O. Yurchenko, “Onset of transverse (shear) waves in strongly-coupled Yukawa fluids,” J. Chem. Phys., 150, 104503 (2019); arXiv:1902.09874v1 [physics.plasm-ph] (2019).
R. E. Ryltsev, N. M. Chtchelkatchev, and V. N. Ryzhov, “Superfragile glassy dynamics of a one-component system with isotropic potential: Competition of diffusion and frustration,” Phys. Rev. Lett., 110, 025701 (2013); arXiv:1301.2162v1 [cond-mat.soft] (2013).
B. G. del Rio and L. E. González, “Longitudinal, transverse, and single-particle dynamics in liquid Zn: Ab initio study and theoretical analysis,” Phys. Rev. B, 95, 224201 (2017).
N. Jakse and T. Bryk, “Pressure evolution of transverse collective excitations in liquid Al along the melting line,” J. Chem. Phys., 151, 034506 (2019).
M. Ropo, J. Akola, and R. O. Jones, “Collective excitations and viscosity in liquid Bi,” J. Chem. Phys., 145, 184502 (2016).
Yu. D. Fomin, E. N. Tsiok, V. N. Ryzhov, and V. V. Brazhkin, “Anomalous behavior of dispersion of longitudinal and transverse collective excitations in water,” J. Mol. Liq., 287, 110992 (2019).
L. Wang, C. Yang, M. T. Dove, A. V. Mokshin, V. V. Brazhkin, and K. Trachenko, “The nature of collective excitations and their crossover at extreme supercritical conditions,” Sci. Rep., 9, 755 (2019); arXiv:1901.10052v1 [cond-mat.stat-mech] (2019).
S. Hosokawa, M. Inui, Y. Kajihara, S. Tsutsui, and A. Q. R. Baron, “Transverse excitations in liquid Fe, Cu and Zn,” J. Phys.: Condens. Matter, 27, 194104 (2015).
P. A. Egelstaff, An Introduction to the Liquid State, Acad. Press, New York (1967).
E. Burkel and H. Sinn, “Inelastic X-ray scattering: A new technique for studying dynamics in liquids,” J. Phys.: Condens. Matter, 6, No. 23A, A225–A228 (1994).
S. Hosokawa, M. Inui, Y. Kajihara, K. Matsuda, T. Ichitsubo, W.-C. Pilgrim, H. Sinn, L. E. González, D. J. González, S. Tsutsui, and A. Q. R. Baron, “Transverse acoustic excitations in liquid Ga,” Phys. Rev. Lett., 102, 105502 (2009).
S. Hosokawa, S. Munejiri, M. Inui, Y. Kajihara, W.-C. Pilgrim, Y. Ohmasa, S. Tsutsui, A. Q. R. Baron, F. Shimojo, and K. Hoshino, “Transverse excitations in liquid Sn,” J. Phys.: Condens. Matter, 25, 112101 (2013).
V. M. Giordano and G. Monaco, “Fingerprints of order and disorder on the high-frequency dynamics of liquids,” Proc. Natl. Acad. Sci. USA, 107, 21985–21989 (2010).
V. M. Giordano and G. Monaco, “Inelastic x-ray scattering study of liquid Ga: Implications for the short-range order,” Phys. Rev. B, 84, 052201 (2011).
R. A. MacPhail and D. Kivelson, “Generalized hydrodynamic theory of viscoelasticity,” J. Chem. Phys., 80, 2102–2114 (1984).
T. Bryk and I. Mryglod, “Generalized hydrodynamics of binary liquids: Transverse collective modes,” Phys. Rev. E, 62, 2188–2199 (2000).
I. P. Omelyan and I. M. Mryglod, “Generalized collective modes of a Lennard-Jones fluid: High mode approximation,” Condens. Matter Phys., 4, 128–160 (1994).
K. Trachenko, “Lagrangian formulation and symmetrical description of liquid dynamics,” Phys. Rev. E, 96, 062134 (2017); arXiv:1710.01390v3 [cond-mat.stat-mech] (2017).
M. Baggioli, M. Vasin, V. Brazhkin, and K. Trachenko, “Gapped momentum states,” Phys. Rep., 865, 1–44 (2020); arXiv:1904.01419v2 [cond-mat.stat-mech] (2019).
N. P. Kryuchkov, L. A. Mistryukova, V. V. Brazhkin, and S. O. Yurchenko, “Excitation spectra in fluids: How to analyze them properly,” Sci. Rep., 9, 10483 (2019).
N. P. Kryuchkov, V. V. Brazhkin, and S. O. Yurchenko, “Anticrossing of longitudinal and transverse modes in simple fluids,” J. Phys. Chem. Lett., 10, 4470–4475 (2019).
E. V. Yakovlev, N. P. Kryuchkov, P. V. Ovcharov, A. V. Sapelkin, V. V. Brazhkin, and S. O. Yurchenko, “Direct experimental evidence of longitudinal and transverse mode hybridization and anticrossing in simple model fluids,” J. Phys. Chem. Lett., 11, 1370–1376 (2020).
Yu. D. Fomin, V. N. Ryzhov, E. N. Tsiok, V. V. Brazhkin, and K. Trachenko, “Corrigendum: Crossover of collective modes and positive sound dispersion in supercritical state,” J. Phys.: Condens. Matter, 29, 059501 (2017).
V. V. Brazhkin, Yu. D. Fomin, V. N. Ryzhov, E. N. Tsiok, and K. Trachenko, “Liquid-like and gas-like features of a simple fluid: An insight from theory and simulation,” Phys. A, 509, 690–702 (2018).
R. M. Yulmetyev, A. V. Mokshin, P. Hänggi, and V. Yu. Shurygin, “Time-scale invariance of relaxation processes of density fluctuation in slow neutron scattering in liquid cesium,” Phys. Rev. E, 64, 057101 (2001); arXiv:cond-mat/0111467v1 (2001).
R. M. Yul’met’yev, A. V. Mokshin, P. Hänggi, and V. Yu. Shurygin, “Dynamic structure factor in liquid cesium on the basis of time-scale invariance of relaxation processes,” JETP Lett., 76, 147–150 (2002).
A. V. Mokshin and B. N. Galimzyanov, “Self-consistent description of local density dynamics in simple liquids: The case of molten lithium,” J. Phys.: Condens. Matter, 30, 085102 (2018); arXiv:1801.04879v1 [cond-mat.soft] (2018).
R. M. Yulmetyev, A. V. Mokshin, T. Scopigno, and P. Hänggi, “New evidence for the idea of timescale invariance of relaxation processes in simple liquids: The case of molten sodium,” J. Phys.: Codens. Matter, 15, 2235–2257 (2003).
A. V. Mokshin, R. M. Yulmetyev, and P. Hänggi, “Relaxation time scales in collective dynamics of liquid alkali metals,” J. Chem. Phys., 121, 7341–7346 (2004); arXiv:cond-mat/0506636v1 (2005).
A. V. Mokshin, R. M. Yulmetyev, R. M. Khusnutdinov, and P. Hänggi, “Collective dynamics in liquid aluminum near the melting temperature: Theory and computer simulation,” JETP, 103, 841–849 (2006).
A. V. Mokshin, R. M. Yulmetyev, R. M. Khusnutdinoff, and P. Hänggi, “Analysis of the dynamics of liquid aluminium: Recurrent relation approach,” J. Phys.: Condens. Matter, 19, 046209 (2007).
R. M. Khusnutdinoff, C. Cockrell, O. A. Dicks, A. C.!S. Jensen, M. D. Le, L. Wang, M. T. Dove, A. V. Mokshin, V. V. Brazhkin, and K. Trachenko, “Collective modes and gapped momentum states in liquid Ga: Experiment, theory, and simulation,” Phys. Rev. B, 101, 214312 (2020); arXiv:2005.00470v4 [cond-mat.soft] (2020).
V. N. Ryzhov, A. F. Barabanov, M. V. Magnitskaya, and E. E. Tareeva, “Theoretical studies of condensed matter,” Phys. Usp., 51, 1077–1083 (2008).
J.-P. Hansen and I. R. McDonald, Theory of Simple Liquids, Acad. Press, London (2006).
R. Zwanzig, Nonequilibrium Statistical Mechanics, Oxford Univ. Press, Oxford (2001).
A. V. Mokshin and R. M. Yulmetyev, Microscopic Dynamics of Simple Liquids [in Russian], Tsentr Innovatsionnykh Tekhnologii, Kazan (2006).
B. A. Klumov, “On melting criteria for complex plasma,” Phys. Usp., 53, 1053–1065 (2010).
U. Balucani, M. H. Lee, and V. Tognetti, “Dynamical correlations,” Phys. Rep., 373, 409–492 (2003).
M. Reed and B. Simon, Methods of Modern Mathematical Physics, Vol. 1, Functional Analysis, Acad. Press, New York (1972).
A. A. Vladimirov, D. Ihle, and N. M. Plakida, “Dynamical spin susceptibility in the \(t\)–\(J\) model: The memory function method,” Theor. Math. Phys., 145, 1576–1589 (2005).
M. H. Lee, “Generalized Langevin equation and recurrence relations,” Phys. Rev. E, 62, 1769–1772 (2000).
A. V. Mokshin, R. M. Yulmetyev, and P. Hänggi, “Simple measure of memory for dynamical processes described by a generalized Langevin equation,” Phys. Rev. Lett., 95, 200601 (2005); arXiv:cond-mat/0511308v1 (2005).
A. V. Mokshin, “Self-consistent approach to the description of relaxation processes in classical multiparticle systems,” Theor. Math. Phys., 183, 449–477 (2015).
N. N. Bogolyubov, Problems of Dynamical Theory in Statistical Physics [in Russian],, Gostekhizdat, Moscow (1946); English transl. (Stud. Statist. Mech., Vol. 1), North-Holland, Amsterdam (1962).
W. Götze, Complex Dynamics of Glass-Forming Liquids: A Mode-Coupling Theory (Intl. Ser. Monogr. Phys., Vol. 143), Oxford Univ. Press, Oxford (2012).
P. Resibua and M. De Lener, Classical Kinetic Theory of Liquids and Gases [in Russian], Mir, Moscow (1980).
R. Mountain, “Spectral distribution of scattered light in a simple fluid,” Rev. Modern Phys., 38, 205–214 (1966).
T. Scopigno, U. Balucani, G. Ruocco, and F. Sette, “Density fluctuations in molten lithium: Inelastic x-ray scattering study,” J. Phys.: Condens. Matter, 12, 8009–8034 (2000).
I. K. Kamilov, A. K. Murtazaev, and Kh. K. Aliev, “Monte Carlo studies of phase transitions and critical phenomena,” Phys. Usp., 42, 689–709 (1999).
R. M. Khusnutdinoff, B. N. Galimzyanov, and A. V. Mokshin, “Dynamics of liquid lithium atoms: Pseudopotential and EAM-type potentials,” JETP, 126, 83–89 (2018).
L. E. González, D. J. González, M. Silbert, and J. A. Alonso, “A theoretical study of the static structure and thermodynamics of liquid lithium,” J. Phys.: Condens. Matter, 5, 4283–4298 (1993).
A. V. Mokshin, A. V. Chvanova, and R. M. Khusnutdinov, “Mode-coupling approximation in a fractional-power generalization: Particle dynamics in supercooled liquids and glasses,” Theor. Math. Phys., 171, 541–552 (2012).
Y. Waseda, The Structure of Non-Crystalline Materials: Liquids and Amorphous Solids, McGraw-Hill, New York (1980).
R. W. Ohse, ed., Handbook of Thermodynamic and Transport Properties of Alkali Metals (Chem. Data Ser., Vol. 30), Blackwell Scientific, Oxford (1985).
A. V. Mokshin and B. N. Galimzyanov, “Corrigendum: Self-consistent description of local density dynamics in simple liquids: The case of molten lithium,” J. Phys.: Condens. Matter, 31, 209501 (2019).
J. R. D. Copley and S. W. Lovesey, “The dynamic properties of monatomic liquids,” Rep. Prog. Phys., 38, 461–563 (1975).
Funding
This research was supported by a grant from the Russian Science Foundation (Project No. 19-12-00022). The part related to the development of a microscopic description was supported by the Russian Foundation for Basic Research (Grant No. 18-02-00407_a).
The research of A. V. Mokshin was supported by the Foundation for Development of Theoretical Physics and Mathematics “BAZIS.”
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
The authors declare no conflicts of interest.
Rights and permissions
About this article
Cite this article
Mokshin, A.V., Khusnutdinoff, R.M., Vilf, Y.Z. et al. Quasi-solid state microscopic dynamics in equilibrium classical liquids: Self-consistent relaxation theory. Theor Math Phys 206, 216–235 (2021). https://doi.org/10.1134/S0040577921020082
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0040577921020082