Reconstruction of Quantum Particle Statistics: Bosons, Fermions, and Transtatistics
arXiv:2306.05919 · doi:10.22331/q-2024-09-12-1473
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.
arXiv commentThe main theorem extended to negative occupation numbers and exceptional statistics found, the paper accepted for publication in Quantum
References in corpus (29)
- Multi-photon entanglement and interferometry
- Matrix Product States and Projected Entangled Pair States: Concepts, Symmetries, and Theorems
- Informational derivation of Quantum Theory
- Quantum Theory From Five Reasonable Axioms
- Fractional Quantum Hall States and Jack Polynomials
- Classical simulation of noninteracting-fermion quantum circuits
- A derivation of quantum theory from physical requirements
- Entanglement in indistinguishable particle systems
- Derivation of the Dirac Equation from Principles of Information Processing
- Quantum theory from questions
- Entanglement between identical particles is a useful and consistent resource
- The Feynman problem and Fermionic entanglement: Fermionic theory versus qubit theory
- Intermediate statistics as a consequence of deformed algebra
- Rainbow statistics
- The parafermion Fock space and explicit so(2n+1) representations
- Asymptotics of Jack polynomials as the number of variables goes to infinity
- Properties of Particles Obeying Ambiguous Statistics
- Pseudo-bosons, so far
- Partition Functions in Statistical Mechanics, Symmetric Functions, and Group Representations
- A relativistic discrete spacetime formulation of 3+1 QED
- Entanglement, Nonlocality, Superluminal Signaling and Cloning
- Quantum statistics of classical particles derived from the condition of free diffusion coefficient
- Persistence and Nonpersistence as Complementary Models of Identical Quantum Particles
- Cyclic Statistics In Three Dimensions
- A Generalization of Quantum Statistics
- Partition functions and thermodynamic properties of paraboson and parafermion systems
- A Novel Spin-Statistics Theorem in (2 + 1)d Chern-Simons Gravity
- Boolean Witt vectors and an integral Edrei-Thoma theorem
- Exotic Statistics for Ordinary Particles in Quantum Gravity