Quantum plasmas with or without a uniform magnetic field. I. General formalism and algebraic tails of correlations

Abstract

Large-distance quantum static correlations are investigated in a fluid of point charges interacting via Coulomb forces in the presence of a uniform magnetic field ${\mathbf{B}}_{0}.$ Moreover, each particle carries a spinorial magnetic momentum which is coupled to ${\mathbf{B}}_{0}.$ In the framework of quantum statistics, the present formalism uses the Feynman-Kac-It\^o formula to represent the matrix elements of the quantum Gibbs factor. Particles which are exchanged with one another under a cyclic permutation are equivalent to loops with random shapes; the latter ones obey Maxwell-Boltzmann statistics and interact via some two-body potential which decays as $1/r$ at large distances $r.$ ${\mathbf{B}}_{0}$ appears only in a phase factor which can be absorbed in some generalized fugacity (which may take negative values in the case of fermions). Collective Debye screening effects show up through exact systematic resummations of long-ranged Coulomb divergencies which are the same in the presence as in the absence of ${\mathbf{B}}_{0}.$ The averages of monopole-monopole and monopole-multipole interactions between sets made by charges and their polarization clouds decay exponentially. ${\mathbf{B}}_{0}$ breaks the rotational symmetry and effective quantum quadrupolar interactions emerge, as can also be seen in an exactly solvable model. As is also the case for a charge of the medium, an external infinitesimal charge is completely screened by the total charge of the induced polarization cloud. The latter decays as ${1/r}^{5}$ as the particle-charge correlation. Subleading tails are also investigated. The interplay with classical Debye screening is discussed.