Consider two identical atoms in a spherical harmonic oscillator interacting with a zero-range interaction which is tuned to produce an s-wave zero-energy bound state. The quantum spectrum of the system is known to be exactly solvable. We note that the same partial wave quantum spectrum is obtained by the one-dimensional scale-invariant inverse square potential. Long known as the Calogero–Sutherland–Moser (CSM) model, it leads to the fractional exclusion statistics (FES) of Haldane and Wu. The statistical parameter is deduced from the analytically calculated second virial coefficient. When FES is applied to a Fermi gas at unitarity, it gives good agreement with experimental data without the use of any free parameter.Consider two identical atoms in a spherical harmonic oscillator interacting with a zero-range interaction which is tuned to produce an s-wave zero-energy bound state. The quantum spectrum of the system is known to be exactly solvable. We note that the same partial wave quantum spectrum is obtained by the one-dimensional scale-invariant inverse square potential. Long known as the Calogero–Sutherland–Moser (CSM) model, it leads to the fractional exclusion statistics (FES) of Haldane and Wu. The statistical parameter is deduced from the analytically calculated second virial coefficient. When FES is applied to a Fermi gas at unitarity, it gives good agreement with experimental data without the use of any free parameter.

arXiv:0910.4878Journal of Physics B Atomic Molecular and Optical PhysicsNov 23, 20096 citations

A Note on Statistical Interactions and the Thermodynamic Bethe Ansatz

Denis Bernard, Yong-Shi Wu

We show that the thermodynamic Bethe ansatz equations for one-dimensional integrable many-body systems can be reinterpreted in such a way that they only code the statistical interactions, in the sense of Haldane, between particles of identical or different momenta. Thus, the thermodynamic properties of these systems can be characterized by the generalized ideal gases recently proposed by one of us. For example, the Yang-Yang $δ$ -function gas is a gas with specific statistical interactions between particles of different momenta, while the Calogero-Sutherland system provides a model for an ideal gas of particles with a fractional statistics.We show that the thermodynamic Bethe ansatz equations for one-dimensional integrable many-body systems can be reinterpreted in such a way that they only code the statistical interactions, in the sense of Haldane, between particles of identical or different momenta. Thus, the thermodynamic properties of these systems can be characterized by the generalized ideal gases recently proposed by one of us. For example, the Yang-Yang $δ$-function gas is a gas with specific statistical interactions between particles of different momenta, while the Calogero-Sutherland system provides a model for an ideal gas of particles with a fractional statistics.

arXiv:cond-mat/9404025Apr 12, 199415 citations

Observation of fractional statistics

V. J. Goldman, Fernando Camino, Wenjing Zhou

Bulletin of the American Physical SocietyMar 24, 20051 citation

Fractional Statistics in One-Dimension

Zachary N. C. Ha

APSMar 1, 19972 citations

Effects of non-Abelian statistics on two-terminal shot noise in a quantum Hall liquid in the Pfaffian state

Cristina Bena B, Chetan Nayak

We study nonequilibrium noise in the tunneling current between the edges of a quantum Hall liquid in the Pfaffian state, which is a strong candidate for the plateau at $\ensuremath{\nu}=5∕2$. To first nonvanishing order in perturbation theory (in the tunneling amplitude) we find that one can extract the value of the fractional charge of the tunneling quasiparticles. We note, however, that no direct information about non-Abelian statistics can be retrieved at this level. If we go to higher order in the perturbative calculation of the nonequilibrium shot noise, we find effects due to non-Abelian statistics. They are subtle, but eventually may have an experimental signature on the frequency-dependent shot noise. We suggest how multiterminal noise measurements might yield a more dramatic signature of non-Abelian statistics and develop some of the relevant formalism.We study nonequilibrium noise in the tunneling current between the edges of a quantum Hall liquid in the Pfaffian state, which is a strong candidate for the plateau at $\ensuremath{\nu}=5∕2$. To first nonvanishing order in perturbation theory (in the tunneling amplitude) we find that one can extract the value of the fractional charge of the tunneling quasiparticles. We note, however, that no direct information about non-Abelian statistics can be retrieved at this level. If we go to higher order in the perturbative calculation of the nonequilibrium shot noise, we find effects due to non-Abelian statistics. They are subtle, but eventually may have an experimental signature on the frequency-dependent shot noise. We suggest how multiterminal noise measurements might yield a more dramatic signature of non-Abelian statistics and develop some of the relevant formalism.

arXiv:cond-mat/0510394Physical Review BApr 27, 200635 citations

δ

-function gas is a gas with specific statistical interactions between particles of different momenta, while the Calogero-Sutherland system provides a model for an ideal gas of particles with a fractional statistics.