9,331 research outputs found
Improved bounds on the number of ternary square-free words
Improved upper and lower bounds on the number of square-free ternary words
are obtained. The upper bound is based on the enumeration of square-free
ternary words up to length 110. The lower bound is derived by constructing
generalised Brinkhuis triples. The problem of finding such triples can
essentially be reduced to a combinatorial problem, which can efficiently be
treated by computer. In particular, it is shown that the number of square-free
ternary words of length n grows at least as 65^(n/40), replacing the previous
best lower bound of 2^(n/17).Comment: 17 pages, AMS LaTeX. Paper has been completely rewritten and
comprises new results on both lower and upper bounds. The Mathematica program
mentioned in the article can be downloaded at
http://mcs.open.ac.uk/ugg2/wordcomb/brinkhuistriples.
N=2 central charge superspace and a minimal supergravity multiplet
We extend the notion of central charge superspace to the case of local
supersymmetry. Gauged central charge transformations are identified as
diffeomorphisms at the same footing as space-time diffeomorphisms and local
supersymmetry transformations. Given the general structure we then proceed to
the description of a particular vector-tensor supergravity multiplet of 24+24
components, identified by means of rather radical constraints
Probing Phases and Quantum Criticality using Deviations from the Local Fluctuation-Dissipation Theorem
Introduction Cold atomic gases in optical lattices are emerging as excellent
laboratories for testing models of strongly interacting particles in condensed
matter physics. Currently, one of the major open questions is how to obtain the
finite temperature phase diagram of a given quantum Hamiltonian directly from
experiments. Previous work in this direction required quantum Monte Carlo
simulations to directly model the experimental situation in order to extract
quantitative information, clearly defeating the purpose of an optical lattice
emulator. Here we propose a new method that utilizes deviations from a local
fluctuation dissipation theorem to construct a finite temperature phase
diagram, for the first time, from local observables accessible by in situ
experimental observations. Our approach extends the utility of the
fluctuation-dissipation theorem from thermometry to the identification of
quantum phases, associated energy scales and the quantum critical region. We
test our ideas using state-of-the-art large-scale quantum Monte Carlo
simulations of the two-dimensional Bose Hubbard model.Comment: 7 pages; 4 figures; also see supplementary material of 7 pages with 3
figure
Spectral weight redistribution in strongly correlated bosons in optical lattices
We calculate the single-particle spectral function for the one-band
Bose-Hubbard model within the random phase approximation (RPA). In the strongly
correlated superfluid, in addition to the gapless phonon excitations, we find
extra gapped modes which become particularly relevant near the superfluid-Mott
quantum phase transition (QPT). The strength in one of the gapped modes, a
precursor of the Mott phase, grows as the QPT is approached and evolves into a
hole (particle) excitation in the Mott insulator depending on whether the
chemical potential is above (below) the tip of the lobe. The sound velocity of
the Goldstone modes remains finite when the transition is approached at a
constant density, otherwise, it vanishes at the transition. It agrees well with
Bogoliubov theory except close to the transition. We also calculate the spatial
correlations for bosons in an inhomogeneous trapping potential creating
alternating shells of Mott insulator and superfluid. Finally, we discuss the
capability of the RPA approximation to correctly account for quantum
fluctuations in the vicinity of the QPT.Comment: 14 pages, 12 figure
Tomographic RF Spectroscopy of a Trapped Fermi Gas at Unitarity
We present spatially resolved radio-frequency spectroscopy of a trapped Fermi
gas with resonant interactions and observe a spectral gap at low temperatures.
The spatial distribution of the spectral response of the trapped gas is
obtained using in situ phase-contrast imaging and 3D image reconstruction. At
the lowest temperature, the homogeneous rf spectrum shows an asymmetric
excitation line shape with a peak at 0.48(4) with respect to the
free atomic line, where is the local Fermi energy
Non-universal behavior for aperiodic interactions within a mean-field approximation
We study the spin-1/2 Ising model on a Bethe lattice in the mean-field limit,
with the interaction constants following two deterministic aperiodic sequences:
Fibonacci or period-doubling ones. New algorithms of sequence generation were
implemented, which were fundamental in obtaining long sequences and, therefore,
precise results. We calculate the exact critical temperature for both
sequences, as well as the critical exponent , and . For
the Fibonacci sequence, the exponents are classical, while for the
period-doubling one they depend on the ratio between the two exchange
constants. The usual relations between critical exponents are satisfied, within
error bars, for the period-doubling sequence. Therefore, we show that
mean-field-like procedures may lead to nonclassical critical exponents.Comment: 6 pages, 7 figures, to be published in Phys. Rev.
Four types of special functions of G_2 and their discretization
Properties of four infinite families of special functions of two real
variables, based on the compact simple Lie group G2, are compared and
described. Two of the four families (called here C- and S-functions) are well
known, whereas the other two (S^L- and S^S-functions) are not found elsewhere
in the literature. It is shown explicitly that all four families have similar
properties. In particular, they are orthogonal when integrated over a finite
region F of the Euclidean space, and they are discretely orthogonal when their
values, sampled at the lattice points F_M \subset F, are added up with a weight
function appropriate for each family. Products of ten types among the four
families of functions, namely CC, CS, SS, SS^L, CS^S, SS^L, SS^S, S^SS^S,
S^LS^S and S^LS^L, are completely decomposable into the finite sum of the
functions. Uncommon arithmetic properties of the functions are pointed out and
questions about numerous other properties are brought forward.Comment: 18 pages, 4 figures, 4 table
Dilute Birman--Wenzl--Murakami Algebra and models
A ``dilute'' generalisation of the Birman--Wenzl--Murakami algebra is
considered. It can be ``Baxterised'' to a solution of the Yang--Baxter algebra.
The vertex models are examples of corresponding solvable
lattice models and can be regarded as the dilute version of the
vertex models.Comment: 11 page
Fluxes and Warping for Gauge Couplings in F-theory
We compute flux-dependent corrections in the four-dimensional F-theory
effective action using the M-theory dual description. In M-theory the 7-brane
fluxes are encoded by four-form flux and modify the background geometry and
Kaluza-Klein reduction ansatz. In particular, the flux sources a warp factor
which also depends on the torus directions of the compactification fourfold.
This dependence is crucial in the derivation of the four-dimensional action,
although the torus fiber is auxiliary in F-theory. In M-theory the 7-branes are
described by an infinite array of Taub-NUT spaces. We use the explicit metric
on this geometry to derive the locally corrected warp factor and M-theory
three-from as closed expressions. We focus on contributions to the 7-brane
gauge coupling function from this M-theory back-reaction and show that terms
quadratic in the internal seven-brane flux are induced. The real part of the
gauge coupling function is modified by the M-theory warp factor while the
imaginary part is corrected due to a modified M-theory three-form potential.
The obtained contributions match the known weak string coupling result, but
also yield additional terms suppressed at weak coupling. This shows that the
completion of the M-theory reduction opens the way to compute various
corrections in a genuine F-theory setting away from the weak string coupling
limit.Comment: 46 page
Non-universality of artificial frustrated spin systems
Magnetic frustration effects in artificial kagome arrays of nanomagnets with
out-of-plane magnetization are investigated using Magnetic Force Microscopy and
Monte Carlo simulations. Experimental and theoretical results are compared to
those found for the artificial kagome spin ice, in which the nanomagnets have
in-plane magnetization. In contrast with what has been recently reported, we
demonstrate that long range (i.e. beyond nearest-neighbors) dipolar
interactions between the nanomagnets cannot be neglected when describing the
magnetic configurations observed after demagnetizing the arrays using a field
protocol. As a consequence, there are clear limits to any universality in the
behavior of these two artificial frustrated spin systems. We provide arguments
to explain why these two systems show striking similarities at first sight in
the development of pairwise spin correlations.Comment: 7 pages, 6 figure
- …