Abstract
We review various exact results concerning the presence of algebraic tails in three-dimensional quantum plasmas. First, we present a solvable model of two quantum charges immersed in a classical plasma. The effective potential between the quantum charges is shown to decay as 1/r 6 at large distances r. Then, we mention semiclassical expansions of the particle correlations for charged systems with Maxwell-Boltzmann statistics and short-ranged regularization of the Coulomb potential. The quantum corrections to the classical quantities, from orderh 4 on, also decay as 1/r 6. We also give the result of an analysis of the charge correlation for the one-component plasma in the framework of the usual many-body perturbation theory; some Feynman graphs beyond the random phase approximation display algebraic tails. Finally, we sketch a diagrammatic study of the correlations for the full many-body problem with quantum statistics and pure 1/r interactions. The particle correlations are found to decay as 1/r 6, while the charge correlation decays faster, as 1/r 10. The coefficients of these tails can be exactly computed in the low-density limit. The absence of exponential screening arises from the quantum fluctuations of partially screened dipolar interactions.
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References
F. J. Dyson and A. Lenard,J. Math. Phys. 8, 423 (1967); 9, 698 (1968).
J. L. Lebowitz and E. Lieb,Adv. Math. 9, 316 (1972); E. H. Lieb,Rev. Mod. Phys. 48, 553 (1976).
P. Debye and E. Hückel,Phys. Z. 9, 185 (1923).
L. H. Thomas,Proc. Camb. Phil Soc. 23, 542 (1927); E. Fermi, Z.Physik 48, 73 (1928); N. F. Mott,Proc. Camb. Phil. Soc. 32, 281 (1936).
D. Pines and Ph. Nozieres,The Theory of Quantum Liquids (Benjamin, New York, 1986).
D. G Brydges and P. Federbush,Commun. Math. Phys. 73, 197 (1980).
D. C. Brydges and P. Federbush,Rigorous Atomic and Molecular Physics, edited by G. Velo and A. S. Wightman (Plenum Press, New York, 1981).
D. G Brydges and E. Seiler,J. Stat. Phys. 42, 405 (1986).
A. Alastuey and Ph. A. Martin,Phys. Rev. A 40, 6485 (1989).
A. Alastuey and Ph. A. Martin,Europhys. Lett. 6, 385 (1988).
F. Cornu and Ph. A. Martin,Phys Rev. A 44, 4893 (1991).
F. Cornu, inPhysics of Strongly Coupled Plasmas, ed. by W. D. Kraeft and M. Schlanges (World Scientific, Singapour, 1996).
F. Cornu,Phys. Rev. E 53, 4562 (1996).
F. Cornu,Phys. Rev. E 53, 4595 (1996).
F. Cornu,Phys. Rev. Lett. 78, 1464 (1997).
Ph. A. Martin,Rev. Mod. Phys. 60, 1075 (1988).
E. H. Lieb and H. Narnhofer,J. Stat. Phys. 12, 291 (1975);J. Stat. Phys. 14, 465 (1976).
A. Alastuey,Annales de Physique (Paris)11, 653 (1986).
B. Jancovici,Mol.Phys. 32, 1177 (1976).
M. M. Gombert and D. Léger,Phys. Lett. A 185, 417 (1994).
A. L. Fetter and J. D. Walecka,Quantum Theory of Many Particle Systems (McGraw-Hill, New York, 1971); J. W. Negele and H. Orland,Quantum Many-Particle Systems, in Frontiers in Physics, vol. 68 (Addison-Wesley, 1988).
B. Jancovici,Physica 91A, 152 (1978).
A. C. Maggs and N. W. Ashcroft,Phys. Rev. Lett. 59, 113 (1987).
D. C. Langreth and S. H. Vosko,Phys. Rev. Lett. 59, 497 (1987).
J. Friedel,Phil. Mag. 43, 153 (1952);Nuovo Cimento 7 Suppl. 2, 287, (1958).
J. Ginibre,J. Math. Phys. 6, 238 (1965);J. Math. Phys. 6, 252 (1965);J. Math. Phys. 6, 1432 (1965); inStatistical Mechanics and Quantum Field Theory, 1971 Les Houches Lectures, ed. by C. de Witt and R. Stora (Gordon and Breach, New York, 1971).
J. S. Høye and G. Stell,J. Stat Phys. 77, 361 (1994).
J. E. Mayer and M. G. Mayer, Statistical Mechanics (Wiley, New York, 1940); J. E. Mayer and E. Montroll,J. Chem. Phys. 9, 2 (1941).
T. Morita and K. Hiroike,Prog. Theor. Phys. 25, 537 (1961).
J. P. Hansen and I. R. McDonald,Theory of Simple Liquids (Academic Press, London, 1976).
E. Meeron,J. Chem. Phys. 28, 630 (1958);Plasma Physics (Mc Graw-Hill, New York, 1961).
Ph. A. Martin, to be published.
D. C. Brydges and G. Keller,J. Stat. Phys. 76, 285 (1994).
Ph. A. Martin and Ch. Oguey,Phys. Rev. A 33, 4191 (1986).
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Alastuey, A., Cornu, F. Part II. Algebraic tails in three-dimensional quantum plasmas. J Stat Phys 89, 20–35 (1997). https://doi.org/10.1007/BF02770752
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DOI: https://doi.org/10.1007/BF02770752