228 research outputs found
Resolution of two apparent paradoxes concerning quantum oscillations in underdoped high- superconductors
Recent quantum oscillation experiments in underdoped high temperature
superconductors seem to imply two paradoxes. The first paradox concerns the
apparent non-existence of the signature of the electron pockets in angle
resolved photoemission spectroscopy (ARPES). The second paradox is a clear
signature of a small electron pocket in quantum oscillation experiments, but no
evidence as yet of the corresponding hole pockets of approximately double the
frequency of the electron pocket. This hole pockets should be present if the
Fermi surface reconstruction is due to a commensurate density wave, assuming
that Luttinger sum rule relating the area of the pockets and the total number
of charge carriers holds. Here we provide possible resolutions of these
apparent paradoxes from the commensurate -density wave theory. To address
the first paradox we have computed the ARPES spectral function subject to
correlated disorder, natural to a class of experiments relevant to the
materials studied in quantum oscillations. The intensity of the spectral
function is significantly reduced for the electron pockets for an intermediate
range of disorder correlation length, and typically less than half the hole
pocket is visible, mimicking Fermi arcs. Next we show from an exact transfer
matrix calculation of the Shubnikov-de Haas oscillation that the usual disorder
affects the electron pocket more significantly than the hole pocket. However,
when, in addition, the scattering from vortices in the mixed state is included,
it wipes out the frequency corresponding to the hole pocket. Thus, if we are
correct, it will be necessary to do measurements at higher magnetic fields and
even higher quality samples to recover the hole pocket frequency.Comment: Accepted version, Phys. Rev. B, brief clarifying comments and updated
reference
Dissipation and criticality in the lowest Landau level of graphene
The lowest Landau level of graphene is studied numerically by considering a
tight-binding Hamiltonian with disorder. The Hall conductance
and the longitudinal conductance are
computed. We demonstrate that bond disorder can produce a plateau-like feature
centered at , while the longitudinal conductance is nonzero in the same
region, reflecting a band of extended states between , whose
magnitude depends on the disorder strength. The critical exponent corresponding
to the localization length at the edges of this band is found to be . When both bond disorder and a finite mass term exist the localization
length exponent varies continuously between and .Comment: 4 pages, 5 figure
Computing Lyapunov spectra with continuous Gram-Schmidt orthonormalization
We present a straightforward and reliable continuous method for computing the
full or a partial Lyapunov spectrum associated with a dynamical system
specified by a set of differential equations. We do this by introducing a
stability parameter beta>0 and augmenting the dynamical system with an
orthonormal k-dimensional frame and a Lyapunov vector such that the frame is
continuously Gram-Schmidt orthonormalized and at most linear growth of the
dynamical variables is involved. We prove that the method is strongly stable
when beta > -lambda_k where lambda_k is the k'th Lyapunov exponent in
descending order and we show through examples how the method is implemented. It
extends many previous results.Comment: 14 pages, 10 PS figures, ioplppt.sty, iopl12.sty, epsfig.sty 44 k
Refining Finite-Time Lyapunov Exponent Ridges and the Challenges of Classifying Them
While more rigorous and sophisticated methods for identifying Lagrangian based coherent structures exist, the finite-time Lyapunov exponent (FTLE) field remains a straightforward and popular method for gaining some insight into transport by complex, time-dependent two-dimensional flows. In light of its enduring appeal, and in support of good practice, we begin by investigating the effects of discretization and noise on two numerical approaches for calculating the FTLE field. A practical method to extract and refine FTLE ridges in two-dimensional flows, which builds on previous methods, is then presented. Seeking to better ascertain the role of a FTLE ridge in flow transport, we adapt an existing classification scheme and provide a thorough treatment of the challenges of classifying the types of deformation represented by a FTLE ridge. As a practical demonstration, the methods are applied to an ocean surface velocity field data set generated by a numerical model. (C) 2015 AIP Publishing LLC.ONR N000141210665Center for Nonlinear Dynamic
Phase transition in a class of non-linear random networks
We discuss the complex dynamics of a non-linear random networks model, as a
function of the connectivity k between the elements of the network. We show
that this class of networks exhibit an order-chaos phase transition for a
critical connectivity k = 2. Also, we show that both, pairwise correlation and
complexity measures are maximized in dynamically critical networks. These
results are in good agreement with the previously reported studies on random
Boolean networks and random threshold networks, and show once again that
critical networks provide an optimal coordination of diverse behavior.Comment: 9 pages, 3 figures, revised versio
Amplitude death in coupled chaotic oscillators
Amplitude death can occur in chaotic dynamical systems with time-delay
coupling, similar to the case of coupled limit cycles. The coupling leads to
stabilization of fixed points of the subsystems. This phenomenon is quite
general, and occurs for identical as well as nonidentical coupled chaotic
systems. Using the Lorenz and R\"ossler chaotic oscillators to construct
representative systems, various possible transitions from chaotic dynamics to
fixed points are discussed.Comment: To be published in PR
Time-reversed symmetry and covariant Lyapunov vectors for simple particle models in and out of thermal equilibrium
Recently, a new algorithm for the computation of covariant Lyapunov vectors
and of corresponding local Lyapunov exponents has become available. Here we
study the properties of these still unfamiliar quantities for a number of
simple models, including an harmonic oscillator coupled to a thermal gradient
with a two-stage thermostat, which leaves the system ergodic and fully time
reversible. We explicitly demonstrate how time-reversal invariance affects the
perturbation vectors in tangent space and the associated local Lyapunov
exponents. We also find that the local covariant exponents vary discontinuously
along directions transverse to the phase flow.Comment: 13 pages, 11 figures submitted to Physical Review E, 201
Measuring Topological Chaos
The orbits of fluid particles in two dimensions effectively act as
topological obstacles to material lines. A spacetime plot of the orbits of such
particles can be regarded as a braid whose properties reflect the underlying
dynamics. For a chaotic flow, the braid generated by the motion of three or
more fluid particles is computed. A ``braiding exponent'' is then defined to
characterize the complexity of the braid. This exponent is proportional to the
usual Lyapunov exponent of the flow, associated with separation of nearby
trajectories. Measuring chaos in this manner has several advantages, especially
from the experimental viewpoint, since neither nearby trajectories nor
derivatives of the velocity field are needed.Comment: 4 pages, 6 figures. RevTeX 4 with PSFrag macro
Critical conductance of two-dimensional chiral systems with random magnetic flux
The zero temperature transport properties of two-dimensional lattice systems
with static random magnetic flux per plaquette and zero mean are investigated
numerically. We study the two-terminal conductance and its dependence on
energy, sample size, and magnetic flux strength. The influence of boundary
conditions and of the oddness of the number of sites in the transverse
direction is also studied. We confirm the existence of a critical chiral state
in the middle of the energy band and calculate the critical exponent nu=0.35
+/- 0.03 for the divergence of the localization length. The sample averaged
scale independent critical conductance _c turns out to be a function of the
amplitude of the flux fluctuations whereas the variance of the respective
conductance distributions appears to be universal. All electronic states
outside of the band center are found to be localized.Comment: to appear in Phys. Rev.
Advection of vector fields by chaotic flows
We have introduced a new transfer operator for chaotic flows whose leading
eigenvalue yields the dynamo rate of the fast kinematic dynamo and applied
cycle expansion of the Fredholm determinant of the new operator to evaluation
of its spectrum. The theory hs been tested on a normal form model of the vector
advecting dynamical flow. If the model is a simple map with constant time
between two iterations, the dynamo rate is the same as the escape rate of
scalar quantties. However, a spread in Poincar\'e section return times lifts
the degeneracy of the vector and scalar advection rates, and leads to dynamo
rates that dominate over the scalar advection rates. For sufficiently large
time spreads we have even found repellers for which the magnetic field grows
exponentially, even though the scalar densities are decaying exponentially.Comment: 12 pages, Latex. Ask for figures from [email protected]
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