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

Nicolás Medina Sánchez; Borivoje Dakić

doi:10.22331/q-2024-09-12-1473

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

Nicolás Medina Sánchez^1,2 and Borivoje Dakić^1,3

¹University of Vienna, Faculty of Physics, Vienna Center for Quantum Science and Technology (VCQ), Boltzmanngasse 5, 1090 Vienna, Austria
²University of Vienna, Vienna Doctoral School in Physics, Boltzmanngasse 5, 1090 Vienna, Austria
³Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria.

Published:	2024-09-12, volume 8, page 1473
Eprint:	arXiv:2306.05919v2
Doi:	https://doi.org/10.22331/q-2024-09-12-1473
Citation:	Quantum 8, 1473 (2024).

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Abstract

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.

► BibTeX data

@article{Sanchez2024reconstructionof,
  doi = {10.22331/q-2024-09-12-1473},
  url = {https://doi.org/10.22331/q-2024-09-12-1473},
  title = {Reconstruction of {Q}uantum {P}article {S}tatistics: {B}osons, {F}ermions, and {T}ranstatistics},
  author = {S{\'{a}}nchez, Nicol{\'{a}}s Medina and Daki{\'{c}}, Borivoje},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {8},
  pages = {1473},
  month = sep,
  year = {2024}
}

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