15 research outputs found
Model of statistically coupled chiral fields on the circle
Starting from a field theoretical description of multicomponent anyons with
mutual statistical interactions in the lowest Landau level, we construct a
model of interacting chiral fields on the circle, with the energy spectrum
characterized by a symmetric matrix with nonnegative entries.
Being represented in a free form, the model provides a field theoretical
realization of (ideal) fractional exclusion statistics for particles with
linear dispersion, with as a statistics matrix. We derive the
bosonized form of the model and discuss the relation to the effective
low-energy description of the edge excitations for abelian fractional quantum
Hall states in multilayer systems.Comment: 26 pages, Latex, 1 Latex figure included. The figure has been
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
Equation of State for Exclusion Statistics in a Harmonic Well
We consider the equations of state for systems of particles with exclusion
statistics in a harmonic well. Paradygmatic examples are noninteracting
particles obeying ideal fractional exclusion statistics placed in (i) a
harmonic well on a line, and (ii) a harmonic well in the Lowest Landau Level
(LLL) of an exterior magnetic field. We show their identity with (i) the
Calogero model and (ii) anyons in the LLL of an exterior magnetic field and in
a harmonic well.Comment: latex file, 11 page
Quantum liquids of particles with generalized statistics
We propose a phenomenological approach to quantum liquids of particles
obeying generalized statistics of a fermionic type, in the spirit of the Landau
Fermi liquid theory. The approach is developed for fractional exclusion
statistics. We discuss both equilibrium (specific heat, compressibility, and
Pauli spin susceptibility) and nonequilibrium (current and thermal
conductivities, thermopower) properties. Low temperature quantities have the
same temperature dependences as for the Fermi liquid, with the coefficients
depending on the statistics parameter. The novel quantum liquids provide
explicit realization of systems with a non-Fermi liquid Lorentz ratio in two
and more dimensions. Consistency of the theory is verified by deriving the
compressibility and -sum rules.Comment: 14 pages, Revtex, no figures; typos correcte
Algebra of one-particle operators for the Calogero model
An algebra of symmetric {\em one-particle} operators is
constructed for the Calogero model. This is an infinite-dimensional
Lie-algebra, which is independent of the interaction parameter of the
model. It is constructed in terms of symmetric polynomials of raising and
lowering operators which satisfy the commutation relations of the -{\em
extended} Heisenberg algebra. We interpret as the algebra of
observables for a system of identical particles on a line. The parameter
, which characterizes (a class of) irreducible representations of the
algebra, is interpreted as a statistics parameter for the identical particles.Comment: 23 pages, LaTe
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
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
Exclusion statistics: A resolution of the problem of negative weights
We give a formulation of the single particle occupation probabilities for a
system of identical particles obeying fractional exclusion statistics of
Haldane. We first derive a set of constraints using an exactly solvable model
which describes an ideal exclusion statistics system and deduce the general
counting rules for occupancy of states obeyed by these particles. We show that
the problem of negative probabilities may be avoided with these new counting
rules.Comment: REVTEX 3.0, 14 page
Conductance and Shot Noise for Particles with Exclusion Statistics
The first quantized Landauer approach to conductance and noise is generalized
to particles obeying exclusion statistics. We derive an explicit formula for
the crossover between the shot and thermal noise limits and argue that such a
crossover can be used to determine experimentally whether charge carriers in
FQHE devices obey exclusion statistics.Comment: 4 pages, revtex, 1 eps figure include
Bosonic and fermionic single-particle states in the Haldane approach to statistics for identical particles
We give two formulations of exclusion statistics (ES) using a variable number
of bosonic or fermionic single-particle states which depend on the number of
particles in the system. Associated bosonic and fermionic ES parameters are
introduced and are discussed for FQHE quasiparticles, anyons in the lowest
Landau level and for the Calogero-Sutherland model. In the latter case, only
one family of solutions is emphasized to be sufficient to recover ES;
appropriate families are specified for a number of formulations of the
Calogero-Sutherland model. We extend the picture of variable number of
single-particle states to generalized ideal gases with statistical interaction
between particles of different momenta. Integral equations are derived which
determine the momentum distribution for single-particle states and distribution
of particles over the single-particle states in the thermal equilibrium.Comment: 6 pages, REVTE