A Quantum Phase Transition in the Cosmic Ray Energy Distribution

Abstract

We here argue that the "knee" of the cosmic ray energy distribution at $E_c \sim 1$ PeV represents a second order phase transition of cosmic proportions. The discontinuity of the heat capacity per cosmic ray particle is given by $\Delta c=0.450196\ k_B$. However the idea of a deeper critical point singularity cannot be ruled out by present accuracy in neither theory nor experiment. The quantum phase transition consists of cosmic rays dominated by bosons for the low temperature phase E<E_c and dominated by fermions for high temperature phase $E > E_c$. The low temperature phase arises from those nuclei described by the usual and conventional collective boson models of nuclear physics. The high temperature phase is dominated by protons. The transition energy $E_c$ may be estimated in terms of the photo-disintegration of nuclei.