Kaiserslautern - Fachbereich Physik
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We consider N coupled linear oscillators with time-dependent coecients. An exact complex amplitude - real phase decomposition of the oscillatory motion is constructed. This decomposition is further used to derive N exact constants of motion which generalise the so-called Ermakov-Lewis invariant of a single oscillator. In the Floquet problem of periodic oscillator coecients we discuss the existence of periodic complex amplitude functions in terms of existing Floquet solutions.
Quantum Chaos
(1999)
The study of dynamical quantum systems, which are classically chaotic, and the search for quantum manifestations of classical chaos, require large scale numerical computations. Special numerical techniques developed and applied in such studies are discussed: The numerical solution of the time-dependent Schr-odinger equation, the construction of quantum phase space densities, quantum dynamics in phase space, the use of phase space entropies for characterizing localization phenomena, etc. As an illustration, the dynamics of a driven one-dimensional anharmonic oscillator is studied, both classically and quantum mechanically. In addition, spectral properties and chaotic tunneling are addressed.
We have computed ensembles of complete spectra of the staggered Dirac operator using four-dimensional SU(2) gauge fields, both in the quenched approximation and with dynamical fermions. To identify universal features in the Dirac spectrum, we compare the lattice data with predictions from chiral random matrix theory for the distribution of the low-lying eigenvalues. Good agreement is found up to some limiting energy, the so-called Thouless energy, above which random matrix theory no longer applies. We determine the dependence of the Thouless energy on the simulation parameters using the scalar susceptibility and the number variance.
It is shown that nonvacuum pseudoparticles can account for quantum tunneling and metastability. In particular the saddle- point nature of the pseudoparticles is demonstrated, and the evaluation of path-integrals in their neighbourhood. Finally the relation between instantons and bounces is used to derive a result conjectured by Bogomolny and Fateyev.
We report results of the switching properties of Stoner-like magnetic particles subject to short magnetic field pulses, obtained by numerical investigations. We discuss the switching properties as a function of the external field pulse strength and direction, the pulse length and the pulse shape. For field pulses long compared to the ferromagnetic resonance precession time the switching behavior is governed by the magnetic damping term, whereas in the limit of short field pulses the switching properties are dominated by the details of the precession of the magnetic moment. In the latter case, by choosing the right field pulse parameters, the magnetic damping term is of minor importance and ultrafast switching can be achieved. Switching can be obtained in an enlarged angular range of the direction of the applied field compared to the case of long pulses.
An unusual interlayer coupling, recently discovered in layered magnetic systems, is analysed from the experimental and theoretical points of view. This coupling favours the 90° orientation of the magnetization of the adjacent magnetic films. It can be phenomenologically described by a term in the energy expression, which is biquadratic with respect to the magnetizations of the two films. The main experimental findings, as well as the theoretical models, explaining the phenomenon are discussed.
The static and spin wave properties of regular square lattices of magnetic dots of 0.5-2 microm dot diameter and 1-4 microm periodicity patterned in permalloy films have been investigated by Brillouin light scattering. The samples have been structured using x-ray lithography and ion beam etching. The Brillouin light scattering spectra reveal both surface and bulk spin wave modes. The spin wave frequencies can be well described taking into account the demagnetization factor of each single dot. For the samples with smallest dot separation of 0.1 microm a fourfold in-plane magnetic anisotropy with the easy axis directed along the pattern diagonal is observed, indicating anisotropic coupling between the dots.
A computer control for a Sandercock-type multipath tandem Fabry-Perot interferometer is described, which offers many advantages over conventionally used analog control: The range of stability is increased due to active control of the laser light intensity and the mirror dither amplitude. The alignment is fully automated enabling start of a measurement within a minute after start of align, including optionally finding the optimum focus on the sample. The software control enables a programmable series of measurements with control of, e.g., the position and rotation of the sample, the angle of light incidence, the sample temperature, or the strength and direction of an applied magnetic field. Built-in fitting routines allow for a precise determination of frequency positions of excitation peaks combined with increased frequency accuracy due to a correction of a residual nonlinearity of the mirror stage drive.