Reconstruction of Quantum Particle Statistics: Bosons, Fermions, and Transtatistics

Autor: Nicolás Medina Sánchez, Borivoje Dakić
Jazyk: angličtina
Rok vydání: 2024
Předmět:
Zdroj: Quantum, Vol 8, p 1473 (2024)
Druh dokumentu: article
ISSN: 2521-327X
DOI: 10.22331/q-2024-09-12-1473
Popis: Identical quantum particles exhibit only two types of statistics: bosonic and fermionic. Theoretically, this restriction is commonly established through the symmetrization postulate or (anti)commutation constraints imposed on the algebra of creation and annihilation operators. The physical motivation for these axioms remains poorly understood, leading to various generalizations by modifying the mathematical formalism in somewhat arbitrary ways. In this work, we take an opposing route and classify quantum particle statistics based on operationally well-motivated assumptions. Specifically, we consider that a) the standard (complex) unitary dynamics defines the set of single-particle transformations, and b) phase transformations act locally in the space of multi-particle systems. We develop a complete characterization, which includes bosons and fermions as basic statistics with minimal symmetry. Interestingly, we have discovered whole families of novel statistics (dubbed transtatistics) accompanied by hidden symmetries, generic degeneracy of ground states, and spontaneous symmetry breaking – effects that are (typically) absent in ordinary statistics.
Databáze: Directory of Open Access Journals