Abstract:
We formulate and solve the problem of finding a distribution function
F(r,p,t) such that calculating statistical averages leads to the same local values of the number of particles, the momentum, and the energy as those in quantum mechanics. The method is based on the quantum mechanical definition of the probability density not limited by the number of particles in the system. The obtained distribution function coincides with the Wigner function only for spatially homogeneous systems. We obtain the chain of Bogoliubov equations, the Liouville equation for quantum distribution functions with an arbitrary number of particles in the system, the quantum kinetic equation with a self-consistent electromagnetic field, and the general expression for the dielectric permittivity tensor of the electron component of the plasma. In addition to the known physical effects that determine the dispersion of longitudinal and transverse waves in plasma, the latter tensor contains a contribution from the exchange Coulomb correlations significant for dense systems.
Citation:
L. S. Kuz'menkov, S. G. Maksimov, “Distribution Functions in Quantum Mechanics and Wigner Functions”, TMF, 131:2 (2002), 231–243; Theoret. and Math. Phys., 131:2 (2002), 641–650
This publication is cited in the following 20 articles:
S. A. Maslov, V. B. Bobrov, S. A. Triger, TVT, 61:4 (2023), 492–496
S. A. Maslov, V. B. Bobrov, S. A. Trigger, “Transverse Dielectric Permittivity of a Nondegenerate Collisional Electron Plasma”, High Temp, 61:4 (2023), 453
Andreev P.A., “Kinetic analysis of spin current contribution to spectrum of electromagnetic waves in spin-1/2 plasma. I. Dielectric permeability tensor for magnetized plasmas”, Phys. Plasmas, 24:2 (2017), 022114
V. B. Bobrov, “On the transverse dielectric permittivity of degenerate electron plasma”, High Temperature, 55:4 (2017), 473–476
V. B. Bobrov, S. A. Triger, “Quantum effects in the transverse dielectric permittivity of a Maxwellian plasma”, Theoret. and Math. Phys., 192:3 (2017), 1396–1407
Andreev P.A., “Quantum Kinetics of Spinning Neutral Particles: General Theory and Spin Wave Dispersion”, Physica A, 432 (2015), 108–126
Ivanov A.Yu. Kuz'menkov L.S., “Influence of Quantum Energy Equation on Electronic Plasma Oscillations”, Int. J. Mod. Phys. B, 29:19 (2015), 1550129
Pavel A. Andreev, “Hydrodynamic and kinetic models for spin-1/2 electron-positron quantum plasmas: Annihilation interaction, helicity conservation, and wave dispersion in magnetized plasmas”, Physics of Plasmas, 22:6 (2015)
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Andreev P.A. Kuz'menkov L.S., “Waves of Magnetic Moment and Generation of Waves by Neutron Beam in Quantum Magnetized Plasma”, Int. J. Mod. Phys. B, 26:32 (2012), 1250186
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Vladimirov S.V., Tyshetskiy Yu.O., “Kinetic Description of Quantum Plasma Dielectric Response”, International Topical Conference on Plasma Science: Strongly Coupled Ultra-Cold and Quantum Plasmas, AIP Conference Proceedings, 1421, eds. Shukla P., Mendonca J., Eliasson B., Resendes D., Amer Inst Physics, 2011
L. S. Kuz'menkov, S. G. Maksimov, “A Generalized Coordinate-Momentum Representation in Quantum Mechanics”, Theoret. and Math. Phys., 143:3 (2005), 821–835
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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
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