27,822 research outputs found
Activation gaps for the fractional quantum Hall effect: realistic treatment of transverse thickness
The activation gaps for fractional quantum Hall states at filling fractions
are computed for heterojunction, square quantum well, as well as
parabolic quantum well geometries, using an interaction potential calculated
from a self-consistent electronic structure calculation in the local density
approximation. The finite thickness is estimated to make 30% correction
to the gap in the heterojunction geometry for typical parameters, which
accounts for roughly half of the discrepancy between the experiment and
theoretical gaps computed for a pure two dimensional system. Certain model
interactions are also considered. It is found that the activation energies
behave qualitatively differently depending on whether the interaction is of
longer or shorter range than the Coulomb interaction; there are indications
that fractional Hall states close to the Fermi sea are destabilized for the
latter.Comment: 32 pages, 13 figure
Band Structure of the Fractional Quantum Hall Effect
The eigenstates of interacting electrons in the fractional quantum Hall phase
typically form fairly well defined bands in the energy space. We show that the
composite fermion theory gives insight into the origin of these bands and
provides an accurate and complete microscopic description of the strongly
correlated many-body states in the low-energy bands. Thus, somewhat like in
Landau's fermi liquid theory, there is a one-to-one correspondence between the
low energy Hilbert space of strongly interacting electrons in the fractinal
quantum Hall regime and that of weakly interacting electrons in the integer
quantum Hall regime.Comment: 10 page
Persistence and the Random Bond Ising Model in Two Dimensions
We study the zero-temperature persistence phenomenon in the random bond Ising model on a square lattice via extensive numerical simulations. We find
strong evidence for ` blocking\rq regardless of the amount disorder present in
the system. The fraction of spins which {\it never} flips displays interesting
non-monotonic, double-humped behaviour as the concentration of ferromagnetic
bonds is varied from zero to one. The peak is identified with the onset of
the zero-temperature spin glass transition in the model. The residual
persistence is found to decay algebraically and the persistence exponent
over the range . Our results are
completely consistent with the result of Gandolfi, Newman and Stein for
infinite systems that this model has ` mixed\rq behaviour, namely positive
fractions of spins that flip finitely and infinitely often, respectively.
[Gandolfi, Newman and Stein, Commun. Math. Phys. {\bf 214} 373, (2000).]Comment: 9 pages, 5 figure
Persistence in a Random Bond Ising Model of Socio-Econo Dynamics
We study the persistence phenomenon in a socio-econo dynamics model using
computer simulations at a finite temperature on hypercubic lattices in
dimensions up to 5. The model includes a ` social\rq local field which contains
the magnetization at time . The nearest neighbour quenched interactions are
drawn from a binary distribution which is a function of the bond concentration,
. The decay of the persistence probability in the model depends on both the
spatial dimension and . We find no evidence of ` blocking\rq in this model.
We also discuss the implications of our results for possible applications in
the social and economic fields. It is suggested that the absence, or otherwise,
of blocking could be used as a criterion to decide on the validity of a given
model in different scenarios.Comment: 11 pages, 4 figure
Composite fermion theory of rapidly rotating two-dimensional bosons
Ultracold neutral bosons in a rapidly rotating atomic trap have been
predicted to exhibit fractional quantum Hall-like states. We describe how the
composite fermion theory, used in the description of the fractional quantum
Hall effect for electrons, can be applied to interacting bosons. Numerical
evidence supporting the formation of composite fermions, each being the bound
state of a boson and one flux quantum, is shown for filling fractions of the
type nu=p/(p+1), both by spectral analysis and by direct comparison with trial
wave functions. The rapidly rotating system of two-dimensional bosons thus
constitutes an interesting example of "statistical transmutation," with bosons
behaving like composite fermions. We also describe the difference between the
electronic and the bosonic cases when p approaches infinity. Residual
interactions between composite fermions are attractive in this limit, resulting
in a paired composite-fermion state described by the Moore-Read wave function.Comment: 12 pages, 9 figures. Conference proceeding. BEC 2005 Ital
Electron-impact rotational and hyperfine excitation of HCN, HNC, DCN and DNC
Rotational excitation of isotopologues of HCN and HNC by thermal
electron-impact is studied using the molecular {\bf R}-matrix method combined
with the adiabatic-nuclei-rotation (ANR) approximation. Rate coefficients are
obtained for electron temperatures in the range 56000 K and for transitions
among all levels up to J=8. Hyperfine rates are also derived using the
infinite-order-sudden (IOS) scaling method. It is shown that the dominant
rotational transitions are dipole allowed, that is those for which . The hyperfine propensity rule is found to be stronger
than in the case of HeHCN collisions. For dipole allowed transitions,
electron-impact rates are shown to exceed those for excitation of HCN by He
atoms by 6 orders of magnitude. As a result, the present rates should be
included in any detailed population model of isotopologues of HCN and HNC in
sources where the electron fraction is larger than 10, for example in
interstellar shocks and comets.Comment: 12 pages, 4 figures, accepted in MNRAS (2007 september 3
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