Relativistic model of interatomic interactions in condensed systems

Keywords: Interatomic potentials, Classical relativistic dynamics, Retarded interactions, Irreversibility phenomenon, Klein-Gordon-Fock equation

Abstract

      A method was proposed to describe the dynamics of systems of interacting atoms in terms of an auxiliary field. The field is equivalent to the specified interatomic potentials at rest, and represents the classical relativistic field under dynamic conditions. It was determined that for central interatomic potentials, allowing for the Fourier transform, the auxiliary field is a superposition of elementary fields satisfying the Klein-Gordon-Fock equation with complex mass parameters

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Author Biographies

Anatoly Yu. Zakharov, Yaroslav-the-Wise Novgorod State University, 41, ul. Bolshaya Saint Petersburgskaya, Veliky Novgorod 173003, Russian Federation

Dr. Sci. (Phys.-Math.), Full
Professor, Professor at the Department of General and
Experimental Physics, Yaroslav-the-Wise Novgorod
State University (Veliky Novgorod, Russian Federation)

Maxim A. Zakharov, Yaroslav-the-Wise Novgorod State University, 41, ul. Bolshaya Saint Petersburgskaya, Veliky Novgorod 173003, Russian Federation

Dr. Sci. (Phys.-Math.), Docent,
Professor at the Department of Solid State Physics and
Microelectronics, Yaroslav-the-Wise Novgorod State
University (Veliky Novgorod, Russian Federation)

References

Uhlenbeck G. E., Ford G. W. Lectures in statistical mechanics. American Mathematical Society (1963). Providence: AMS; 1963. 171 p.

Ritz W., Einstein A. Zum gegenwärtigen Stand des Strahlungsproblems. Physikalische Zeitschrift. 1909; 10(9): 323–324.

Kac M. Some remarks on the use of probability in classical statistical mechanics. Bull. de l’Académie Royale de Belgique (Classe des Sciences). 1956;42(5): 356–361. https://doi.org/10.3406/barb.1956.68352

Synge J. L. The electromagnetic two-body problem. Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences. 1940;177(968): 118–139. http://dx.doi.org/10.1098/rspa.1940.0114

Driver R. D. A two-body problem of classical electrodynamics: the one-dimensional case. Annals of Physics. 1963;21(1): 122–142. http://dx.doi.org/10.1016/0003-4916(63)90227-6

Hsing D. K. Existence and uniqueness theorem for the one-dimensional backwards twobody problem of electrodynamics. Physical Review D. 1977;16(4): 974–982. https://doi.org/10.1103/physrevd.16.974

Hoag J. T.; Driver R. D. A delayed-advanced model for the electrodynamics two-body problem. Nonlinear analysis: Theory, Methods & Applications. 1990;15(2): 165–184. https://doi.org/10.1016/0362-546x(90)90120-6

Zakharov A. Yu. On physical principles and mathematical mechanisms of the phenomenon of irreversibility. Physica A: Statistical Mechanics and its Applications. 2019;525: 1289–1295. https://doi.org/10.1016/j.physa.2019.04.047

Zakharov A. Y., Zakharov M. A. Microscopic dynamic mechanism of irreversible thermodynamic equilibration of crystals. Quantum Reports. 2021;3(4): 724–730. https://doi.org/10.3390/quantum3040045

Khrennikov A. Yu. Interpretations of probability. Berlin – New York: Walter de Gruyter; 2009. 237 p. https://doi.org/10.1515/9783110213195

Borel E. Introduction géométrique à quelques théories physiques. Paris: Gauthier-Villars; 1914. 147 p.

Levy P. Specific problems of functional analysis*. Moscow: Nauka Publ., 1967. 511 p. (In Russ.)

Rowlinson J. S. C. A scientific history of intermolecular forces. Cambridge: Cambridge University Press; 2002. 343 p.

Kaplan I. G. Intermolecular interactions: physical picture, computational methods and model potentials. Chichester: Wiley; 2006. 375 p. https://doi.org/10.1002/047086334x

Stone A. The theory of intermolecular forces. Oxford: Oxford University Press; 2013. 352 p. https://doi.org/10.1093/acprof:oso/9780199672394.001.0001

Molecular dynamics method in physical chemistry*. (Ed. Yu. K. Tovbin). Moscow: Nauka Publ., 1996; 169 p. (In Russ.)

Kamberaj H. Molecular dynamics simulations in statistical physics: theory and applications. Cham: Springer; 2020. 470 p. https://doi.org/10.1007/978-3-030-35702-3

Kun Zhou, Bo Liu. Molecular dynamics simulation: fundamentals and applications. Amsterdam: Elsevier; 2022. 374 p. https://doi.org/10.1016/b978-0-12-816419-8.00006-4

Planck M. Zur Dynamik bewegter Systeme. Annalen der Physik. 1908;331(6): 1–34. https://doi.org/10.1002/andp.19083310602

Jüttner F. Das Maxwellsche Gesetz der Geschwindigkeitsverteilung in der Relativtheorie. Annalen der Physik. 1911;339(5): 856–882. https://doi.org/10.1002/andp.19113390503

Jüttner F. Die dynamik eines bewegten Gases in der Relativtheorie. Annalen der Physik. 1911;340(6): 145–161. https://doi.org/10.1002/andp.19113400608

Synge J. L. The relativistic gas. Amsterdam: North-Holland; 1957. 119 p.

Tolman R. C. Thermodynamics and relativity. Bulletin of the American Mathematical Society. 1933;39(2): 49–74. https://doi.org/10.1090/s0002-9904-1933-05559-3

ter Haar D., Wergeland H. Thermodynamics and statistical mechanics in the special theory of relativity. Physics Reports. 1971;1(2): 31–54. https://doi.org/10.1016/0370-1573(71)90006-8

Nakamura T. K. Three views of a secret in relativistic thermodynamics. Progress of Theoretical Physics. 2012;128(3): 463–475. https://doi.org/10.1143/ptp.128.463

Chernikov N. A. Derivation of the equations of relativistic hydrodynamics from the relativistic transport equation. Physics Letters. 1963;5(2): 115–117. https://doi.org/10.1016/s0375-9601(63)91750-x

de Groot S. R., van Leeuwen W. A., van Weert Ch. G. Relativistic kinetic theory: principles and applications. Amsterdam: North-Holland; 1980. 433 p.

Trump M. A., Schieve W. C. Classical relativistic many-body dynamics. Dordrecht: Springer; 1999. 375 p. https://doi.org/10.1007/978-94-015-9303-8

Cercignani C., Kremer G. M. The relativistic Boltzmann equation: theory and applications. Basel: Birkhдuser; 2002. 394 p. https://doi.org/10.1007/978-3-0348-8165-4

Hakim R. Introduction to relativistic statisticalmechanics: classical and quantum. New Jersey: World Scientific; 2011. 566 p. https://doi.org/10.1142/7881

Kuz’menkov L. S. Field form of dynamics and statistics of systems of particles with electromagnetic interaction. Theoretical and Mathematical Physics. 1991;86(2): 159–168. https://doi.org/10.1007/bf01016167

Liboff R. Kinetic theory: classical quantum and relativistic descriptions. New York: Springer; 2003. 587 p.

Balescu R., Kotera T. On the covariant formulation of classical relativistic statistical mechanics. Physica. 1967;33(3): 558–580. https://doi.org/10.1016/0031-8914(67)90204-2

Schieve W. C. Covariant relativistic statistical mechanics of many particles. Foundations of Physics. 2005;35(8): 1359–1381. ttps://doi.org/10.1007/s10701-005-6441-9

Lusanna L. From relativistic mechanics towards relativistic statistical mechanics. Entropy. 2017;19(9): 436. https://doi.org/10.3390/e19090436

Currie D. G. Interaction contra classical relativistic Hamiltonian particle mechanics. Journal of Mathematical Physics. 1963;4(12): 1470-1488. https://doi.org/10.1063/1.1703928

Currie D. G., Jordan T. F., Sudarshan E. C. G. Relativistic invariance and Hamiltonian theories of interacting particles. Reviews of Modern Physics. 1963;35(2): 350-375. https://doi.org/10.1103/revmodphys.35.350

Leutwyler H. A no-interaction theorem in classical relativistic Hamiltonian particle mechanics. Nuovo Cimento. 1965;37(2): 556–567. https://doi.org/10.1007/bf02749856

Dirac P. A. M. Forms of relativistic dynamics. Reviews of Modern Physics. 1949,21(3): 392–399. https://doi.org/10.1103/revmodphys.21.392

van Dam H., Wigner E. P. Classical relativistic mechanics of interacting point particles. Physical Review. 1965;138(6B): 1576–1582. https://doi.org/10.1103/physrev.138.b1576

van Dam H., Wigner E. P. Instantaneous and asymptotic conservation laws for classical relativistic mechanics of interacting point particles. Physical Review. 1966;142(4): 838–843. https://doi.org/10.1103/physrev.142.838

Zakharov A. Y., Zubkov V. V. Field-theoretical representation of interactions between particles: classical relativistic probability-free kinetic theory. Universe. 2022;8(281): 1–11. http://dx.doi.org/10.3390/universe8050281

Debye P., Hückel E. Zur Theorie der Elektrolyte. Physikalische Zeitschrift. 1923;24(9): 185–206.

Ali A., Kramer G. JETS and QCD: a historical review of the discovery of the quark and gluon jets and its impact on QCD. The European Physical Journal H. 2011;36: 245–326. https://doi.org/10.1140/epjh/e2011-10047-1

Sazdjian H. The interplay between compact and molecular structures in tetraquarks. Symmetry. 2022; 14, 515. https://doi.org/10.3390/sym14030515

Loktionov I. K. Application of two-parameter oscillating interaction potentials for specifying the thermophysical properties of simple liquids. High Temperature. 2012;50(6): 708–716. https://doi.org/10.1134/S0018151X12050094

Loktionov I. K. Studying equilibrium thermophysical properties of simple liquids based on a four-parameter oscillating interaction potential. High Temperature. 2014;52(3): 390–402. https://doi.org/10.1134/S0018151X14020151

Lorenz L. On the identity of the vibrations of light with electrical currents. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science. 1867;34(230): 287–301. https://doi.org/10.1080/14786446708639882

Riemann B. A contribution to electrodynamics. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science. 1867;34(231): 368–372. https://doi.org/10.1080/14786446708639897

Ivanenko D. D.; Sokolov A. A. The classical theory of fields*. Moscow: GITTL Publ., 1949. 480 p. (In Russ.)

Landau L. D., Lifshitz E.M. The classical theory of fields*. Oxford.: Pergamon Press; 1975. 402 p.

Published
2023-10-12
How to Cite
Zakharov, A. Y., & Zakharov, M. A. (2023). Relativistic model of interatomic interactions in condensed systems. Condensed Matter and Interphases, 25(4), 494-504. https://doi.org/10.17308/kcmf.2023.25/11480
Section
Original articles