1,974 research outputs found
Universal behaviour of ideal and interacting quantum gases in two dimensions
I discuss ideal and interacting quantum gases obeying general fractional
exclusion statistics. For systems with constant density of single-particle
states, described in the mean field approximation, the entropy depends neither
on the microscopic exclusion statistics, nor on the interaction. Such systems
are called {\em thermodynamically equivalent} and I show that the microscopic
reason for this equivalence is a one-to-one correspondence between the excited
states of these systems. This provides a method, different from the
bosonisation technique, to transform between systems of different exclusion
statistics. In the last section the macroscopic aspects of this method are
discussed.
In Appendix A I calculate the fluctuation of the ground state population of a
condensed Bose gas in grandcanonical ensemble and mean field approximation,
while in Appendix B I show a situation where although the system exhibits
fractional exclusion properties on microscopic energy intervals, a rigorous
calculation of the population of single particle states reveals a condensation
phenomenon. This also implies a malfunction of the usual and simplified
calculation technique of the most probable statistical distributions.Comment: About 14 journal pages, with 1 figure. Changes: Body of paper: same
content, with slight rephrasing. Apendices are new. In the original
submission I just mentioned the condensation, which is now detailed in
Appendix B. They were intended for a separate paper. Reason for changes:
rejection from Phys. Rev. Lett., resubmission to J. Phys. A: Math. Ge
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
Analytical theory for proton correlations in common water ice
We provide a fully analytical microscopic theory for the proton correlations
in water ice . We compute the full diffuse elastic neutron scattering
structure factor, which we find to be in excellent quantitative agreement with
Monte Carlo simulations. It is also in remarkable qualitative agreement with
experiment, in the absence of any fitting parameters. Our theory thus provides
a tractable analytical starting point to account for more delicate features of
the proton correlations in water ice. In addition, it directly determines an
effective field theory of water ice as a topological phase.Comment: 5 pages, 3 figure
Relativistic Nuclear Energy Density Functionals: adjusting parameters to binding energies
We study a particular class of relativistic nuclear energy density
functionals in which only nucleon degrees of freedom are explicitly used in the
construction of effective interaction terms. Short-distance (high-momentum)
correlations, as well as intermediate and long-range dynamics, are encoded in
the medium (nucleon density) dependence of the strength functionals of an
effective interaction Lagrangian. Guided by the density dependence of
microscopic nucleon self-energies in nuclear matter, a phenomenological ansatz
for the density-dependent coupling functionals is accurately determined in
self-consistent mean-field calculations of binding energies of a large set of
axially deformed nuclei. The relationship between the nuclear matter volume,
surface and symmetry energies, and the corresponding predictions for nuclear
masses is analyzed in detail. The resulting best-fit parametrization of the
nuclear energy density functional is further tested in calculations of
properties of spherical and deformed medium-heavy and heavy nuclei, including
binding energies, charge radii, deformation parameters, neutron skin thickness,
and excitation energies of giant multipole resonances.Comment: 53 pages, 23 figures, accepted for publication in Physical Review
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
On the isospin dependence of the mean spin-orbit field in nuclei
By the use of the latest experimental data on the spectra of Sb and
Sn and on the analysis of properties of other odd nuclei adjacent to
doubly magic closed shells the isospin dependence of a mean spin-orbit
potential is defined. Such a dependence received the explanation in the
framework of different theoretical approaches.Comment: 52 pages, Revtex, no figure
Exclusion Statistics in a two-dimensional trapped Bose gas
We briefly explain the notion of exclusion statistics and in particular
discuss the concept of an ideal exclusion statistics gas. We then review a
recent work where it is demonstrated that a {\em two-dimensional} Bose gas with
repulsive delta function interactions obeys ideal exclusion statistics, with a
fractional parameter related to the interaction strength.Comment: 10 pages, RevTeX. Proceedings of the Salerno workshop "Theory of
Quantum Gases and Quantum Coherence", to appear in a special issue of J.Phys.
B, Dec. 200
Exclusion statistics for fractional quantum Hall states on a sphere
We discuss exclusion statistics parameters for quasiholes and quasielectrons
excited above the fractional quantum Hall states near . We
derive the diagonal statistics parameters from the (``unprojected'') composite
fermion (CF) picture. We propose values for the off-diagonal (mutual)
statistics parameters as a simple modification of those obtained from the
unprojected CF picture, by analyzing finite system numerical spectra in the
spherical geometry.Comment: 9 pages, Revtex, 4 Postscript figures. Universality of the statistics
parameters is stressed, 2 figs adde
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
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
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