Fractional exclusion statistics and shot noise in ballistic conductors

Gomila, Gabriel; Reggiani, L.

doi:10.1103/physrevb.63.165404

Cited by 5 publications

(7 citation statements)

References 33 publications

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“…On the one hand, Haldane's definition (42) stems from an arbitrary combinatorial point of view, inspired by the Bose and Fermi counting of states. On the other hand, in the LLL-anyon model, ( 39) is obtained from a somehow ad-hoc mean field ansatz.…”

Section: The Lll-anyon Modelmentioning

confidence: 99%

“…The duality relation (72,73) can be interpreted as a particle-hole symmetry relation. Setting t = ze −βωc , one also has a simple expression [42] for dn(t)/dt…”

Section: Lll-anyon Thermodynamicsmentioning

confidence: 99%

“…In the case of Haldane statistics as defined in (42), there is no Hamiltonian and no N -body spectrum to begin with. One rather starts from the Bose counting factor (56) and bluntly replaces, in accordance with (42)…”

Section: Lll-anyon Thermodynamicsmentioning

confidence: 99%

“…Let us mention their relevance in more abstract contexts, such as conformal field theories [48]. On the experimental side, FQHE edge currents can be modelled by quasiparticles with fractional statistics, which in turn might affect their transport properties such as the current shot noise [49,42].…”

Section: Lll-anyon Thermodynamicsmentioning

confidence: 99%

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Anyons and Lowest Landau Level Anyons

Ouvry

2009

The Spin

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Intermediate statistics interpolating from Bose statistics to Fermi statistics are allowed in two dimensions. This is due to the particular topology of the two dimensional configuration space of identical particles, leading to non trivial braiding of particles around each other. One arrives at quantum many-body states with a multivalued phase factor, which encodes the anyonic nature of particle windings. Bosons and fermions appear as two limiting cases. Gauging away the phase leads to the so-called anyon model, where the charge of each particle interacts "à la AharonovBohm" with the fluxes carried by the other particles. The multivaluedness of the wave function has been traded off for topological interactions between ordinary particles. An alternative Lagrangian formulation uses a topological Chern-Simons term in 2+1 dimensions. Taking into account the short distance repulsion between particles leads to an Hamiltonian well defined in perturbation theory, where all perturbative divergences have disappeared. Together with numerical and semi-classical studies, perturbation theory is a basic analytical tool at disposal to study the model, since finding the exact N -body spectrum seems out of reach (except in the 2-body case which is solvable, or for particular classes of N -body eigenstates which generalize some 2-body eigenstates). However, a simplification arises when the anyons are coupled to an external homogeneous magnetic field. In the case of a strong field, by projecting the system on its lowest Landau level (LLL, thus the LLL-anyon model), the anyon model becomes solvable, i.e. the classes of exact eigenstates alluded to above provide for a complete interpolation from the LLL-Bose spectrum to the LLL-Fermi spectrum. Being a solvable model allows for an explicit knowledge of the equation of state and of the mean occupation number in the LLL, which do interpolate from the Bose to the Fermi cases. It also provides for a combinatorial interpretation of LLL-anyon braiding statistics in terms of occupation of single particle states. The LLL-anyon model might also be relevant experimentally: a gas of electrons in a strong magnetic field is known to exhibit a quantized Hall conductance, leading to the integer and fractional quantum Hall effects. Haldane/exclusion statistics, introduced to describe FQHE edge excitations, is a priori different from 1 arXiv:0712.2174v1 [cond-mat.stat-mech] 13 Dec 2007 anyon statistics, since it is not defined by braiding considerations, but rather by counting arguments in the space of available states. However, it has been shown to lead to the same kind of thermodynamics as the LLL-anyon thermodynamics (or, in other words, the LLL-anyon model is a microscopic quantum mechanical realization of Haldane's statistics). The one dimensional Calogero model is also shown to have the same kind of thermodynamics as the LLL-anyons thermodynamics. This is not a coincidence: the LLL-anyon model and the Calogero model are intimately related, the latter being a particular limit of the former...

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Section: The Lll-anyon Modelmentioning

confidence: 99%

“…The duality relation (72,73) can be interpreted as a particle-hole symmetry relation. Setting t = ze −βωc , one also has a simple expression [42] for dn(t)/dt…”

Section: Lll-anyon Thermodynamicsmentioning

confidence: 99%

Section: Lll-anyon Thermodynamicsmentioning

confidence: 99%

Section: Lll-anyon Thermodynamicsmentioning

confidence: 99%

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Anyons and Lowest Landau Level Anyons

Ouvry

2009

The Spin

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“…This result is also different from relaxation rates predicted using Boltzman transport [41][42][43][44] , obtained assuming that the occupations of different energy levels are independent, rather than fully accounting for the constraints. Interestingly, even in the absence of an exact treatment of the constraints, HES systems have been found to exhibit a universal 1D ballistic thermal conductance 45 , though both electrical conductance 45 and shot noise 46 depend on the details of the exclusion statistics.…”

Section: Introductionmentioning

confidence: 99%

Many-body constraints and nonthermal behavior in one-dimensional open systems with Haldane exclusion statistics

Xiong

Burnell

2022

Phys. Rev. B

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We study the impact of the inter-level energy constraints imposed by Haldane Exclusion Statistics on energy relaxation processes in 1-dimensional systems coupled to a bosonic bath. By formulating a second-quantized description of the relevant Fock space, we identify certain universal features of this relaxation dynamics, and show that it is generically slower than that of spinless fermions. Our study focuses on the Calogero-Sutherland model, which realizes Haldane Exclusion statistics exactly in one dimension; however our results apply to any system that has the associated pattern of inter-level occupancy constraints in Fock space.

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Noise properties of ballistic exclusons: dimensionality effects

Gomila

Reggiani

2002

Physica B: Condensed Matter

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Fractional exclusion statistics and shot noise in ballistic conductors

Cited by 5 publications

References 33 publications

Anyons and Lowest Landau Level Anyons

Anyons and Lowest Landau Level Anyons

Many-body constraints and nonthermal behavior in one-dimensional open systems with Haldane exclusion statistics

Noise properties of ballistic exclusons: dimensionality effects

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