17 research outputs found
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
Calculation of the Aharonov-Bohm wave function
A calculation of the Aharonov-Bohm wave function is presented. The result is
a series of confluent hypergeometric functions which is finite at the forward
direction.Comment: 12 pages in LaTeX, and 3 PostScript figure
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
Haldane's Fractional Statistics and the Lowest Landau Level on a Torus
The Lowest Landau Level on a torus is studied. The dimension of the many-body
Hilbert space is obtained and is found to be different from the formula given
by Haldane. Our result can be tested in numerical investigations of the
low-energy spectrum of fractional quantum Hall states on a torus.Comment: 4 pages, Revtex. Small modifications. The modified version to appear
in Phys. Rev. Lett., Feb., 199
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
Finite-size anyons and perturbation theory
We address the problem of finite-size anyons, i.e., composites of charges and
finite radius magnetic flux tubes. Making perturbative calculations in this
problem meets certain difficulties reminiscent of those in the problem of
pointlike anyons. We show how to circumvent these difficulties for anyons of
arbitrary spin. The case of spin 1/2 is special because it allows for a direct
application of perturbation theory, while for any other spin, a redefinition of
the wave function is necessary. We apply the perturbative algorithm to the
N-body problem, derive the first-order equation of state and discuss some
examples.Comment: 18 pages (RevTex) + 4 PS figures (all included); a new section on
equation of state adde
On the virial coefficients of nonabelian anyons
We study a system of nonabelian anyons in the lowest Landau level of a strong
magnetic field. Using diagrammatic techniques, we prove that the virial
coefficients do not depend on the statistics parameter. This is true for all
representations of all nonabelian groups for the statistics of the particles
and relies solely on the fact that the effective statistical interaction is a
traceless operator.Comment: 9 pages, 3 eps figure
Thermodynamics of Relativistic Fermions with Chern-Simons Coupling
We study the thermodynamics of the relativistic Quantum Field Theory of
massive fermions in three space-time dimensions coupled to an Abelian
Maxwell-Chern-Simons gauge field. We evaluate the specific heat at finite
temperature and density and find that the variation with the statistical angle
is consistent with the non-relativistic ideas on generalized statistics.Comment: 12 pages, REVTe
Exclusion Statistics in a trapped two-dimensional Bose gas
We study the statistical mechanics of a two-dimensional gas with a repulsive
delta function interaction, using a mean field approximation. By a direct
counting of states we establish that this model obeys exclusion statistics and
is equivalent to an ideal exclusion statistics gas.Comment: 3 pages; minor changes in notation; typos correcte
Quasi-particles in Fractional Quantum Hall Effect Edge Theories
We propose a quasi-particle formulation of effective edge theories for the
fractional quantum Hall effect. For the edge of a Laughlin state with filling
fraction \nu=1/m, our fundamental quasi-particles are edge electrons of charge
-e and edge quasi-holes of charge +e/m. These quasi-particles satisfy exclusion
statistics in the sense of Haldane. We exploit algebraic properties of edge
electrons to derive a kinetic equation for charge transport between a \nu=1/m
fractional quantum Hall edge and a normal metal. We also analyze alternative
`Boltzmann' equations that are directly based on the exclusion statistics
properties of edge quasi-particles. Generalizations to more general filling
fractions (Jain series) are briefly discussed.Comment: 20 pages, 2 eps figures, revtex, references updated, Phys. Rev. B in
pres