Extending bosons and fermions beyond pairwise exchange symmetry

Abstract

We study quantum many-body states of immanons, hypothetical particles that obey an exchange symmetry defined for more than two participating particles. Immanons thereby generalize bosons and fermions, which are defined by their behavior under pairwise symmetric and anti-symmetric exchange processes. The scalar product of two many-body states with fermionic, bosonic or generalized exchange symmetry becomes the determinant, permanent or immanant of the matrix containing all mutual scalar products of the occupied single-particle states. As a measurable consequence, immanons are shown to obey a partial Pauli principle that forbids the multiple occupation of single-particle states above a certain threshold. The tendency to favor or oppose multiple occupation of single-particle modes, i.e. the degree of bunching, is the determinant, permanent or immanant of a hermitian positive semi-definite matrix. We exploit this identity to devise a Gedankenexperiment that corroborates the permanental dominance conjecture.

11 pages, 4 figures

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• Coincidence landscapes for polarized bosons
• Unified framework for generalized quantum statistics: canonical partition function, maximum occupation number, and permutation phase of wave function
• Boson-fermion complementarity in a linear interferometer: An identity relating the determinant and permanent of a matrix