Abstract:
It is shown that the equations of the dynamics of N interacting particles can be represented for any N in the form of a BBGKY hierarchy and a Liouville equation. A similar representation has been obtained for systems of charged particles in their electromagnetic self-field. This has made it possible to use the BBGKY hierarchy as a method of obtaining
statistical equations. Transition to nondeterministic states of a particle-field system has the consequence that both the particle and the field states become nondeterministic due to the appearance of transition probabilities. The BBGKY hierarchy of evolution equations
branches. In 7N-dimensional phase spaces, there is no branching.
Citation:
L. S. Kuz'menkov, “Field form of dynamics and statistics of systems of particles with electromagnetic interaction”, TMF, 86:2 (1991), 231–243; Theoret. and Math. Phys., 86:2 (1991), 159–168
\Bibitem{Kuz91}
\by L.~S.~Kuz'menkov
\paper Field form of dynamics and statistics of systems of particles with electromagnetic interaction
\jour TMF
\yr 1991
\vol 86
\issue 2
\pages 231--243
\mathnet{http://mi.mathnet.ru/tmf5438}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1107704}
\transl
\jour Theoret. and Math. Phys.
\yr 1991
\vol 86
\issue 2
\pages 159--168
\crossref{https://doi.org/10.1007/BF01016167}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1991GH61300007}
Linking options:
https://www.mathnet.ru/eng/tmf5438
https://www.mathnet.ru/eng/tmf/v86/i2/p231
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A Yu Zakharov, V V Zubkov, “Toward a relativistic microscopic substantiation of thermodynamics: classical relativistic many-particle dynamics”, J. Phys.: Conf. Ser., 2052:1 (2021), 012054
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Andreev P.A. Kuz'menkov L.S., “On the Equation of State For the “Thermal” Part of the Spin Current: the Pauli Principle Contribution in the Spin Wave Spectrum in a Cold Fermion System”, Prog. Theor. Exp. Phys., 2019, no. 5, 053J01
Andreev P.A., “Radiative Corrections to the Coulomb Law and Model of Dense Quantum Plasmas: Dispersion of Longitudinal Waves in Magnetized Quantum Plasmas”, Phys. Plasmas, 25:4 (2018), 042103
Andreev P.A., “NLSE for quantum plasmas with the radiation damping”, Mod. Phys. Lett. B, 30:13 (2016), 1650180
Andreev P.A., “Quantum Kinetics of Spinning Neutral Particles: General Theory and Spin Wave Dispersion”, Physica A, 432 (2015), 108–126
Ivanov A.Yu. Andreev P.A. Kuz'menkov L.S., “Balance Equations in Semi-Relativistic Quantum Hydrodynamics”, Int. J. Mod. Phys. B, 28:21 (2014), 1450132
I. M. Aleshin, O. O. Trubachev, “Equilibrium State of Inhomogeneous Plasma”, Theoret. and Math. Phys., 138:1 (2004), 134–141
L. S. Kuz'menkov, S. G. Maksimov, “Distribution Functions in Quantum Mechanics and Wigner Functions”, Theoret. and Math. Phys., 131:2 (2002), 641–650
L. S. Kuz'menkov, S. G. Maksimov, “Quantum hydrodynamics of particle systems with Coulomb interaction and quantum Bohm potential”, Theoret. and Math. Phys., 118:2 (1999), 227–240
I. M. Aleshin, “Magnetohydrodynamics with regard to electron inertia: Some exact solutions”, Theoret. and Math. Phys., 116:3 (1998), 1011–1020
M. A. Drofa, L. S. Kuz'menkov, “Continual approach to the multiparticle systems with long-range interaction. Hierarchy of macroscopic fields and some physical consequences”, Theoret. and Math. Phys., 108:1 (1996), 849–859
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