37 research outputs found
One-Dimensional Statistical Mechanics for Identical Particles : The Calogero and Anyon Cases
The thermodynamic of particles with intermediate statistics interpolating
between Bose and Fermi statistics is adressed in the simple case where there is
one quantum number per particle. Such systems are essentially one-dimensional.
As an illustration, one considers the anyon model restricted to the lowest
Landau level of a strong magnetic field at low temperature, the generalization
of this model to several particles species, and the one dimensional Calogero
model. One reviews a unified algorithm to compute the statistical mechanics of
these systems. It is pointed out that Haldane's generalization of the Pauli
principle can be deduced from the anyon model in a strong magnetic field at low
temperature.Comment: 17 page
Equation of State of an Anyon Gas in a Strong Magnetic Field
The statistical mechanics of an anyon gas in a magnetic field is addressed.
An harmonic regulator is used to define a proper thermodynamic limit. When the
magnetic field is sufficiently strong, only exact -anyon groundstates, where
anyons occupy the lowest Landau level, contribute to the equation of state.
Particular attention is paid to the interval of definition of the statistical
parameter where a gap exists. Interestingly enough, one finds
that at the critical filling where the pressure diverges, the
external magnetic field is entirely screened by the flux tubes carried by the
anyons.Comment: 14 pages, PACS numbers: 03.65.-w, 05.30.-d, 05.70.Ce, IPNO/TH 93-16
(MAY 1993), e-mail: OUVRY@FRCPN1
ON THERMODYNAMICS OF MULTISPECIES ANYONS
We address the problem of multispecies anyons, i.e. particles of different
species whose wave function is subject to anyonlike conditions. The cluster and
virial coefficients are considered. Special attention is paid to the case of
anyons in the lowest Landau level of a strong magnetic field, when it is
possible (i) to prove microscopically the equation of state,
in particular in terms of Aharonov-Bohm charge-flux composite systems, and
(ii) to formulate the problem in terms of single-state statistical
distributions.Comment: Latex, 19 page
Towards a quantum-mechanical model for multispecies exclusion statistics
It is shown how to construct many-particle quantum-mechanical spectra of
particles obeying multispecies exclusion statistics, both in one and in two
dimensions. These spectra are derived from the generalized exclusion principle
and yield the same thermodynamic quantities as deduced from Haldane's
multiplicity formula.Comment: 12 pages, REVTE
The third virial coefficient of anyons revisited
We use the method of solving the three-anyon problem developed in our earlier
publication to evaluate numerically the third virial coefficient of free
anyons. In order to improve precision, we explicitly correct for truncation
effects. The present calculation is about three orders of magnitude more
precise than the previous Monte Carlo calculation and indicates the presence of
a term with a very small coefficient .Comment: 10 pages, LATEX 2.09, 4 Postscript figures attached; explanations
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The Lowest Landau Level Anyon Equation of State in the Anti-screening Regime
The thermodynamics of the anyon model projected on the lowest Landau level
(LLL) of an external magnetic field is addressed in the anti-screening regime,
where the flux tubes carried by the anyons are parallel to the magnetic field.
It is claimed that the LLL-anyon equation of state, which is known in the
screening regime, can be analytically continued in the statistical parameter
across the Fermi point to the antiscreening regime up to the vicinity (whose
width tends to zero when the magnetic field becomes infinite) of the Bose
point. There, an unphysical discontinuity arises due to the dropping of the
non-LLL eigenstates which join the LLL, making the LLL approximation no longer
valid. However, taking into account the effect of the non-LLL states at the
Bose point would only smoothen the discontinuity and not alter the physics
which is captured by the LLL projection: Close to the Bose point, the critical
filling factor either goes to infinity (usual bosons) in the screening
situation, or to 1/2 in the anti-screening situation, the difference between
the flux tubes orientation being relevant even when they carry an infinitesimal
fraction of the flux quantum. An exclusion statistics interpretation is
adduced, which explains this situation in semiclassical terms. It is further
shown how the exact solutions of the 3-anyon problem support this scenario as
far as the third cluster coefficient is concerned.Comment: 14 pages, 3 figures, LaTex 2
Discrete Thermodynamic Bethe Ansatz
We propose discrete TBA equations for models with discrete spectrum. We
illustrate our construction on the Calogero-Moser model and determine the
discrete 2-body TBA function which yields the exact N-body Calogero-Moser
thermodynamics. We apply this algorithm to the Lieb-Liniger model in a harmonic
well, a model which is relevant for the microscopic description of harmonically
trapped Bose-Einstein condensates in one dimension. We find that the discrete
TBA reproduces correctly the N-body groundstate energy of the Lieb-Liniger
model in a harmonic well at first order in perturbation theory, but corrections
do appear at second order
Virial Coefficients of Multispecies Anyons
A path integral formalism for multispecies anyons is introduced, whereby
partition functions are expressed in terms of generating functions of winding
number probability distributions. In a certain approximation, the equation of
state for exclusion statistics follows. By Monte Carlo simulation, third-order
cluster and virial coefficients are found numerically.Comment: 9 pages, 5 figures, LaTeX 2
Thermodynamics for Fractional Exclusion Statistics
We discuss the thermodynamics of a gas of free particles obeying Haldane's
exclusion statistics, deriving low temperature and low density expansions. For
gases with a constant density of states, we derive an exact equation of state
and find that temperature-dependent quantities are independent of the
statistics parameter.Comment: 9 pages, Revtex, no figures. References correcte
Algebra of Observables for Identical Particles in One Dimension
The algebra of observables for identical particles on a line is formulated
starting from postulated basic commutation relations. A realization of this
algebra in the Calogero model was previously known. New realizations are
presented here in terms of differentiation operators and in terms of
SU(N)-invariant observables of the Hermitian matrix models. Some particular
structure properties of the algebra are briefly discussed.Comment: 13 pages, Latex, uses epsf, 1 eps figure include