26,147 research outputs found
Incommensurability and edge states in the one-dimensional S=1 bilinear-biquadratic model
Commensurate-incommensurate change on the one-dimensional S=1
bilinear-biquadratic model () is examined. The gapped
Haldane phase has two subphases (the commensurate Haldane subphase and the
incommensurate Haldane subphase) and the commensurate-incommensurate change
point (the Affleck-Kennedy-Lieb-Tasaki point, ). There have been
two different analytical predictions about the static structure factor in the
neighborhood of this point. By using the S{\o}rensen-Affleck prescription,
these static structure factors are related to the Green functions, and also to
the energy gap behaviors. Numerical calculations support one of the
predictions. Accordingly, the commensurate-incommensurate change is recognized
as a motion of a pair of poles in the complex plane.Comment: 29 pages, 15 figure
Observation of resonant interactions among surface gravity waves
We experimentally study resonant interactions of oblique surface gravity
waves in a large basin. Our results strongly extend previous experimental
results performed mainly for perpendicular or collinear wave trains. We
generate two oblique waves crossing at an acute angle, while we control their
frequency ratio, steepnesses and directions. These mother waves mutually
interact and give birth to a resonant wave whose properties (growth rate,
resonant response curve and phase locking) are fully characterized. All our
experimental results are found in good quantitative agreement with four-wave
interaction theory with no fitting parameter. Off-resonance experiments are
also reported and the relevant theoretical analysis is conducted and validated.Comment: 11 pages, 7 figure
Meta-Learning by the Baldwin Effect
The scope of the Baldwin effect was recently called into question by two
papers that closely examined the seminal work of Hinton and Nowlan. To this
date there has been no demonstration of its necessity in empirically
challenging tasks. Here we show that the Baldwin effect is capable of evolving
few-shot supervised and reinforcement learning mechanisms, by shaping the
hyperparameters and the initial parameters of deep learning algorithms.
Furthermore it can genetically accommodate strong learning biases on the same
set of problems as a recent machine learning algorithm called MAML "Model
Agnostic Meta-Learning" which uses second-order gradients instead of evolution
to learn a set of reference parameters (initial weights) that can allow rapid
adaptation to tasks sampled from a distribution. Whilst in simple cases MAML is
more data efficient than the Baldwin effect, the Baldwin effect is more general
in that it does not require gradients to be backpropagated to the reference
parameters or hyperparameters, and permits effectively any number of gradient
updates in the inner loop. The Baldwin effect learns strong learning dependent
biases, rather than purely genetically accommodating fixed behaviours in a
learning independent manner
Quantum phase transitions beyond Landau-Ginzburg theory in one-dimensional space revisited
The phase diagram of the quantum spin-1/2 antiferromagnetic
- XXZ chain was obtained by Haldane using bosonization
techniques. It supports three distinct phases for , i.e., a gapless algebraic spin liquid phase, a
gapped long-range ordered Neel phase, and a gapped long-range ordered dimer
phase. Even though the Neel and dimer phases are not related hierarchically by
a pattern of symmetry breaking, it was shown that they meet along a line of
quantum critical points with a U(1) symmetry and central charge . Here, we
extend the analysis made by Haldane on the quantum spin-1/2 antiferromagnetic
- XYZ chain using both bosonization and numerical
techniques. We show that there are three Neel phases and the dimer phase that
are separated from each other by six planes of phase boundaries realizing U(1)
criticality when . We also show that each
long-range ordered phase harbors topological point defects (domain walls) that
are dual to those across the phase boundary in that a defect in one ordered
phase locally binds the other type of order around its core. By using the
bosonization approach, we identify the critical theory that describes
simultaneous proliferation of these dual point defects, and show that it
supports an emergent U(1) symmetry that originates from the discrete symmetries
of the XYZ model. To confirm this numerically, we perform DMRG calculation and
show that the critical theory is characterized by the central charge with
critical exponents that are consistent with those obtained from the
bosonization approach. Furthermore, we generalize the field theoretic
description of direct continuous phase transition to higher dimensions,
especially in , by using a non-linear sigma model (NLSM) with a
topological term.Comment: 25 pages with 14 figure
Collection and processing of data from a phase-coherent meteor radar
An analysis of the measurement accuracy requirement of a high resolution meteor radar for observing short period, atmospheric waves is presented, and a system which satisfies the requirements is described. A medium scale, real time computer is programmed to perform all echo recognition and coordinate measurement functions. The measurement algorithms are exercised on noisy data generated by a program which simulates the hardware system, in order to find the effects of noise on the measurement accuracies
Pulsar timing analysis in the presence of correlated noise
Pulsar timing observations are usually analysed with least-square-fitting
procedures under the assumption that the timing residuals are uncorrelated
(statistically "white"). Pulsar observers are well aware that this assumption
often breaks down and causes severe errors in estimating the parameters of the
timing model and their uncertainties. Ad hoc methods for minimizing these
errors have been developed, but we show that they are far from optimal.
Compensation for temporal correlation can be done optimally if the covariance
matrix of the residuals is known using a linear transformation that whitens
both the residuals and the timing model. We adopt a transformation based on the
Cholesky decomposition of the covariance matrix, but the transformation is not
unique. We show how to estimate the covariance matrix with sufficient accuracy
to optimize the pulsar timing analysis. We also show how to apply this
procedure to estimate the spectrum of any time series with a steep red
power-law spectrum, including those with irregular sampling and variable error
bars, which are otherwise very difficult to analyse.Comment: Accepted by MNRA
Identification of the bulk pairing symmetry in high-temperature superconductors: Evidence for an extended s-wave with eight line nodes
we identify the intrinsic bulk pairing symmetry for both electron and
hole-doped cuprates from the existing bulk- and nearly bulk-sensitive
experimental results such as magnetic penetration depth, Raman scattering,
single-particle tunneling, Andreev reflection, nonlinear Meissner effect,
neutron scattering, thermal conductivity, specific heat, and angle-resolved
photoemission spectroscopy. These experiments consistently show that the
dominant bulk pairing symmetry in hole-doped cuprates is of extended s-wave
with eight line nodes, and of anisotropic s-wave in electron-doped cuprates.
The proposed pairing symmetries do not contradict some surface- and
phase-sensitive experiments which show a predominant d-wave pairing symmetry at
the degraded surfaces. We also quantitatively explain the phase-sensitive
experiments along the c-axis for both Bi_{2}Sr_{2}CaCu_{2}O_{8+y} and
YBa_{2}Cu_{3}O_{7-y}.Comment: 11 pages, 9 figure
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