Abstract:
Exact commutation relations are obtained for the operators of quasiparticles in a periodic lattice (Frenkel' excitons, magnons). The commutation relations are
trilinear in the operators of creation and annihilation of quasipartieles and contain
a conservation law of the quasimomentum. The statistical properties of the quasiparticles are described by modified parastatistics of rank N (N is the number of sites of the lattice in the delocalization region of the excitation). It is shown that a gas of quasiparticles satisfying parastatistics is always nonideal since the corrections for the non-Bose nature of the quasiparticle operators are of the same order as the corrections for the nonideal behavior. The number of quasiparticles does not exceed the rank of the parastatistics describing them, which shows that there are no fundamental prohibitions of the phenomenon of Bose condensation. The commutation relations can be used to take into account exactly the kinematic interaction in any order in the dynamical interaction.
Citation:
I. G. Kaplan, “Statistics of molecular excitons and magnons at high concentrations”, TMF, 27:2 (1976), 254–261; Theoret. and Math. Phys., 27:2 (1976), 466–471
\Bibitem{Kap76}
\by I.~G.~Kaplan
\paper Statistics of molecular excitons and magnons at high concentrations
\jour TMF
\yr 1976
\vol 27
\issue 2
\pages 254--261
\mathnet{http://mi.mathnet.ru/tmf3324}
\transl
\jour Theoret. and Math. Phys.
\yr 1976
\vol 27
\issue 2
\pages 466--471
\crossref{https://doi.org/10.1007/BF01051239}
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https://www.mathnet.ru/eng/tmf3324
https://www.mathnet.ru/eng/tmf/v27/i2/p254
This publication is cited in the following 19 articles:
Ronald Columbié-Leyva, Alberto López-Vivas, Jacques Soullard, Ulises Miranda, Ilya G. Kaplan, “Symmetry of Identical Particles, Modern Achievements in the Pauli Exclusion Principle, in Superconductivity and in Some Other Phenomena”, Symmetry, 15:3 (2023), 701
Ilya G. Kaplan, “Modern State of the Pauli Exclusion Principle and the Problems of Its Theoretical Foundation”, Symmetry, 13:1 (2020), 21
I. G. Kaplan, “The Pauli Exclusion Principle and the Problems of its Theoretical Substantiation1”, Russ Phys J, 63:8 (2020), 1305
The Pauli Exclusion Principle, 2016, 1
The Pauli Exclusion Principle, 2016, 106
I. G. Kaplan, “The Pauli Exclusion Principle. Can It Be Proved?”, Found Phys, 43:10 (2013), 1233
I. G. Kaplan, Fundamental World of Quantum Chemistry, 2003, 183
I. G. Kaplan, “Is the Pauli exclusive principle an independent quantum mechanical postulate?”, Int J of Quantum Chemistry, 89:4 (2002), 268
I.G. Kaplan, O. Navarro, “Statistics and properties of coupled hole pairs in superconducting ceramics”, Physica C: Superconductivity, 341-348 (2000), 217
O. Navarro, I.G. Kaplan, “Theoretical Study of Hole-Pair System in a Periodical Lattice”, phys. stat. sol. (b), 220:1 (2000), 493
H.O. Frota, F.S. de Aguiar, “Statistical mechanics of relativistic anyons”, Physica A: Statistical Mechanics and its Applications, 269:2-4 (1999), 418
I G Kaplan, O Navarro, “Charge transfer and the statistics of holons in a periodical lattice”, J. Phys.: Condens. Matter, 11:32 (1999), 6187
Ilya G. Kaplan, “Exclusion principle and indistinguishability of identical particles in quantum mechanics”, Journal of Molecular Structure, 272 (1992), 187
H.O. Frota, A.C.R. Bittencourt, “The magnetized d-dimensional ideal paragas”, Physica A: Statistical Mechanics and its Applications, 160:3 (1989), 386
Nguyen Ba An, “Exciton Nonequilibrium Steady States in Laser‐Excited Molecular Crystals”, Physica Status Solidi (b), 150:2 (1988), 845
M. C. de Sousa Vieira, C. Tsallis, “D-Dimensional ideal gas in parastatistics: Thermodynamic properties”, J Stat Phys, 48:1-2 (1987), 97
A. Yu. Gaevskii, I. G. Kaplan, M. A. Puvinskii, “Density-density correlation function of a system of molecular excitons”, Theoret. and Math. Phys., 48:1 (1981), 653–658
D. Bonchev, “Information theory interpretation of the Pauli principle and Hund rule”, Int J of Quantum Chemistry, 19:4 (1981), 673
Eugene S. Kryachko, “Constructive approach to symmetrized two-particle expansions”, Reports on Mathematical Physics, 18:1 (1980), 67
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