35,128 research outputs found
Luttinger theorem for the strongly correlated Fermi liquid of composite fermions
While an ordinary Fermi sea is perturbatively robust to interactions, the
paradigmatic composite-fermion (CF) Fermi sea arises as a non-perturbative
consequence of emergent gauge fields in a system where there was no Fermi sea
to begin with. A mean-field picture suggests two Fermi seas, of composite
fermions made from electrons or holes in the lowest Landau level, which occupy
different areas away from half filling and thus appear to represent distinct
states. We show that in the microscopic theory of composite fermions, which
satisfies particle-hole symmetry in the lowest Landau level to an excellent
degree, the Fermi wave vectors at filling factors and are the
same, and are generally consistent with the experimental findings of Kamburov
{\em et al.} [Phys. Rev. Lett. {\bf 113}, 196801 (2014)]. Our calculations
suggest that the area of the CF Fermi sea may slightly violate the Luttinger
area rule.Comment: 21 pages, 17 figures including supplemental material, published
versio
Adaptation dynamics of the quasispecies model
We study the adaptation dynamics of an initially maladapted population
evolving via the elementary processes of mutation and selection. The evolution
occurs on rugged fitness landscapes which are defined on the multi-dimensional
genotypic space and have many local peaks separated by low fitness valleys. We
mainly focus on the Eigen's model that describes the deterministic dynamics of
an infinite number of self-replicating molecules. In the stationary state, for
small mutation rates such a population forms a {\it quasispecies} which
consists of the fittest genotype and its closely related mutants. The
quasispecies dynamics on rugged fitness landscape follow a punctuated (or
step-like) pattern in which a population jumps from a low fitness peak to a
higher one, stays there for a considerable time before shifting the peak again
and eventually reaches the global maximum of the fitness landscape. We
calculate exactly several properties of this dynamical process within a
simplified version of the quasispecies model.Comment: Proceedings of Statphys conference at IIT Guwahati, to be published
in Praman
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
Number of adaptive steps to a local fitness peak
We consider a population of genotype sequences evolving on a rugged fitness
landscape with many local fitness peaks. The population walks uphill until it
encounters a local fitness maximum. We find that the statistical properties of
the walk length depend on whether the underlying fitness distribution has a
finite mean. If the mean is finite, all the walk length cumulants grow with the
sequence length but approach a constant otherwise. Experimental implications of
our analytical results are also discussed
Fragmentation with a Cut on Thrust: Predictions for B-factories
When high-energy single-hadron production takes place inside an identified
jet, there are important correlations between the fragmentation and phase-space
cuts. For example, when one-hadron yields are measured in on-resonance
B-factory data, a cut on the thrust event shape T is required to remove the
large b-quark contribution. This leads to a dijet final state restriction for
the light-quark fragmentation process. Here we complete our analysis of
unpolarized fragmentation of (light) quarks and gluons to a light hadron h with
energy fraction z in e+ e- -> dijet + h at the center-of-mass energy Q=10.58
GeV. In addition to the next-to-next-to-leading order resummation of logarithms
of 1-T, we include the next-to-leading order (NLO) nonsingular O(1-T)
contribution to the cross section, the resummation of threshold logarithms of
1-z, and the leading nonperturbative contribution to the soft function. Our
results for the correlations between fragmentation and the thrust cut are
presented in a way that can be directly tested against B-factory data. These
correlations are also observed in Pythia, but are surprisingly smaller at NLO.Comment: 10 pages + appendices, 13 figures, v2:updated discussion, journal
versio
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