vestnovsuВестник Новгородского государственного университетаVestnik of Novgorod State University2076-8052Новгородский государственный университет имени Ярослава Мудрого10.34680/2076-8052.2022.3(128).11-14vestnovsu-11Research ArticleЭлектроникаElectronicsОдномерная классическая модель динамики кристаллической решетки с учетом запаздывающих взаимодействийOne-dimensional classical model of crystal lattice dynamics taking into account the retardation of interactionsЗахаровА. Ю.ZakharovA. Yu.Anatoly.Zakharov@novsu.ruЗахаровМ. А.ZakharovM. A.Новгородский государственный университет имени Ярослава МудрогоRussian Federation20221809202303(128)1114Copyright © Захаров А.Ю., Захаров М.А., 20232023Захаров А.Ю., Захаров М.А.Zakharov A.Y., Zakharov M.A.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://vestnovsu.elpub.ru/jour/article/view/11

Динамика колебаний одномерной атомной цепочки исследуется в гармоническом приближении с учетом запаздывания межатомных взаимодействий. Обнаружено, что запаздывание взаимодействий между частицами приводит к радикальной перестройке динамики одномерной гармонической цепочки. В частности, из-за запаздывания взаимодействий стационарные свободные колебания в атомной цепочке невозможны. Получен критерий отсутствия нарастающих колебаний в системе, этот критерий является условием стабильности цепочки. Показано, что при погружении устойчивой цепочки частиц с запаздывающими взаимодействиями между ними в переменное внешнее поле система переходит в стационарное состояние, которое зависит как от свойств системы, так и от характеристик внешнего поля. Это стационарное состояние было интерпретировано как динамическое равновесие между атомной цепочкой и внешним полем.

The dynamics of oscillations of a one-dimensional atomic chain is investigated in the harmonic approximation, taking into  account the retardation of interatomic interactions. It is found that the retardation of interactions between particles leads to a radical restructuring of the dynamics of a one-dimensional harmonic chain. In particular, due to the retardation of interactions, stationary free oscillations in the atomic chain are impossible. A criterion for the absence of growing oscillations in the system has been obtained, and this criterion is a condition for the stability of the chain. It is shown that when a stable chain of particles with retarded interactions between them is immersed in an alternating external field, the system passes into a stationary state, which depends both on the properties of the system and on the characteristics of the external field. This stationary state has been interpreted as a dynamic equilibrium between an atomic chain and an external field.

динамика многочастичных системзапаздывающие взаимодействиянеобратимостьтермодинамическое равновесиеmulti-particle system dynamicsretarded interactionsirreversibilitythermodynamic equilibrationReferencesBorn M., von Karman T. Über Schwingungen im Raumgittern. Physikalische Zeitschrift, 1912, vol. 13(8), pp. 297–309.Born M., von Karman T. Über Schwingungen im Raumgittern. Physikalische Zeitschrift, 1912, vol. 13(8), pp. 297–309.Born M., Huang K. Dynamical Theory of Crystal Lattices. Oxford: Clarendon Press, 1954.Born M., Huang K. Dynamical Theory of Crystal Lattices. Oxford: Clarendon Press, 1954.Brillouin L. Wave Propagation in Periodic Structures: Electric Filters and Crystal Lattices. N.Y., Dover Publications Publ., USA, 1953.Brillouin L. Wave Propagation in Periodic Structures: Electric Filters and Crystal Lattices. N.Y., Dover Publications Publ., USA, 1953.Maradudin A.A., Montroll E.W., Weiss G.H., Ipatova I.P. Theory of Lattice Dynamics in the Harmonic Approximation. N.Y., Academic Press Publ., USA, 1971.Maradudin A.A., Montroll E.W., Weiss G.H., Ipatova I.P. Theory of Lattice Dynamics in the Harmonic Approximation. N.Y., Academic Press Publ., USA, 1971.Kosevich A.M. The Crystal Lattice: Phonons, Solitons, Dislocations, Superlattices. Weinheim, Wiley-VCH Verlag Publ., 2005.Kosevich A.M. The Crystal Lattice: Phonons, Solitons, Dislocations, Superlattices. Weinheim, Wiley-VCH Verlag Publ., 2005.Lamb H. On a peculiarity of the wave-system due to the free vibrations of a nucleus in an extended medium. Proc. London Math. Soc., 1900, vol. s1-32(1), pp. 208–211.Lamb H. On a peculiarity of the wave-system due to the free vibrations of a nucleus in an extended medium. Proc. London Math. Soc., 1900, vol. s1-32(1), pp. 208–211.Love A.E.H. Some illustrations of modes of decay of vibratory motions. Proc. London Math. Soc., 1905, vol. s22(1), pp. 88–113.Love A.E.H. Some illustrations of modes of decay of vibratory motions. Proc. London Math. Soc., 1905, vol. s22(1), pp. 88–113.Jahan A. The Lamb problem with a nonuniform string. Physics Letters A, 2021, vol. 392, pp. 127–133.Jahan A. The Lamb problem with a nonuniform string. Physics Letters A, 2021, vol. 392, pp. 127–133.Jahan A. The Lamb problem with a nonuniform string II: Perturbative Solutions. Physics Letters A, 2021, vol. 400, 127320.Jahan A. The Lamb problem with a nonuniform string II: Perturbative Solutions. Physics Letters A, 2021, vol. 400, 127320.Synge J.L. The electromagnetic two-body problem. Proc. Roy. Soc. A, 1940, vol. 177(968), pp. 118–139.Synge J.L. The electromagnetic two-body problem. Proc. Roy. Soc. A, 1940, vol. 177(968), pp. 118–139.Driver R.D. A two-body problem of classical electrodynamics: The one-dimensional case. Ann. Physics, 1963, vol.21(1), pp. 122–142.Driver R.D. A two-body problem of classical electrodynamics: The one-dimensional case. Ann. Physics, 1963, vol.21(1), pp. 122–142.Hsing D.K. Existence and uniqueness theorem for the onedimensional backwards Two-body problem of electrodynamics. Physic Rev. D, 1977, vol. 16(04), pp. 974–982.Hsing D.K. Existence and uniqueness theorem for the onedimensional backwards Two-body problem of electrodynamics. Physic Rev. D, 1977, vol. 16(04), pp. 974–982.Hoag J.T., Driver R.D. A delayed-advanced model for the electrodynamics two-body problem. Nonlinear Analysis: Theory, Methods & Applications, 1990, vol. 15(2), pp. 165–184.Hoag J.T., Driver R.D. A delayed-advanced model for the electrodynamics two-body problem. Nonlinear Analysis: Theory, Methods & Applications, 1990, vol. 15(2), pp. 165–184.Zakharov A.Yu. On physical principles and mathematical mechanisms of the phenomenon of irreversibility. Physica A: Statistical Mechanics and its Applications, 2019, vol. 525, pp. 1289–1295.Zakharov A.Yu. On physical principles and mathematical mechanisms of the phenomenon of irreversibility. Physica A: Statistical Mechanics and its Applications, 2019, vol. 525, pp. 1289–1295.Zakharov A.Yu. Probability-free relativistic kinetic theory of classical systems of charged particles. Journal of Physics: Conference Series, 2020, vol. 1658(1), 012076.Zakharov A.Yu. Probability-free relativistic kinetic theory of classical systems of charged particles. Journal of Physics: Conference Series, 2020, vol. 1658(1), 012076.Landau L.D., Lifshitz E.M. Mechanics. Amsterdam, Elsevier Publ., Netherlands, 2007.Landau L.D., Lifshitz E.M. Mechanics. Amsterdam, Elsevier Publ., Netherlands, 2007.

The authors declare that there are no conflicts of interest present.