The Pauli principle in collective motion: Reimagining and reinterpreting Cooper pairs, the Fermi sea, Pauli blocking and superfluidity

Abstract

Typically visualized from an independent particle viewpoint, the Pauli principle's role in collective motion is analyzed leading to a reimagination of the microscopic dynamics underlying superfluidity/superconductivity and a reinterpretation of several interrelated phenomena: Cooper pairs, the Fermi sea, and Pauli blocking. The current approach, symmetry-invariant perturbation theory is a first principles method with no adjustable parameters. An adiabatic evolution is employed to transfer the well-known Pauli restrictions for identical, independent particles with two spin values to restrictions on the collective modes of an ensemble of ``spin up'' ``spin down'' particles. The collective modes, analytic N-body normal modes, are obtained from a group theoretic exact solution of the first-order equations. Cooper pairing is reinterpreted not as the pairing of two fermions with total zero momentum, but as the convergence of the momentum of the entire ensemble to two values, +k and -k, as the particles in the normal mode move back and forth with a single frequency and phase. The Fermi sea and Pauli blocking, commonly described using independent fermions that occupy lower states to create a ``sea'' in energy space and block occupation is redescribed as a collective energy phenomena of the entire ensemble. Superfluidity, which has always been viewed as a collective phenomena as Cooper pairs are assumed to condense into a macroscopic occupation of a single lowest state, is now reimagined without two-body pairing in real space, but as a macroscopic occupation of a low-energy phonon normal mode resulting in the convergence of the momentum to two equal and opposite values. The expected properties of superfluidity including the rigidity of the wave function, interactions between fermions in different pairs, convergence of the momentum and the gap in the excitation spectrum are discussed.