Biomedical subjects

P Schmelcher

Publications and source records attributed to P Schmelcher.

At least 19 recordsLinked to original sources

PubMed2006

Suppression of quantum scattering in strongly confined systems.

We demonstrate that scattering of particles strongly interacting in three dimensions (3D) can be suppressed at low energies in a quasi-one-dimensional (1D) confinement. The underlying mechanism is the interference of the s- and p-wave scattering contributions with large s- and p-wave 3D scattering lengths being a necessary prerequisite. This low-dimensional quantum scattering effect might be useful in "interacting" quasi-1D ultracold atomic gases, guided atom interferometry, and impurity scattering in strongly confined quantum wire-based electronic devices.

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PubMed2006

Hyperacceleration in a stochastic Fermi-Ulam model.

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.

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PubMed2004

Scattering off two oscillating disks: dilute chaos.

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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PubMed2001

Detecting unstable periodic orbits in chaotic continuous-time dynamical systems.

We extend the recently developed method for detecting unstable periodic points of chaotic time-discrete dynamical systems to find unstable periodic orbits in time-continuous systems, given by a set of ordinary differential equations. This is achieved by the reduction of the continuous flow to a Poincaré map which is then searched for periodic points. The algorithm has global convergence properties and needs no a priori knowledge of the system. It works well for both dissipative and Hamiltonian dynamical systems which is demonstrated by exploring the Lorenz system and the hydrogen atom in a strong magnetic field. The advantages and general features of the approach are discussed in detail.

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PubMed2001

Stability of negatively charged ions moving in a magnetic field.

In a magnetic field the center of mass (c.m.) motion of an atom or molecule couples to the electronic motion. It is demonstrated that this coupling dramatically influences the properties of negative ions. Neglecting c.m. effects the external field gives rise to a series of infinitely many bound states of the ion. Center of mass effects terminate this series and turn bound states into short-lived resonance states. Whether bound states exist at all, their number and properties as well as the lifetimes of the resonance states depend on the neutral system to which an electron is attached, and on the magnetic field.

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PubMed2000

Quantum energy flow in atomic ions moving in magnetic fields

Using a combination of semiclassical and recently developed wave packet propagation techniques we find the quantum self-ionization process of highly excited ions moving in magnetic fields which has its origin in the energy transfer from the center of mass to the electronic motion. It obeys a time scale orders of magnitude larger than the corresponding classical process. Importantly a quantum coherence phenomenon leading to the intermittent behavior of the ionization signal is found and analyzed. Universal properties of the ionization process are established.

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PubMed2000

Theory and applications of the systematic detection of unstable periodic orbits in dynamical systems

A topological approach and understanding to the detection of unstable periodic orbits based on a recently proposed method [Phys. Rev. Lett. 78, 4733 (1997)] is developed. This approach provides a classification of the set of transformations necessary for finding the orbits. Applications to the Ikeda and Henon map are performed, allowing a study of the distributions of Lyapunov exponents for high periods. In particular, the properties of the least unstable orbits up to period 36 are investigated and discussed.

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PubMed2000

Analyzing lyapunov spectra of chaotic dynamical systems

It is shown that the asymptotic spectra of finite-time Lyapunov exponents of a variety of fully chaotic dynamical systems can be understood in terms of a statistical analysis. Using random matrix theory, we derive numerical and in particular, analytical results that provide insights into the overall behavior of the Lyapunov exponents particularly for strange attractors. The corresponding distributions for the unstable periodic orbits are investigated for comparison.

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PubMed1996