Boltzmann factor exp(-hf/kT)
hf/kTnon-eq = hf/kTeq +/- (sigma)P/hf^2 Ansatz 2 (dimensionless equation)
Sigma = coupling cross-section of external pump power flux real quanta to target quanta
“real” = on mass shell (QFT) “virtual” = off mass shell
P ~ external pump power flux [P] = energy/area x time
f = frequency of real pump quanta
+ for continuous energy eigenvalues of real target quanta Tnon-eq remains positive —> 0 with a Tc > 0 for BEC Frohlich-Glauber coherent state
- for discrete energy eigenvalues of real target quanta Tnon-eq goes negative (discrete energy eigenvalue population inversion) creating BEC above critical pump threshold Pc at Tnon-eq = 0 critical point for non-equilibrium dynamical quantum phase transition.