Nonperiodic delay mechanism and fractallike behavior in classical time-dependent scattering

Papachristou, P. K.; Diakonos, F. K.; Mavrommatis, E.; Constantoudis, Vassilios

doi:10.1103/physreve.64.016205

Cited by 10 publications

(14 citation statements)

References 18 publications

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“…3 numerical results for the random setup outlined above are presented. These are obtained utilizing the exact map [28], as well as the corresponding hopping and static approximative maps [29]. Consequently, it can be inferred that the development of hyper-acceleration is common to many driven dynamical systems, and features in any billiard which allows Fermi acceleration to develop.…”

Section: ±1mentioning

confidence: 99%

Hyperacceleration in a Stochastic Fermi-Ulam Model

et al. 2006

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Fermi acceleration in a Fermi-Ulam model, consisting of an ensemble of particles bouncing between two, infinitely heavy, stochastically oscillating hard walls, is investigated. It is shown that the widely used approximation, neglecting the displacement of the walls (static wall approximation), leads to a systematic underestimation of particle acceleration. An improved approximative map is introduced, which takes into account the effect of the wall displacement, and in addition allows the analytical estimation of the long term behavior of the particle mean velocity as well as the corresponding probability distribution, in complete agreement with the numerical results of the exact dynamics. This effect accounting for the increased particle acceleration -Fermi hyperacceleration-is also present in higher dimensional systems, such as the driven Lorentz gas. In 1949 Fermi [1] proposed an acceleration mechanism of cosmic ray particles interacting with a time dependent magnetic field (for a review see [2]). Ever since, this has been a subject of intense study in a broad range of systems in various areas of physics, including astrophysics [3,4,5], plasma physics [6,7], atom optics [8,9] and has even been used for the interpretation of experimental results in atomic physics [10]. Furthermore, when the mechanism is linked to higher dimensional timedependent billiards, such as a time-dependent variant of the classic Lorentz Gas, it has profound implications on statistical and solid state physics [11]. Several modifications of the original model have been suggested, one of which is the well-known Fermi-Ulam model (FUM) [12,13,14] which describes the bouncing of a ball between an oscillating and a fixed wall. FUM and its variants have been the subject of extensive theoretical (see Ref.[13] and references therein) and experimental [15,16,17] studies as they are simple to conceive but hard to understand in that their behavior is quite complicated. A standard simplification [13] widely used in the literature, the static wall approximation (SWA), ignores the displacement of the moving wall but retains the time dependence in the momentum exchange between particle and wall at the instant of collision as if the wall were oscillating. The SWA speeds up time-consuming numerical simulations and allows semi-analytical treatments as well as a deeper understanding of the system [13,18,19,20,21]. However, as shown by Einstein in his treatment of the Brownian random walk [22], taking account of the full phase space trajectory (instead of the momentum component only) is essential for the correct description of diffusion processes. More recently, in the context of diffusion in the deterministic FUM, Lieberman et al have shown that one has to employ both canonical conjugate variables (position and momentum) in order to obtain the correct momentum distribution in the asymptotic steady state [20]. The present work shows that even in the absence of an asymptotic steady state the diffusion in velocity space is deeply affected by the location of th...

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Section: ±1mentioning

confidence: 99%

Hyperacceleration in a Stochastic Fermi-Ulam Model

et al. 2006

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“…This dynamics can be described using both theoretical and experimental approaches and can be considered using either classical or quantum characterization. Several applications have been discussed, including ballistic conductance in a periodically modulated channel [2], magnetotransport through heterostructures of GaAs/AlGaAs [3], sequential resonant tunneling in semiconductor superlattices due to intense electrical fields [4], influence of transport in the presence of microwaves [5], anomalous transmission in periodic waveguides [6], trapping in driven barriers [7], characterization of traversal time [8,9], symmetry breaking and drift of particles in a chain of potential barriers [10], Lyapunov characterization of chaotic dynamics and destruction of invariant tori [11], among many others [12,13].…”

Section: Introductionmentioning

confidence: 99%

Escape of particles in a time-dependent potential well

2011

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We investigate the escape of an ensemble of noninteracting particles inside an infinite potential box that contains a time-dependent potential well. The dynamics of each particle is described by a two-dimensional nonlinear area-preserving mapping for the variables energy and time, leading to a mixed phase space. The chaotic sea in the phase space surrounds periodic islands and is limited by a set of invariant spanning curves. When a hole is introduced in the energy axis, the histogram of frequency for the escape of particles, which we observe to be scaling invariant, grows rapidly until it reaches a maximum and then decreases toward zero at sufficiently long times. A plot of the survival probability of a particle in the dynamics as function of time is observed to be exponential for short times, reaching a crossover time and turning to a slower-decay regime, due to sticky regions observed in the phase space.

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“…The other singularity is a so called low velocity peak, [33]. It only appears if the width of the barrier is larger than twice the oscillation amplitude, l > 2, and if the potential height is greater than the effective potential, V 0 > 1.…”

Section: Fig 11mentioning

confidence: 99%

Dynamical trapping and chaotic scattering of the harmonically driven barrier

et al. 2008

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A detailed analysis of the classical nonlinear dynamics of a single driven square potential barrier with harmonically oscillating position is performed. The system exhibits dynamical trapping which is associated with the existence of a stable island in phase space. Due to the unstable periodic orbits of the KAM-structure, the driven barrier is a chaotic scatterer and shows stickiness of scattering trajectories in the vicinity of the stable island. The transmission function of a suitably prepared ensemble yields results which are very similar to tunneling resonances in the quantum mechanical regime. However, the origin of these resonances is different in the classical regime.

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Nonperiodic delay mechanism and fractallike behavior in classical time-dependent scattering

Cited by 10 publications

References 18 publications

Hyperacceleration in a Stochastic Fermi-Ulam Model

Hyperacceleration in a Stochastic Fermi-Ulam Model

Escape of particles in a time-dependent potential well

Dynamical trapping and chaotic scattering of the harmonically driven barrier

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