## Fachbereich Physik

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- Wannier-Stark states of a quantum particle in 2D lattices (2000)
- A simple method of calculating the Wannier-Stark resonances in 2D lattices is suggested. Using this method we calculate the complex Wannier-Stark spectrum for a non-separable 2D potential realized in optical lattices and analyze its general structure. The dependence of the lifetime of Wannier-Stark states on the direction of the static field (relative to the crystallographic axis of the lattice) is briefly discussed.

- Wannier-Stark Ladders in Driven Optical Lattices (2000)
- The paper studies the effect of a weak periodic driving on metastable Wannier-Stark states. The decay rate of the ground Wannier-Stark states as a continuous function of the driving frequency is calculated numerically. The theoretical results are compared with experimental data of Wilkinson et at. [Phys.Rev.Lett.76, 4512 (1996)] obtained for cold sodium atoms in an accelerated optical lattice.

- Wall energy and wall thickness of exchange-coupled rare-earth transition-metal triple layer stacks (1999)
- The room-temperature wall energy sw 54.0310 23 J/m 2 of an exchange-coupled Tb 19.6 Fe 74.7 Co 5.7 /Dy 28.5 Fe 43.2 Co 28.3 double layer stack can be reduced by introducing a soft magnetic intermediate layer in between both layers exhibiting a significantly smaller anisotropy compared to Tb+- FeCo and Dy+- FeCo. sw will decrease linearly with increasing intermediate layer thickness, d IL , until the wall is completely located within the intermediate layer for d IL d w , where d w denotes the wall thickness. Thus, d w can be obtained from the plot sw versus d IL .We determined sw and d w on Gd+- FeCo intermediate layers with different anisotropy behavior ~perpendicular and in-plane easy axis! and compared the results with data obtained from Brillouin light-scattering measurements, where exchange stiffness, A, and uniaxial anisotropy, K u , could be determined. With the knowledge of A and K u , wall energy and thickness were calculated and showed an excellent agreement with the magnetic measurements. A ten times smaller perpendicular anisotropy of Gd 28.1 Fe 71.9 in comparison to Tb+- FeCo and Dy+- FeCo resulted in a much smaller sw 51.1310 23 J/m 2 and d w 524 nm at 300 K. A Gd 34.1 Fe 61.4 Co 4.5 with in-plane anisotropy at room temperature showed a further reduced sw 50.3310 23 J/m 2 and d w 517 nm. The smaller wall energy was a result of a different wall structure compared to perpendicular layers.

- The 'Ermakov-Lewis' invariants for Coupled Linear Oscillators (1998)
- 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.

- Static and dynamic properties of patterned magnetic permalloy films (1997)
- Static magnetic and spin wave properties of square lattices of permalloy micron dots with thicknesses of 500 Å and 1000 Å and with varying dot separations have been investigated. The spin wave frequencies can be well described taking into account the demagnetization factor of each single dot. A magnetic four-fold anisotropy was found for the lattice with dot diameters of 1 micrometer and a dot separation of 0.1 micrometer. The anisotropy is attributed to an anisotropic dipole-dipole interaction between magnetically unsaturated parts of the dots. The anisotropy strength (order of 100000 erg/cm^3 ) decreases with increasing in-plane applied magnetic field.

- Stark Resonances in dc fields from short time propagation of the field-free Hamiltonian (1999)
- A new method for calculating Stark resonances is presented and applied for illustration to the simple case of a one-particle, one-dimensional model Hamiltonian. The method is applicable for weak and strong dc fields. The only need, also for the case of many particles in multi-dimensional space, are either the short time evolution matrix elements or the eigenvalues and Fourier components of the eigenfunctions of the field-free Hamiltonian.

- Spin waves and magnetic anisotropy in ultrathin (111)-oriented cubic films (1998)
- The dispersions of dipolar (Damon-Eshbach modes) and exchange dominated spin waves are calculated for in-plane magnetized thin and ultrathin cubic films with (111) crystal orientation and the results are compared with those obtained for the other principal planes. The properties of these magnetic excitations are examined from the point of view of Brillouin light scattering experiments. Attention is paid to study the spin-wave frequency variation as a function of the magnetization direction in the film plane for different film thicknesses. Interface anisotropies and the bulk magnetocrystalline anisotropy are considered in the calculation. A quantitative comparison between an analytical expression obtained in the limit of small film thickness and wave vector and the full numerical calculation is given.

- Some Remarks on Complex Hamiltonian Systems (2000)
- The analyticity property of the one-dimensional complex Hamiltonian system H(x,p)=H_1(x_1,x_2,p_1,p_2)+iH_2(x_1,x_2,p_1,p_2) with p=p_1+ix_2, x=x_1+ip_2 is exploited to obtain a new class of the corresponding two-dimensional integrable Hamiltonian systems where H_1 acts as a new Hamiltonian and H_2 is a second integral of motion. Also a possible connection between H_1 and H_2 is sought in terms of an auto-B"acklund transformation.

- Semiclassical Quantization of a System with Mixed Regular/Chaotic Dynamics (1998)
- The quasienergy spectrum of a periodically driven quantum system is constructed from classical dynamics by means of the semiclassical initial value representation using coherent states. For the first time, this method is applied to explicitly time dependent systems. For an anharmonic oscillator system with mixed chaotic and regular classical dynamics, the entire quantum spectrum (both regular and chaotic states) is reproduced semiclassically with surprising accuracy. In particular, the method is capable to account for the very small tunneling splittings.