Generalized Particle Statistics| Generalized Particle Statistics |
In General
> s.a. cosmological constant; fock space;
information; particle statistics.
* Idea: Statistics is usually
dictated by representations of the permutation group; However, examples of
non-permutation group statistics are known from anyons in 2D and from
\(\mathbb Z\)n, cyclic statistics
for a certain non-gravitational system.
@ General references: Fivel PRL(90);
Chen et al MPLA(96);
Medvedev PRL(97) [ambiguous statistics];
Greenberg qp/99;
Polychronakos ht/99-ln [1D];
Greenberg in(00)ht [rev];
Marcinek m.QA/01 [Fock space];
Marcinek in(03)m.QA/04 [categorical approach];
Greenberg in(09)-a0804 [rev];
Swain IJMPD(08)-a0805 [quantum-gravity effects];
Arzano & Benedetti IJMPA(09)-a0809
[momentum-dependent "rainbow statistics" in non-commutative field theory];
Cattani & Bassalo a0903;
Lavagno & Narayana Swami PhyA(10) [and deformed algebras];
Dahlsten et al a1307 [in generalized quantum theory];
Goyal a1309 [no generalized statistics];
Neori a1603-PhD [anyons and the symmetrization postulate];
Wang et al AP(19)-a1901 [and spacetime topology].
@ Examples:
Greenberg PRL(90) [infinite statistics];
Balachandran et al MPLA(01)ht/00 [geons in 2+1 Chern-Simons theory];
Surya JMP(04)ht/03 [cyclic statistics];
Baez et al ATMP(07)gq/06 [loop defects in BF theory];
Salvitti CMP(07) [2D massive Dirac fields];
Niven & Grendar PLA(09);
Maslov TMP(09) [generalied Bose-Einstein distribution];
Bagarello RPMP(11)-a1106,
JMP(13)-a1309 [pseudo-bosons];
Matthews et al SRep(13)-a1106 [simulations with entangled photons];
Lundholm & Solovej AHP(14)-a1301 [intermediate and fractional statistics, Lieb-Thirring inequalities];
Palev a1412-proc [A-, B-, C- and D- (super)statistics];
Hoyuelos JSM(18)-a1802 [general statistics, ewkons];
Ramakrishna a2005 [interpolating algebra]; > s.a. non-commutative geometry.
@ Fermions: Niemi & Semenoff PLB(84),
PRP(86) [fractional fermion number];
Arik & Tekin JPA(02);
Narayana Swami qp/05,
Conroy et al PLA(10) [q-deformed];
Treumann a1305 [fermionic fractional statistics].
@ Phenomenology: Marinho & Brito a1907
[q-deformed statistics and thermoelectric properties of solids].
Fractional Statistics in 2+1 Dimensions
> s.a. Anyons [including 3D]; chern-simons field theories;
photons; supersymmetric theories.
* Idea: Objects with intermediate
statistics, arising in some 2D systems, because particle world-lines may braid;
Wave functions may change by any real phase under particle exchange; They
belong to a 1D representation of the braid group.
* Features: Fractional
statistics can be exchanged for extra charges/fluxes in 2D; They imply
P and T violation; They do not violate the spin-statistics
theorem, because in 2D spin is not quantized.
* Quons: Elementary excitations
of fields with intermediate statistics, particles characterized by a parameter
q which permits smooth interpolation between Bose and Fermi statistics;
q = 1 gives bosons, q = −1 gives fermions.
* Simplest type: Semion (the phase
changes by π/2; ground state probably superfluid – superconducting if charged).
* History: Proposed by F Wilczek in 1982;
Applications in the fractal quantum Hall effect, high-\(T_{\rm c}\) superconductivity,
and edge conduction modes of 2D insulators.
@ I: Khurana PT(89)nov;
Canright & Girvin Sci(90)mar;
Wilczek PW(91)jan, SA(91)may.
@ General references: Leinaas & Myrheim NCB(77);
Sorkin PRD(83);
Wu PRL(84);
Wu PRL(84) [many-body wave functions];
Haldane & Wu PRL(85) [for vortices in 2D superfluids];
Goldin in(87);
Mackenzie & Wilczek IJMPA(88);
Semenoff PRL(88);
Lavenda & Dunning-Davies JMP(89);
Wetterich NPB(89);
Imbo et al PLB(90);
Aneziris et al IJMPA(91) [1D];
Haldane PRL(91);
Hessling & Tscheuschner IJTP(91);
Forte RMP(92);
Gamboa IJMPA(92);
Canright & Johnson JPA(94);
Goldin & Sharp PRL(96);
Tang & Finkelstein ht/96/PRD;
Delves et al PRS(97);
Hagen PLB(99)ht [Pauli term];
Khare 05 [text];
Negro et al JMP(06)mp/05 [formalism];
Lima & Landim EPL(06)ht [fractional spin];
Wilczek in(09)-a0812 [rev];
Fitzpatrick et al a1205;
Vleeshouwers & Gritsev a2012 [topological field theory approach].
@ Quons:
Goodison & Toms PLA(94) [canonical partition function];
Greenberg & Hilborn FP(99)ht/98;
Chow & Greenberg PLA(01)ht/00 [in relativistic quantum theory];
Jackson & Hogan IJMPD(08)-ht/07 [and the cosmological constant].
@ Models, phenomenology:
Fendley & Fradkin PRB(05)cm [non-Abelian statistics];
Bishara et al PRB(09)
+ Moore Phy(09);
Shtengel Phy(10);
Bonderson et al PRB(11)
+ Wilczek Phy(11) [Hall effect];
Klinovaja & Loss PRL(13)-a1301;
Levin PRX(13) [edge conduction modes in 2D insulators].
@ Related topics:
Müller ZPC(90) [2D, lattice];
Acharya & Narayana Swami JPA(94) [statistical mechanics],
JPA(04) [and detailed balance];
Isakov et al PLA(96) [thermodynamics];
Ramanathan PS(99) [Laughlin liquids];
Pachos AP(07) [lattice];
Sree Ranjani et al AP(09)-a0812 [in 1D three-particle Calogero model];
Freedman & Levaillant a1501 [measuring topological charge];
> s.a. carbon [graphene];
quantum computation [topological];
quantum oscillators.
Parastatistics, Paraparticles > s.a. Bosons [bosonization];
path integrals.
* Idea: They can arise only
if 3 or more particles are present (but in generally covariant theories, new
possibilities arise even with only two particles); They correspond to higher
than 1D representations of the permutation group.
* Para-Fermi: At most
p particles (p ∈ \(\mathbb N\)) may occupy a
quantum state, antisymmetric; The ordinary case is p = 1.
* Para-Bose: Similar
to para-Fermi, but different symmetry under interchange.
@ General references:
Green PR(53) [proposal];
Ohnuki & Kamefuchi 82 [and quantum field theory];
Meljanac et al MPLA(98) [as triple operator algebras];
Stoilova & Van der Jeugt JMP(05),
JMP(05)mp [and Lie (super)algebras];
Maslov TMP(07);
Nelson a1912;
Stoilova & Van der Jeugt PLA(20)-a2005 [statistical mechanics, thermodynamics].
@ Examples: Greenberg PRL(64) [quarks];
Ringwood & Woodward PRL(84) [monopoles];
Cobanera & Ortíz PRA(14)-a1307 [Fock parafermions].
@ Parafermions: Campoamor-Stursberg & Rausch de Traubenberg
AIP(10)-a0910 [and ternary superspaces];
Dovgard & Gepner PLB(10) [non-abelian].
@ Related topics: Aneziris et al IJMPA(89),
MPLA(89) [and general covariance];
Govorkov TMP(94) [non-existence];
Tamura & Ito JMP(07) [and random point fields];
Tichy & Mølmer PRA(17)-a1702 [immanons].
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