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Understanding the emergence of collective organizational phenomena is a majorgoal in many fields of physics from condensed matter to cosmology. Using arecently introduced manybody perturbation formalism for fermions, we propose amechanism for the emergence of collective behavior, specifically superfluidity,driven by quantum statistics and the enforcement of the Pauli principle throughthe selection of normal modes. The method, which is called symmetry invariantperturbation theory (SPT), uses group theory and graphical techniques to solvethe manybody Schrodinger equation through first order exactly. The solution atfirst order defines collective coordinates in terms of five N-body normalmodes, identified as breathing, center of mass, single particle angularexcitation, single particle radial excitation and phonon. A correspondence isestablished "on paper" that enforces the Pauli principle through the assignmentof specific normal mode quantum numbers. Applied in the unitary regime, thisnormal mode assignment yields occupation only in an extremely low frequencyN-body phonon mode at ultralow temperatures. A single particle radialexcitation mode at a much higher frequency creates a gap that stabilizes thesuperfluidity at low temperatures. Coupled with the corresponding values forthe frequencies at unitarity obtained by this manybody calculation, we obtaingood agreement with experimental thermodynamic results including the lambdatransition in the specific heat. Our results suggest that the emergence ofcollective behavior in macroscopic systems is driven by the Pauli principle andits selection of the correct collective coordinates in the form of N-bodynormal modes.

The Pauli principle, normal modes and superfluidity: the emergence of collective organizational phenomena