# Local Exclusion and Lieb–Thirring Inequalities for Intermediate and Fractional Statistics

@article{Lundholm2013LocalEA, title={Local Exclusion and Lieb–Thirring Inequalities for Intermediate and Fractional Statistics}, author={Douglas Lundholm and Jan Philip Solovej}, journal={Annales Henri Poincar{\'e}}, year={2013}, volume={15}, pages={1061-1107} }

In one and two spatial dimensions there is a logical possibility for identical quantum particles different from bosons and fermions, obeying intermediate or fractional (anyon) statistics. We consider applications of a recent Lieb–Thirring inequality for anyons in two dimensions, and derive new Lieb–Thirring inequalities for intermediate statistics in one dimension with implications for models of Lieb–Liniger and Calogero–Sutherland type. These inequalities follow from a local form of the…

## 33 Citations

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A local exclusion principle is observed for identical particles obeying intermediate and fractional exchange statistics in one and two dimensions, leading to bounds for the kinetic energy in terms of…

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We construct and study relativistic anyons in $1+1$ dimensions generalizing well-known models of Dirac fermions. First, a model of free anyons is constructed and then extended in two ways: (i) by…

## References

SHOWING 1-10 OF 68 REFERENCES

Local exclusion principle for identical particles obeying intermediate and fractional statistics

- Mathematics
- 2013

A local exclusion principle is observed for identical particles obeying intermediate and fractional exchange statistics in one and two dimensions, leading to bounds for the kinetic energy in terms of…

Hardy and Lieb-Thirring Inequalities for Anyons

- Mathematics
- 2013

We consider the many-particle quantum mechanics of anyons, i.e. identical particles in two space dimensions with a continuous statistics parameter $${\alpha \in [0, 1]}$$α∈[0,1] ranging from bosons…

Anyons and lowest Landau level Anyons

- Physics
- 2007

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…

Thomas-Fermi Method for Particles Obeying Generalized Exclusion Statistics.

- PhysicsPhysical review letters
- 1995

The Thomas-Fermi method is used to examine the thermodynamics of particles obeying Haldane exclusion statistics and obtains the exact one-particle spatial density and a closed form for the equation of state at finite temperature, which are both new results.

STATISTICS IN ONE DIMENSION

- Mathematics
- 1991

We show that there are novel generalizations of statistics for identical particles in one dimension. These arise due to possible boundary conditions on wave functions, or equivalently due to…

Statistics in Space Dimension Two

- Mathematics
- 1997

We construct as a selfadjoint operator the Schrödinger Hamiltonian for a system of N identical particles on a plane, obeying the statistics defined by a representation π1 of the braid group. We use…

Fractional statistics and anyon superconductivity

- Physics
- 1990

The occurrence of fractional statistics has been discovered in more and more quantum field theory models, including some of the most geometrical and canonical ones. In a remarkable case, the…