Freiburg 2024 – wissenschaftliches Programm
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A: Fachverband Atomphysik
A 24: Fermionic Quantum Gases II (joint session Q/A)
A 24.5: Vortrag
Mittwoch, 13. März 2024, 15:30–15:45, Aula
A generalized formalism to describe multi-channel Hartree-Fock-Bogoliubov interactions in fermionic systems — •Nikolai Kaschewski1, Axel Pelster1, and Carlos A. R. Sá de Melo2 — 1Physics Department and Research Center OPTIMAS, RPTU Kaiserslautern-Landau, Germany — 2School of Physics, Georgia Institute of Technology, Atlanta, USA
A simplified description of fermionic systems relies on the Hartree-Fock-Bogoliubov (HFB) approximation, where the interaction is decomposed into distinct channels. However, an major issue with this procedure is that the separation between the channels is somewhat arbitrary. In some cases, only one interaction channel is considered, e.g the pairing channel in the BCS theory and the BCS-BEC crossover, or in other cases, two different interaction channels are artificially separated like in the Jellium model. In this talk, we present a generalized self-consistent theory by using weighting parameters for each channel. Our approach removes the arbitrariness of channel separation and provides a minimization principle for the optimal partitioning. We present this formalism for any type of spatially non local potentials without memory and derive the respective HFB self-consistency equations on a mean-field level and show how inter-channel interactions arise. We illustrate the power of our technique with a simple example before showing on a formal level how to include pairing, density, and exchange fluctuations simultaneously without miscounting or double-counting states.
Keywords: Hartree-Fock-Bogoliubov; mean-field theory; fermionic system