Formation of Binary Correlations in Plasma

Abstract

SummaryThe characteristic time of formation of correlations at high temperature limit is given by the inverse plasma frequency \( \tau _C \approx \frac{1} {{\omega _p }} = \frac{{\sqrt 2 }} {{\upsilon _{th} \kappa }} \) . The inverse plasma frequency indicates that the dominant role play the long range fluctuation. On the other hand, we also see that the correlation time is found to be given by the time a particle needs to travel through the range of the potential with a thermal velocity υth. This confirms the numerical finding of [12] that the correlation or memory time is proportional to the range of interaction. In the low temperature region, i.e., in highly degenerated system μ 》 T one finds a differentpicture. From (3) we can calculate the formationofcorrelationsaswell. 13,14 Unlike in the classical case, the equilibrium limit of the degenerated case is rapidly built up and then oscillates around the equilibrium value. We can define the build up time τ C as the time where the correlation energy reaches its first maximum, \( \tau _C = 1.0\frac{\hbar } {\mu } \) . Note that τ C is in agreement with the quasiparticle formation time known as Landau’s criterion for is the Fermi energy. Indeed, the quasiparticle formation and the build up of correlations are two alternative views of the same phenomena. The formation of binary correlations is very fast on the time scale of dissipative process. Under extremely fast external perturbations, like the massive femto second laser pulses, the dynamics of binary correlations will hopefully become experimentally accessible. Even if related measurement will not reveal any unexpected features, the experimental justification of basic concepts of the non-equilibrium many-body physics is very desirable.