Classical scattering from oscillating targets

Papachristou, P. K.; Diakonos, F. K.; Constantoudis, Vassilios; Schmelcher, Peter; Benet, Luis

doi:10.1016/s0375-9601(02)01366-x

Cited by 11 publications

(19 citation statements)

References 24 publications

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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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Section: Introductionmentioning

confidence: 99%

Escape of particles in a time-dependent potential well

2011

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“…The set of the observed peaks possesses a self-similar structure either in an approximative sense occurring only between two scales determined by the geometry of the particular setup [24] or in a local sense in the neighborhood of specific isolated points in phase space [25]. The significant role of processes with maximum energy exchange in the scattering off a time-dependent hard potential becomes more transparent in the case of scattering off a single oscillating disc [26]. Despite the absence of UPOs in this system the scattering functions possess a nontrivial structure dictated by elementary processes involving single or multiple collisions between the projectile and the oscillating target.…”

Section: Introductionmentioning

confidence: 97%

Scattering off an oscillating target: Basic mechanisms and their impact on cross sections

et al. 2008

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We investigate classical scattering off a harmonically oscillating target in two spatial dimensions. The shape of the scatterer is assumed to have a boundary which is locally convex at any point and does not support the presence of any periodic orbits in the corresponding dynamics. As a simple example we consider the scattering of a beam of non-interacting particles off a circular hard scatterer. The performed analysis is focused on experimentally accessible quantities, characterizing the system, like the differential cross sections in the outgoing angle and velocity. Despite the absence of periodic orbits and their manifolds in the dynamics, we show that the cross sections acquire rich and multiple structure when the velocity of the particles in the beam becomes of the same order of magnitude as the maximum velocity of the oscillating target. The underlying dynamical pattern is uniquely determined by the phase of the first collision between the beam particles and the scatterer and possesses a universal profile, dictated by the manifolds of the parabolic orbits, which can be understood both qualitatively as well as quantitatively in terms of scattering off a hard wall. We discuss also the inverse problem concerning the possibility to extract properties of the oscillating target from the differential cross sections.

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“…One therefore could expect naively that chaotic scattering should naturally appear, provided that the corresponding dynamics support the presence of UPOs, and connections among them. The situation is in fact more complicated [20][21][22]. Time dependence allows important energy transfer processes to take place between the target and the projectile.…”

Section: Introductionmentioning

confidence: 99%

“…Time dependence allows important energy transfer processes to take place between the target and the projectile. These events may lead to a large decrease of the projectile's velocity, which manifest in the scattering functions as low-velocity peaks (LVPs) [21,22]. Even in the case of one oscillating disk, where no periodic orbit is present, a set of discontinuous peaks occurs [21].…”

Section: Introductionmentioning

confidence: 99%

“…These events may lead to a large decrease of the projectile's velocity, which manifest in the scattering functions as low-velocity peaks (LVPs) [21,22]. Even in the case of one oscillating disk, where no periodic orbit is present, a set of discontinuous peaks occurs [21]. In fact, these peaks are related to the intersection of the set of initial conditions with the stable manifold of the LVPs, or gate.…”

Section: Introductionmentioning

confidence: 99%

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Scattering off two oscillating disks: Dilute chaos

et al. 2004

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We investigate the role of the unstable periodic orbits and their manifolds in the dynamics of a time-dependent two-dimensional scattering system. As a prototype we use two oscillating disks on the plane with the oscillation axes forming an angle theta. The phase space of the system is five dimensional and it possesses a variety of families of unstable periodic orbits (UPOs) with intersecting manifolds. We perform numerical experiments to probe the structure of distinct scattering functions, in one and two dimensions, near the location of the UPOs. We find that the corresponding manifolds occur only in a very particular and localized way in the high-dimensional phase space. As a consequence the underlying fractal structure is ubiquitous only in higher-dimensional, e.g., two-dimensional, scattering functions. Both two-dimensional and one-dimensional scattering functions are dominated by seemingly infinite sequences of discontinuities characterized by small values of the magnitude of the projectile's outgoing velocity. These peaks accumulate toward the phase-space locations of the UPOs, with a rate which monotonically depends on the corresponding instability exponent. They represent the intersections of the set of the initial conditions with invariant sets of larger dimensionality embedded in the phase space of the system, which are not directly related with the UPOs. We adopt the term "dilute chaos" to characterize these phenomenological aspects of the scattering dynamics.

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Classical scattering from oscillating targets

Cited by 11 publications

References 24 publications

Escape of particles in a time-dependent potential well

Escape of particles in a time-dependent potential well

Scattering off an oscillating target: Basic mechanisms and their impact on cross sections

Scattering off two oscillating disks: Dilute chaos

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