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Transport properties in nontwist area-preserving maps

Szezech Junior, Jose Danilo; Caldas, Ibere Luiz; Lopes, Sergio Roberto; Viana, Ricardo Luiz; Morrison, Philip James
Fonte: AMER INST PHYSICS Publicador: AMER INST PHYSICS
Tipo: Artigo de Revista Científica
ENG
Relevância na Pesquisa
56.24%
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]

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

Costa, Diogo Ricardo da; Caldas, Ibere L.; Leonel, Edson D.
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.

Chaotic Transport in Planar Periodic Vortical Flows

Ahn, Taehoon; Kim, Seunghwan
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)

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

Whitney, Robert S.
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)...

Semiclassical approach to universality in quantum chaotic transport

Novaes, Marcel
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

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

Novaes, Marcel
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 09/02/2015
Relevância na Pesquisa
46.18%
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

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

Chabreyrie, Rodolphe; Smith, Stefan G. Llewellyn
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

Controlling Chaotic transport on Periodic Surfaces

Chacon, R.; Lacasta, A. M.
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.

Dephasing in quantum chaotic transport: a semiclassical approach

Whitney, Robert S.; Jacquod, Philippe; Petitjean, Cyril
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...

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

da Fonseca, J. D.; del-Castillo-Negrete, D.; Caldas, I. L.
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

Microscopic Theory for the Quantum to Classical Crossover in Chaotic Transport

Whitney, Robert S.; Jacquod, Ph.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
56.17%
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)

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

Ciraolo, Guido; Chandre, Cristel; Lima, Ricardo; Vittot, Michel; Pettini, Marco; Figarella, Charles; Ghendrih, Philippe
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.

Directed Chaotic Transport in Hamiltonian Ratchets

Schanz, Holger; Dittrich, Thomas; Ketzmerick, Roland
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

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

Soskin, S. M.; Yevtushenko, O. M.; Mannella, R.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
56.29%
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)

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

Uleysky, M. Yu.; Budyansky, M. V.; Prants, S. V.
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.

Regular and chaotic transport of discrete solitons in asymmetric potentials

Cuevas, J.; Sánchez-Rey, B.; Salerno, M.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 21/11/2010
Relevância na Pesquisa
46.27%
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.

Chaotic Jets

Leoncini, Xavier; Zaslavsky, George M.
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)

Chaotic Transport and Current Reversal in Deterministic Ratchets

Mateos, Jose L.
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)

Reduction of the chaotic transport of impurities in turbulent magnetized plasmas

Chandre, Cristel; Ciraolo, Guido; Vittot, Michel
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.

Stochastic webs and quantum transport in superlattices: an introductory review

Soskin, S. M.; McClintock, P. V. E.; Fromhold, T. M.; Khovanov, I. A.; Mannella, R.
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"