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TMF, 1999, Volume 118, Number 2, Pages 287–304 (Mi tmf700)  

This article is cited in 45 scientific papers (total in 45 papers)

Quantum hydrodynamics of particle systems with Coulomb interaction and quantum Bohm potential

L. S. Kuz'menkov, S. G. Maksimov

M. V. Lomonosov Moscow State University, Faculty of Physics

Abstract: The quantum hydrodynamics of $N$ interacting particles with Coulomb interaction in an external electromagnetic field can be described by the field equations for the microscopic dynamics in the physical space. Macroscopic hydrodynamic equations are obtained by local averaging. Quantum corrections to the hydrodynamic equations are due to the multiparticle quantum Bohm potential. Specific properties of Fermi- and Bose-system hydrodynamics are investigated. The Cauchy-type integral for the quantum system and the corresponding one-particle Schrцdinger equation are found under the standard classical hydrodynamic assumptions.

DOI: https://doi.org/10.4213/tmf700

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English version:
Theoretical and Mathematical Physics, 1999, 118:2, 227–240

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Received: 03.07.1998

Citation: L. S. Kuz'menkov, S. G. Maksimov, “Quantum hydrodynamics of particle systems with Coulomb interaction and quantum Bohm potential”, TMF, 118:2 (1999), 287–304; Theoret. and Math. Phys., 118:2 (1999), 227–240

Citation in format AMSBIB
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\paper Quantum hydrodynamics of particle systems with Coulomb interaction and quantum Bohm potential
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\pages 287--304
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\jour Theoret. and Math. Phys.
\yr 1999
\vol 118
\issue 2
\pages 227--240
\crossref{https://doi.org/10.1007/BF02557315}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. L. S. Kuz'menkov, S. G. Maksimov, V. V. Fedoseev, “Microscopic Quantum Hydrodynamics of Systems of Fermions: Part I”, Theoret. and Math. Phys., 126:1 (2001), 110–120  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. L. S. Kuz'menkov, S. G. Maksimov, “Distribution Functions in Quantum Mechanics and Wigner Functions”, Theoret. and Math. Phys., 131:2 (2002), 641–650  mathnet  crossref  crossref  zmath  isi
    3. Maximov SG, Kuzmenkov LS, Zavala JLG, “Local equilibrium approach for Fermi systems and quantum hydrodynamics”, International Journal of Quantum Chemistry, 100:4 (2004), 311–323  crossref  isi  scopus  scopus  scopus
    4. Andreev, PA, “Generation of Waves by a Neutron Beam in a Two-Component System Formed by Charged Particles of Nonzero Spin”, Physics of Atomic Nuclei, 71:10 (2008), 1724  crossref  adsnasa  isi  scopus  scopus  scopus
    5. Andreev, PA, “Problem with the single-particle description and the spectra of intrinsic modes of degenerate boson-fermion systems”, Physical Review A, 78:5 (2008), 053624  crossref  adsnasa  isi  elib  scopus  scopus  scopus
    6. Zamanian, J, “Dynamics of a dusty plasma with intrinsic magnetization”, New Journal of Physics, 11 (2009), 073017  crossref  adsnasa  isi  scopus  scopus  scopus
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    8. Andreev P.A., Kuzmenkov L.S., Trukhanova M.I., “Quantum hydrodynamics approach to the formation of waves in polarized two-dimensional systems of charged and neutral particles”, Physical Review B, 84:24 (2011), 245401  crossref  adsnasa  isi  elib  scopus  scopus  scopus
    9. Mahajan S.M., Asenjo F.A., “Vortical Dynamics of Spinning Quantum Plasmas: Helicity Conservation”, Physical Review Letters, 107:19 (2011), 195003  crossref  adsnasa  isi  elib  scopus  scopus  scopus
    10. Trukhanova M.I., “Spinovye i polyarizatsionnye volny v sisteme neitralnykh paramagnitnykh chastits s sobstvennym dipolnym momentom”, Naukoemkie tekhnologii, 12:2 (2011), 10–24  elib
    11. Trukhanova M.I., “Spin and Polarization Waves in a System of Paramagnetic Particles With An Intrinsic Dipole Moment”, Internat J Modern Phys B, 26:1 (2012)  crossref  zmath  isi  elib  scopus  scopus  scopus
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    14. Andreev P.A., “Quantum Hydrodynamics of Charge Carriers in Graphene”, Piers 2012 Moscow: Progress in Electromagnetics Research Symposium, Progress in Electromagnetics Research Symposium, Electromagnetics Acad, 2012, 154–157  isi
    15. Kuzmenkov L.S. Andreev P.A., “Microscopic Classic Hydrodynamic and Methods of Averaging”, Piers 2012 Moscow: Progress in Electromagnetics Research Symposium, Progress in Electromagnetics Research Symposium, Electromagnetics Acad, 2012, 158–162  isi
    16. Andreev P.A., Kuzmenkov L.S., “Spin and Electric Polarization Waves in Dielectric Systems of Different Dimensions”, Piers 2012 Moscow: Progress in Electromagnetics Research Symposium, Progress in Electromagnetics Research Symposium, Electromagnetics Acad, 2012, 1055–1059  isi
    17. Andreev P.A. Kuz'menkov L.S., “Self-Consistent Field Theory of Polarised Bose–Einstein Condensates: Dispersion of Collective Excitations”, Eur. Phys. J. D, 67:10 (2013), 216  crossref  adsnasa  isi  scopus  scopus  scopus
    18. Ivanov A.Yu. Andreev P.A., “Dispersion of Waves in a Weakly Relativistic Quantum Plasma and Beam of Particles”, Russ. Phys. J., 56:3 (2013), 325–329  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    19. Zezyulin K.V. Andreev P.A. Kuz'menkov L.S., “Soliton Appearing in Boson-Fermion Mixture at the Third Order of the Interaction Radius”, Eur. Phys. J. D, 67:7 (2013), 140  crossref  adsnasa  isi
    20. Andreev P.A., “Nonintegral Form of the Gross–Pitaevskii Equation for Polarized Molecules”, Mod. Phys. Lett. B, 27:13 (2013), 1350096  crossref  adsnasa  isi  elib  scopus  scopus  scopus
    21. Andreev P.A., “First Principles Derivation of NLS Equation for Bec with Cubic and Quintic Nonlinearities at Nonzero Temperature: Dispersion of Linear Waves”, Int. J. Mod. Phys. B, 27:6 (2013), 1350017  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus  scopus
    22. Trukhanova M.I., “Quantum Hydrodynamics Approach to the Research of Quantum Effects and Vorticity Evolution in Spin Quantum Plasmas”, Prog. Theor. Exp. Phys., 2013, no. 11, 111I01  crossref  isi  scopus  scopus  scopus
    23. Andreev P.A., Kuz'menkov L.S., “Dispersion Properties of Transverse Waves in Electrically Polarized Becs”, J. Phys. B-At. Mol. Opt. Phys., 47:22 (2014), 225301  crossref  adsnasa  isi  scopus  scopus  scopus
    24. Andreev P.A., “Exchange Effects in Coulomb Quantum Plasmas: Dispersion of Waves in 2D and 3D Quantum Plasmas”, Ann. Phys., 350 (2014), 198–210  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    25. 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  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    26. Trukhanova M.I. Andreev P.A., “Exchange Interaction Effects on Waves in Magnetized Quantum Plasmas”, Phys. Plasmas, 22:2 (2015), 022128  crossref  adsnasa  isi  scopus  scopus  scopus
    27. Andreev P.A., Ivanov A.Yu., “Weakly Relativistic Quantum Effects in a Two-Dimensional Electron Gas: Dispersion of Langmuir Waves”, Russ. Phys. J., 57:9 (2015), 1210–1219  crossref  zmath  isi  scopus  scopus
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    31. Andreev P.A. Ivanov A.Yu., “Exchange Coulomb Interaction in Nanotubes: Dispersion of Langmuir Waves”, Phys. Plasmas, 22:7 (2015), 072101  crossref  adsnasa  isi  elib  scopus  scopus  scopus
    32. Trukhanova M.I., “Energy Evolution in Many-Particle Quantum Hydrodynamics of Spinning Plasmas”, Mod. Phys. Lett. B, 30:4 (2016), 1650023  crossref  mathscinet  adsnasa  isi  scopus  scopus  scopus
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