Breakdown of Debye screening in quantum Coulomb systems and van der Waals forces

Screening of the 1/r Coulomb potential is one of the most fundamental properties of systems made of charged particles at thermal equilibrium. According to the familiar Debye description, the effective potential between two charges surrounded by their polarization clouds decays exponentially fast. In the classical case, this mean-field prediction is confirmed by rigorous proofs. However, when quantum mechanics is taken into account, we show that exponential screening is lost. Indeed, the intrinsic quantum fluctuations of the charges generate residual multipole-like interactions which are only partially screened. The particle correlations then decay as 1/r6, i.e. the square of dipolar interactions. This mechanism is illustrated in the simple framework of a solvable model of two quantum charges immersed in a classical plasma. The corresponding effective interactions between the charges are quite similar to the usual van der Waals forces between two atoms in the vacuum. In fact, as strongly suggested by a path integral analysis of the Hydrogen plasma at low temperature and low density, the effective interactions between any neutral and/or charged entities in a partially ionized gas, all behave as 1/r6 at large distances. Thus, the presence of free charges does not modify the 1/r6 nature of van der Waals forces, contrarily to what is expected in a classical description of screening effects. Possible implications of the breakdown of Debye screening due to quantum fluctuations are briefly evocated