12,531 research outputs found
Discrete Nonlinear Schr{\"o}dinger Breathers in a Phonon Bath
We study the dynamics of the discrete nonlinear Schr{\"o}dinger lattice
initialized such that a very long transitory period of time in which standard
Boltzmann statistics is insufficient is reached. Our study of the nonlinear
system locked in this {\em non-Gibbsian} state focuses on the dynamics of
discrete breathers (also called intrinsic localized modes). It is found that
part of the energy spontaneously condenses into several discrete breathers.
Although these discrete breathers are extremely long lived, their total number
is found to decrease as the evolution progresses. Even though the total number
of discrete breathers decreases we report the surprising observation that the
energy content in the discrete breather population increases. We interpret
these observations in the perspective of discrete breather creation and
annihilation and find that the death of a discrete breather cause effective
energy transfer to a spatially nearby discrete breather. It is found that the
concepts of a multi-frequency discrete breather and of internal modes is
crucial for this process. Finally, we find that the existence of a discrete
breather tends to soften the lattice in its immediate neighborhood, resulting
in high amplitude thermal fluctuation close to an existing discrete breather.
This in turn nucleates discrete breather creation close to a already existing
discrete breather
Nonparametric Bayesian Mixed-effect Model: a Sparse Gaussian Process Approach
Multi-task learning models using Gaussian processes (GP) have been developed
and successfully applied in various applications. The main difficulty with this
approach is the computational cost of inference using the union of examples
from all tasks. Therefore sparse solutions, that avoid using the entire data
directly and instead use a set of informative "representatives" are desirable.
The paper investigates this problem for the grouped mixed-effect GP model where
each individual response is given by a fixed-effect, taken from one of a set of
unknown groups, plus a random individual effect function that captures
variations among individuals. Such models have been widely used in previous
work but no sparse solutions have been developed. The paper presents the first
sparse solution for such problems, showing how the sparse approximation can be
obtained by maximizing a variational lower bound on the marginal likelihood,
generalizing ideas from single-task Gaussian processes to handle the
mixed-effect model as well as grouping. Experiments using artificial and real
data validate the approach showing that it can recover the performance of
inference with the full sample, that it outperforms baseline methods, and that
it outperforms state of the art sparse solutions for other multi-task GP
formulations.Comment: Preliminary version appeared in ECML201
Bulk and surface magnetoinductive breathers in binary metamaterials
We study theoretically the existence of bulk and surface discrete breathers
in a one-dimensional magnetic metamaterial comprised of a periodic binary array
of split-ring resonators. The two types of resonators differ in the size of
their slits and this leads to different resonant frequencies. In the framework
of the rotating-wave approximation (RWA) we construct several types of breather
excitations for both the energy-conserved and the dissipative-driven systems by
continuation of trivial breather solutions from the anticontinuous limit to
finite couplings. Numerically-exact computations that integrate the full model
equations confirm the quality of the RWA results. Moreover, it is demonstrated
that discrete breathers can spontaneously appear in the dissipative-driven
system as a results of a fundamental instability.Comment: 10 pages, 16 figure
SLE-type growth processes and the Yang-Lee singularity
The recently introduced SLE growth processes are based on conformal maps from
an open and simply-connected subset of the upper half-plane to the half-plane
itself. We generalize this by considering a hierarchy of stochastic evolutions
mapping open and simply-connected subsets of smaller and smaller fractions of
the upper half-plane to these fractions themselves. The evolutions are all
driven by one-dimensional Brownian motion. Ordinary SLE appears at grade one in
the hierarchy. At grade two we find a direct correspondence to conformal field
theory through the explicit construction of a level-four null vector in a
highest-weight module of the Virasoro algebra. This conformal field theory has
central charge c=-22/5 and is associated to the Yang-Lee singularity. Our
construction may thus offer a novel description of this statistical model.Comment: 12 pages, LaTeX, v2: thorough revision with corrections, v3: version
to be publishe
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Magnetoinductive breathers in magnetic metamaterials
The existence and stability of discrete breathers (DBs) in one-dimensional
and two-dimensional magnetic metamaterials (MMs), which consist of periodic
arrangem ents (arrays) of split-ring resonators (SRRs), is investigated
numerically. We consider different configurations of the SRR arrays, which are
related to the relative orientation of the SRRs in the MM, both in one and two
spatial dimensions. In the latter case we also consider anisotropic MMs. Using
standard numerical methods we construct several types of linearly stable
breather excitations both in Hamiltonian and dissipative MMs (dissipative
breathers). The study of stability in both cases is performed using standard
Floquet analysi s. In both cases we found that the increase of dimensionality
from one to two spatial dimensions does not destroy the DBs, which may also
exist in the case of moderate anisotropy (in two dimensions). In dissipative
MMs, the dynamics is governed by a power balance between the mainly Ohmic
dissipation and driving by an alternating magnetic field. In that case it is
demonstrated that DB excitation locally alters the magnetic response of MMs
from paramagnetic to diamagnetic. Moreover, when the frequency of the applied
field approaches the SRR resonance frequency, the magnetic response of the MM
in the region of the DB excitation may even become negative (extreme
diamagnetic).Comment: 12 pages 15 figure
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Extreme events in discrete nonlinear lattices
We perform statistical analysis on discrete nonlinear waves generated though
modulational instability in the context of the Salerno model that interpolates
between the intergable Ablowitz-Ladik (AL) equation and the nonintegrable
discrete nonlinear Schrodinger (DNLS) equation. We focus on extreme events in
the form of discrete rogue or freak waves that may arise as a result of rapid
coalescence of discrete breathers or other nonlinear interaction processes. We
find power law dependence in the wave amplitude distribution accompanied by an
enhanced probability for freak events close to the integrable limit of the
equation. A characteristic peak in the extreme event probability appears that
is attributed to the onset of interaction of the discrete solitons of the AL
equation and the accompanied transition from the local to the global
stochasticity monitored through the positive Lyapunov exponent of a nonlinear
map.Comment: 5 pages, 4 figures; reference added, figure 2 correcte
Solvable Critical Dense Polymers
A lattice model of critical dense polymers is solved exactly for finite
strips. The model is the first member of the principal series of the recently
introduced logarithmic minimal models. The key to the solution is a functional
equation in the form of an inversion identity satisfied by the commuting
double-row transfer matrices. This is established directly in the planar
Temperley-Lieb algebra and holds independently of the space of link states on
which the transfer matrices act. Different sectors are obtained by acting on
link states with s-1 defects where s=1,2,3,... is an extended Kac label. The
bulk and boundary free energies and finite-size corrections are obtained from
the Euler-Maclaurin formula. The eigenvalues of the transfer matrix are
classified by the physical combinatorics of the patterns of zeros in the
complex spectral-parameter plane. This yields a selection rule for the
physically relevant solutions to the inversion identity and explicit finitized
characters for the associated quasi-rational representations. In particular, in
the scaling limit, we confirm the central charge c=-2 and conformal weights
Delta_s=((2-s)^2-1)/8 for s=1,2,3,.... We also discuss a diagrammatic
implementation of fusion and show with examples how indecomposable
representations arise. We examine the structure of these representations and
present a conjecture for the general fusion rules within our framework.Comment: 35 pages, v2: comments and references adde
Quantum transport in carbon nanotubes
Carbon nanotubes are a versatile material in which many aspects of condensed
matter physics come together. Recent discoveries, enabled by sophisticated
fabrication, have uncovered new phenomena that completely change our
understanding of transport in these devices, especially the role of the spin
and valley degrees of freedom. This review describes the modern understanding
of transport through nanotube devices.
Unlike conventional semiconductors, electrons in nanotubes have two angular
momentum quantum numbers, arising from spin and from valley freedom. We focus
on the interplay between the two. In single quantum dots defined in short
lengths of nanotube, the energy levels associated with each degree of freedom,
and the spin-orbit coupling between them, are revealed by Coulomb blockade
spectroscopy. In double quantum dots, the combination of quantum numbers
modifies the selection rules of Pauli blockade. This can be exploited to read
out spin and valley qubits, and to measure the decay of these states through
coupling to nuclear spins and phonons. A second unique property of carbon
nanotubes is that the combination of valley freedom and electron-electron
interactions in one dimension strongly modifies their transport behaviour.
Interaction between electrons inside and outside a quantum dot is manifested in
SU(4) Kondo behavior and level renormalization. Interaction within a dot leads
to Wigner molecules and more complex correlated states.
This review takes an experimental perspective informed by recent advances in
theory. As well as the well-understood overall picture, we also state clearly
open questions for the field. These advances position nanotubes as a leading
system for the study of spin and valley physics in one dimension where
electronic disorder and hyperfine interaction can both be reduced to a very low
level.Comment: In press at Reviews of Modern Physics. 68 pages, 55 figure
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