prof. dr hab. David Blaschke (IFT)

Generalized Beth--Uhlenbeck formulas from the $Phi-$derivable approach in 2-loop approximation

A dense fermion system with strong two-particle correlations (bound and scattering states = composite bosons) is considered within the Phi-derivable approach to the thermodynamic potential. It is shown that in the two-loop approximation for the Phi-functional of this fermion-composite boson system important cancellations hold which are one key element in the proof that the thermodynamic potential takes the form of a generalized Beth-Uhlenbeck formula. The other element are generalized optical theorems. It is shown that generalized Beth-Uhlenbeck formulas also hold for the other thermodynamic functions (entropy, density) which all assume the generic form of an energy-momentum integral over a statistical distribution function multiplied with a unique spectral density. In the near mass-shell limit, contrary to naive expectations, the latter reduces not to a Lorentzian but rather to a so-called "squared Lorentzian" shape. The developed formalism extends the validity of the Beth-Uhlenbeck approach beyond the low-density limit. It includes the Mott-dissociation of bound states in accordance with the Levinson theorem and the selfconsistent backreaction of the correlations to the propagation of the elementary fermions.