The Mathematical Structure of the BCS-Model and Related Models

Walter E Thirring

Rudolf Haag

Alissa Geisinger

In this thesis we study mathematical aspects of BCS theory and its connection to Ginzburg-Landau theory. Furthermore we investigate the exponential decay of solutions to the Kac master equation. A full abstract is contained in the document.

Walter E Thirring, Alfred Wehrl

Using the theoretical formalism of T. H. Johnson etal.[PRL,116,240403 (2016)], Y. Nishida [PRL 114, 115302 (2015)], W. Yi and X. Chi[Phys.Rev. A92, 013623 (2015)] and A. Sindona etal.[PRL 111, 165303 (2013)], we have theoretically evaluated the dynamic structure factor (DSF) and spectral density of Fermi super fluid along BCS-BEC crossover regime.The evaluation is based on a model in which an impurity atom is trapped by an anharmonic potential with attractive interaction.We have evaluated impurity decay rate 4 (10 ) F E   as a function of vibrational energy A F E  for BCS limit ( 1 Fs ka =-0.5), unitarity limit ( 1 Fs ka =0.0) and BEC limit ( 1 Fs ka =1.0) respectively.Our theoretically obtained results show that

I. A. Bernadskii, R. A. Minlos