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## Transport properties in nontwist area-preserving maps

Fonte: AMER INST PHYSICS
Publicador: AMER INST PHYSICS

Tipo: Artigo de Revista Científica

ENG

Relevância na Pesquisa

56.24%

#MAGNETIC-FIELD LINES#HAMILTONIAN-SYSTEMS#CHAOTIC TRANSPORT#PERIODIC-ORBITS#TOKAMAKS#SHEAR#RECONNECTION#TRANSITION#EXISTENCE#CRITERION#Mathematics, Applied

Nontwist systems, common in the dynamical descriptions of fluids and plasmas, possess a shearless curve with a concomitant transport barrier that eliminates or reduces chaotic transport, even after its breakdown. In order to investigate the transport properties of nontwist systems, we analyze the barrier escape time and barrier transmissivity for the standard nontwist map, a paradigm of such systems. We interpret the sensitive dependence of these quantities upon map parameters by investigating chaotic orbit stickiness and the associated role played by the dominant crossing of stable and unstable manifolds. (C) 2009 American Institute of Physics. [doi: 10.1063/1.3247349]; CNPq; Coordenacao de Aperfeicoamento de Pessoal de Nivel Superior (CAPES); FAPESP; FINEP/CNEN; U.S. Department of Energy (DOE)[DEFG03-96ER-54346]

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## Phase space properties and chaotic transport for a particle moving in a time dependent step potential well

Fonte: Elsevier B.V.
Publicador: Elsevier B.V.

Tipo: Artigo de Revista Científica
Formato: 215-228

ENG

Relevância na Pesquisa

56.35%

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES); Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq); Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP); Processo FAPESP: 10/52709-5; Processo FAPESP: 12/18962-0; Processo FAPESP: 12/23688-5; Processo FAPESP: 08/57528-9; Processo FAPESP: 05/56253-8; Some dynamical properties for an ensemble of non-interacting classical particles along chaotic orbits and transport properties over the chaotic sea for the problem of a step and time dependent potential well are considered. The dynamics of each particle is described by a two-dimensional, nonlinear and area preserving mapping for the variables energy and time. The phase space is of mixed-type and contains periodic islands, a set of invariant KAM curves and chaotic seas. The chaotic orbits are characterized by the use of Lyapunov exponents. Transport over the chaotic sea is considered and scaling exponents are obtained. A sticky region around a chain of periodic islands produces local and temporarily trapping of the dynamics and discussions of the rearrangement of the phase space are made. (C) 2014 Elsevier Inc. All rights reserved.

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## Chaotic Transport in Planar Periodic Vortical Flows

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Relevância na Pesquisa

56.12%

We have studied a chaotic transport in a two-dimensional periodic vortical
flow under a time-dependent perturbation with period T where the global
diffusion occurs along the stochastic web. By using the Melnikov method we
construct the separatrix map describing the approximate dynamics near the
saddle separatrices. Focusing on the small T, the width of the stochastic layer
is calculated analytically by using the residue criterion and the diffusion
constant by using the random phase assumption and correlated random walks. The
analytical results are in good agreements with the results of two different
types of numerical simulations by integrations of the Hamilton's equation of
motion and by iterations of the separatrix map, which establishes the validity
of the use of the separatrix map.; Comment: LaTex, 26 pages, 8 PostScript figures (uuencoded, tar-compressed)

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## Suppression of weak-localization (and enhancement of noise) by tunnelling in semiclassical chaotic transport

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Relevância na Pesquisa

56.17%

We add simple tunnelling effects and ray-splitting into the recent
trajectory-based semiclassical theory of quantum chaotic transport. We use this
to derive the weak-localization correction to conductance and the shot-noise
for a quantum chaotic cavity (billiard) coupled to $n$ leads via
tunnel-barriers. We derive results for arbitrary tunnelling rates and arbitrary
(positive) Ehrenfest time, $\tau_{\rm E}$. For all Ehrenfest times, we show
that the shot-noise is enhanced by the tunnelling, while the weak-localization
is suppressed. In the opaque barrier limit (small tunnelling rates with large
lead widths, such that Drude conductance remains finite), the weak-localization
goes to zero linearly with the tunnelling rate, while the Fano factor of the
shot-noise remains finite but becomes independent of the Ehrenfest time. The
crossover from RMT behaviour ($\tau_{\rm E}=0$) to classical behaviour
($\tau_{\rm E}=\infty$) goes exponentially with the ratio of the Ehrenfest time
to the paired-paths survival time. The paired-paths survival time varies
between the dwell time (in the transparent barrier limit) and half the dwell
time (in the opaque barrier limit). Finally our method enables us to see the
physical origin of the suppression of weak-localization; it is due to the fact
that tunnel-barriers ``smear'' the coherent-backscattering peak over reflection
and transmission modes.; Comment: 20 pages (version3: fixed error in sect. VC - results unchanged) -
Contents: Tunnelling in semiclassics (3pages)...

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## Semiclassical approach to universality in quantum chaotic transport

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Relevância na Pesquisa

46.18%

The statistics of quantum transport through chaotic cavities with two leads
is encoded in transport moments $M_m={\rm Tr}[(t^\dag t)^m]$, where $t$ is the
transmission matrix, which have a known universal expression for systems
without time-reversal symmetry. We present a semiclassical derivation of this
universality, based on action correlations that exist between sets of long
scattering trajectories. Our semiclassical formula for $M_m$ holds for all
values of $m$ and arbitrary number of open channels. This is achieved by
mapping the problem into two independent combinatorial problems, one involving
pairs of set partitions and the other involving factorizations in the symmetric
group.; Comment: Published version. Changes in presentation

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## Semiclassical matrix model for quantum chaotic transport with time-reversal symmetry

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 09/02/2015

Relevância na Pesquisa

46.18%

#Nonlinear Sciences - Chaotic Dynamics#Condensed Matter - Mesoscale and Nanoscale Physics#Mathematical Physics

We show that the semiclassical approach to chaotic quantum transport in the
presence of time-reversal symmetry can be described by a matrix model, i.e. a
matrix integral whose perturbative expansion satisfies the semiclassical
diagrammatic rules for the calculation of transport statistics. This approach
leads very naturally to the semiclassical derivation of universal predictions
from random matrix theory.; Comment: 12 pages, 4 figures

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## Short- and Long- Time Transport Structures in a Three Dimensional Time Dependent Flow

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 08/05/2014

Relevância na Pesquisa

46.31%

Lagrangian transport structures for three-dimensional and time-dependent
fluid flows are of great interest in numerous applications, particularly for
geophysical or oceanic flows. In such flows, chaotic transport and mixing can
play important environmental and ecological roles, for examples in pollution
spills or plankton migration. In such flows, where simulations or observations
are typically available only over a short time, understanding the difference
between short-time and long-time transport structures is critical. In this
paper, we use a set of classical (i.e. Poincar\'e section, Lyapunov exponent)
and alternative (i.e. finite time Lyapunov exponent, Lagrangian coherent
structures) tools from dynamical systems theory that analyze chaotic transport
both qualitatively and quantitatively. With this set of tools we are able to
reveal, identify and highlight differences between short- and long-time
transport structures inside a flow composed of a primary horizontal
contra-rotating vortex chain, small lateral oscillations and a weak Ekman
pumping. The difference is mainly the existence of regular or extremely slowly
developing chaotic regions that are only present at short time.; Comment: 9 pages, 9 figures

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## Controlling Chaotic transport on Periodic Surfaces

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 25/03/2010

Relevância na Pesquisa

56.27%

We uncover and characterize different chaotic transport scenarios on perfect
periodic surfaces by controlling the chaotic dynamics of particles subjected to
periodic external forces in the absence of a ratchet effect. After identifying
relevant {\it symmetries} of chaotic solutions, analytical estimates in
parameter space for the occurrence of different transport scenarios are
provided and confirmed by numerical simulations. These scenarios are highly
sensitive to variations of the system's asymmetry parameters, including the
eccentricity of the periodic surface and the direction of dc and ac forces,
which could be useful for particle sorting purposes in those cases where chaos
is unavoidable.

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## Dephasing in quantum chaotic transport: a semiclassical approach

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Relevância na Pesquisa

46.23%

We investigate the effect of dephasing/decoherence on quantum transport
through open chaotic ballistic conductors in the semiclassical limit of small
Fermi wavelength to system size ratio, $\lambda_F/L << 1$. We use the
trajectory-based semiclassical theory to study a two-terminal chaotic dot with
decoherence originating from:
(i) an external closed quantum chaotic environment,
(ii) a classical source of noise,
(iii) a voltage probe, i.e. an additional current-conserving terminal.
We focus on the pure dephasing regime, where the coupling to the external
source of dephasing is so weak that it does not induce energy relaxation. In
addition to the universal algebraic suppression of weak localization, we find
an exponential suppression of weak-localization $\propto
\exp[-\tilde{\tau}/\tau_\phi]$, with the dephasing rate $\tau_\phi^{-1}$. The
parameter $\tilde{\tau}$ depends strongly on the source of dephasing. For a
voltage probe, $\tilde{\tau}$ is of order the Ehrenfest time $\propto \ln
[L/\lambda_F ]$. In contrast, for a chaotic environment or a classical source
of noise, it has the correlation length $\xi$ of the coupling/noise potential
replacing the Fermi wavelength $\lambda_F $. We explicitly show that the Fano
factor for shot noise is unaffected by decoherence. We connect these results to
earlier works on dephasing due to electron-electron interactions...

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## Area-preserving maps models of gyro-averaged ${\bf E} \times {\bf B}$ chaotic transport

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 10/09/2014

Relevância na Pesquisa

56.29%

Discrete maps have been extensively used to model 2-dimensional chaotic
transport in plasmas and fluids. Here we focus on area-preserving maps
describing finite Larmor radius (FLR) effects on ${\bf E} \times {\bf B}$
chaotic transport in magnetized plasmas with zonal flows perturbed by
electrostatic drift waves. FLR effects are included by gyro-averaging the
Hamiltonians of the maps which, depending on the zonal flow profile, can have
monotonic or non-monotonic frequencies. In the limit of zero Larmor radius, the
monotonic frequency map reduces to the standard Chirikov-Taylor map, and, in
the case of non-monotonic frequency, the map reduces to the standard nontwist
map. We show that in both cases FLR leads to chaos suppression, changes in the
stability of fixed points, and robustness of transport barriers. FLR effects
are also responsible for changes in the phase space topology and zonal flow
bifurcations. Dynamical systems methods based on recurrence time statistics are
used to quantify the dependence on the Larmor radius of the threshold for the
destruction of transport barriers.; Comment: Accepted for publication in Physics of Plasmas

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## Microscopic Theory for the Quantum to Classical Crossover in Chaotic Transport

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Relevância na Pesquisa

56.17%

#Condensed Matter - Mesoscale and Nanoscale Physics#Condensed Matter - Disordered Systems and Neural Networks#Nonlinear Sciences - Chaotic Dynamics

We present a semiclassical theory for the scattering matrix ${\cal S}$ of a
chaotic ballistic cavity at finite Ehrenfest time. Using a phase-space
representation coupled with a multi-bounce expansion, we show how the Liouville
conservation of phase-space volume decomposes ${\cal S}$ as ${\cal S}={\cal
S}^{\rm cl} \oplus {\cal S}^{\rm qm}$. The short-time, classical contribution
${\cal S}^{\rm cl}$ generates deterministic transmission eigenvalues T=0 or 1,
while quantum ergodicity is recovered within the subspace corresponding to the
long-time, stochastic contribution ${\cal S}^{\rm qm}$. This provides a
microscopic foundation for the two-phase fluid model, in which the cavity acts
like a classical and a quantum cavity in parallel, and explains recent
numerical data showing the breakdown of universality in quantum chaotic
transport in the deep semiclassical limit. We show that the Fano factor of the
shot-noise power vanishes in this limit, while weak localization remains
universal.; Comment: PRL version, added comment about 2 Ehrenfest times (4pages, 2figs)

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## Controlling chaotic transport in a Hamiltonian model of interest to magnetized plasmas

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 25/02/2004

Relevância na Pesquisa

56.12%

We present a technique to control chaos in Hamiltonian systems which are
close to integrable. By adding a small and simple control term to the
perturbation, the system becomes more regular than the original one. We apply
this technique to a model that reproduces turbulent ExB drift and show
numerically that the control is able to drastically reduce chaotic transport.

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## Directed Chaotic Transport in Hamiltonian Ratchets

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 11/08/2004

Relevância na Pesquisa

46.35%

We present a comprehensive account of directed transport in one-dimensional
Hamiltonian systems with spatial and temporal periodicity. They can be
considered as Hamiltonian ratchets in the sense that ensembles of particles can
show directed ballistic transport in the absence of an average force. We
discuss general conditions for such directed transport, like a mixed classical
phase space, and elucidate a sum rule that relates the contributions of
different phase-space components to transport with each other. We show that
regular ratchet transport can be directed against an external potential
gradient while chaotic ballistic transport is restricted to unbiased systems.
For quantized Hamiltonian ratchets we study transport in terms of the evolution
of wave packets and derive a semiclassical expression for the distribution of
level velocities which encode the quantum transport in the Floquet band
spectra. We discuss the role of dynamical tunneling between transporting
islands and the chaotic sea and the breakdown of transport in quantum ratchets
with broken spatial periodicity.; Comment: 22 pages

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## Divergence of the Chaotic Layer Width and Strong Acceleration of the Spatial Chaotic Transport in Periodic Systems Driven by an Adiabatic ac Force

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Relevância na Pesquisa

56.29%

#Nonlinear Sciences - Chaotic Dynamics#Condensed Matter - Mesoscale and Nanoscale Physics#Condensed Matter - Statistical Mechanics

We show for the first time that a {\it weak} perturbation in a Hamiltonian
system may lead to an arbitrarily {\it wide} chaotic layer and {\it fast}
chaotic transport. This {\it generic} effect occurs in any spatially periodic
Hamiltonian system subject to a sufficiently slow ac force. We explain it and
develop an explicit theory for the layer width, verified in simulations.
Chaotic spatial transport as well as applications to the diffusion of particles
on surfaces, threshold devices and others are discussed.; Comment: 4 pages including 3 EPS figures, this is an improved version of the
paper (accepted to PRL, 2005)

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## Effect of dynamical traps on chaotic transport in a meandering jet flow

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 19/12/2011

Relevância na Pesquisa

46.27%

We continue our study of chaotic mixing and transport of passive particles in
a simple model of a meandering jet flow [Prants, et al, Chaos {\bf 16}, 033117
(2006)]. In the present paper we study and explain phenomenologically a
connection between dynamical, topological, and statistical properties of
chaotic mixing and transport in the model flow in terms of dynamical traps,
singular zones in the phase space where particles may spend arbitrary long but
finite time [Zaslavsky, Phys. D {\bf 168--169}, 292 (2002)]. The transport of
passive particles is described in terms of lengths and durations of zonal
flights which are events between two successive changes of sign of zonal
velocity. Some peculiarities of the respective probability density functions
for short flights are proven to be caused by the so-called rotational-islands
traps connected with the boundaries of resonant islands (including the vortex
cores) filled with the particles moving in the same frame and the saddle traps
connected with periodic saddle trajectories. Whereas, the statistics of long
flights can be explained by the influence of the so-called ballistic-islands
traps filled with the particles moving from a frame to frame.

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## Regular and chaotic transport of discrete solitons in asymmetric potentials

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 21/11/2010

Relevância na Pesquisa

46.27%

#Nonlinear Sciences - Pattern Formation and Solitons#Condensed Matter - Other Condensed Matter#Condensed Matter - Statistical Mechanics

Ratchet dynamics of topological solitons of the forced and damped discrete
double sine-Gordon system are studied. Directed transport occurring both in
regular and in chaotic regions of the phase space and its dependence on
damping, amplitude and frequency of the driving, asymmetry parameter, coupling
constant, has been extensively investigated. We show that the passage from
ratchet phase-locked regime to chaotic ratchets occurs via a period doubling
route to chaos and that, quite surprisingly, pinned states can exist inside
phase-locking and chaotic transport regions for intermediate values of the
coupling constant. The possibility to control chaotic discrete soliton ratchets
by means of both small subharmonic signals and more general periodic drivings,
has also been investigated.

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## Chaotic Jets

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 21/02/2006

Relevância na Pesquisa

46.23%

The problem of characterizing the origin of the non-Gaussian properties of
transport resulting from Hamiltonian dynamics is addressed. For this purpose
the notion of chaotic jet is revisited and leads to the definition of a
diagnostic able to capture some singular properties of the dynamics. This
diagnostic is applied successfully to the problem of advection of passive
tracers in a flow generated by point vortices. We present and discuss this
diagnostic as a result of which clues on the origin of anomalous transport in
these systems emerge.; Comment: Proceedings of the workshop Chaotic transport and complexity in
classical and quantum dynamics, Carry le rouet France (2002)

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## Chaotic Transport and Current Reversal in Deterministic Ratchets

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 20/12/1999

Relevância na Pesquisa

46.17%

We address the problem of the classical deterministic dynamics of a particle
in a periodic asymmetric potential of the ratchet type. We take into account
the inertial term in order to understand the role of the chaotic dynamics in
the transport properties. By a comparison between the bifurcation diagram and
the current, we identify the origin of the current reversal as a bifurcation
from a chaotic to a periodic regime. Close to this bifurcation, we observed
trajectories revealing intermittent chaos and anomalous deterministic
diffusion.; Comment: (7 figures) To appear in Physical Review Letters (in January 2000)

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## Reduction of the chaotic transport of impurities in turbulent magnetized plasmas

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 14/10/2009

Relevância na Pesquisa

56.27%

The chaotic transport of charged particles in a turbulent electrostatic
potential sets the conditions of a severe limitation to the plasma confinement
in devices such as tokamaks. In this chapter, we consider the motion of
impurities driven by the ExB velocity where a strong magnetic field B (which
allows for the guiding center approximation) is uniform and constant, and a
turbulent electric field is obtained from models or from numerical fluid codes.
Hamiltonian dynamics rule the transport properties of these impurities.
Therefore a technique to reduce chaotic diffusion in Hamiltonian systems is
able to address the issue of reducing the radial transport of impurities under
some approximations. The general idea is to build barriers in phase space by a
small and apt modification of the Hamiltonian. We show numerically that such
perturbations are able to drastically reduce the diffusion of test-particles,
and we discuss the robustness of such additional modifications.

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## Stochastic webs and quantum transport in superlattices: an introductory review

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 11/11/2009

Relevância na Pesquisa

46.24%

Stochastic webs were discovered, first by Arnold for multi-dimensional
Hamiltonian systems, and later by Chernikov et al. for the low-dimensional
case. Generated by weak perturbations, they consist of thread-like regions of
chaotic dynamics in phase space. Their importance is that, in principle, they
enable transport from small energies to high energies. In this introductory
review, we concentrate on low-dimensional stochastic webs and on their
applications to quantum transport in semiconductor superlattices subject to
electric and magnetic fields. We also describe a recently-suggested
modification of the stochastic web to enhance chaotic transport through it and
we discuss its possible applications to superlattices. keywords: stochastic
webs; quantum transport; superlattices; separatrix chaos; Comment: Review, to be published in "Contemporary Physics"

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