8,670 research outputs found
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
Superconducting properties of very high quality NbN thin films grown by high temperature chemical vapor deposition
Niobium nitride (NbN) is widely used in high-frequency superconducting
electronics circuits because it has one of the highest superconducting
transition temperatures ( 16.5 K) and largest gap among
conventional superconductors. In its thin-film form, the of NbN is very
sensitive to growth conditions and it still remains a challenge to grow NbN
thin film (below 50 nm) with high . Here, we report on the superconducting
properties of NbN thin films grown by high-temperature chemical vapor
deposition (HTCVD). Transport measurements reveal significantly lower disorder
than previously reported, characterized by a Ioffe-Regel ()
parameter of 14. Accordingly we observe 17.06 K (point of
50% of normal state resistance), the highest value reported so far for films of
thickness below 50 nm, indicating that HTCVD could be particularly useful for
growing high quality NbN thin films
Implementing the one-dimensional quantum (Hadamard) walk using a Bose-Einstein Condensate
We propose a scheme to implement the simplest and best-studied version of
quantum random walk, the discrete Hadamard walk, in one dimension using
coherent macroscopic sample of ultracold atoms, Bose-Einstein condensate (BEC).
Implementation of quantum walk using BEC gives access to the familiar quantum
phenomena on a macroscopic scale. This paper uses rf pulse to implement
Hadamard operation (rotation) and stimulated Raman transition technique as
unitary shift operator. The scheme suggests implementation of Hadamard
operation and unitary shift operator while the BEC is trapped in long Rayleigh
range optical dipole trap. The Hadamard rotation and a unitary shift operator
on BEC prepared in one of the internal state followed by a bit flip operation,
implements one step of the Hadamard walk. To realize a sizable number of steps,
the process is iterated without resorting to intermediate measurement. With
current dipole trap technology it should be possible to implement enough steps
to experimentally highlight the discrete quantum random walk using a BEC
leading to further exploration of quantum random walks and its applications.Comment: 7 pages, 3 figure
Multi-Channel Atomic Scattering and Confinement-Induced Resonances in Waveguides
We develop a grid method for multi-channel scattering of atoms in a waveguide
with harmonic confinement. This approach is employed to extensively analyze the
transverse excitations and deexcitations as well as resonant scattering
processes. Collisions of identical bosonic and fermionic as well as
distinguishable atoms in harmonic traps with a single frequency
permitting the center-of-mass (c.m.) separation are explored in depth. In the
zero-energy limit and single mode regime we reproduce the well-known
confinement-induced resonances (CIRs) for bosonic, fermionic and heteronuclear
collisions. In case of the multi-mode regime up to four open transverse
channels are considered. Previously obtained analytical results are extended
significantly here. Series of Feshbach resonances in the transmission behaviour
are identified and analyzed. The behaviour of the transmission with varying
energy and scattering lengths is discussed in detail. The dual CIR leading to a
complete quantum suppression of atomic scattering is revealed in multi-channel
scattering processes. Possible applications include, e.g., cold and ultracold
atom-atom collisions in atomic waveguides and electron-impurity scattering in
quantum wires.Comment: 35 pages, 18 figure
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