Domain wall motion in ferromagnetic nanowires driven by arbitrary time-dependent fields: An exact result

We address the dynamics of magnetic domain walls in ferromagnetic nanowires under the influence of external time-dependent magnetic fields. We report a new exact spatiotemporal solution of the Landau-Lifshitz-Gilbert equation for the case of soft ferromagnetic wires and nanostructures with uniaxial anisotropy. The solution holds for applied fields with arbitrary strength and time dependence. We further extend this solution to applied fields slowly varying in space and to multiple domain walls.Comment: 3 pages, 1 figur

Loschmidt echo decay from local boundary perturbations

We investigate the sensitivity of the time evolution of semiclassical wave packets in two-dimensional chaotic billiards with respect to local perturbations of their boundaries. For this purpose, we address, analytically and numerically, the time decay of the Loschmidt echo (LE). We find the LE to decay exponentially in time, with the rate equal to the classical escape rate from an open billiard obtained from the original one by removing the perturbation-affected region of its boundary. Finally, we propose a principal scheme for the experimental observation of the LE decay.Comment: Final version; 4 pages, 3 figure

Long-Time Coherence in Echo Spectroscopy with π/2\pi/2--π\pi--π/2\pi/2 Pulse Sequence

Motivated by atom optics experiments, we investigate a new class of fidelity functions describing the reconstruction of quantum states by time-reversal operations as $M_{\mathrm{Da}}(t) = | <\psi | e^{i H_2 t / 2} e^{i H_1 t / 2} e^{-i H_2 t / 2} e^{-i H_1 t / 2} | \psi >|^2$. We show that the decay of $M_{\mathrm{Da}}$ is quartic in time at short times, and that it freezes well above the ergodic value at long times, when $H_2-H_1$ is not too large. The long-time saturation value of $M_{\mathrm{Da}}$ contains easily extractable information on the strength of decoherence in these systems.Comment: 5 pages, 3 figure

Domain wall motion in thin ferromagnetic nanotubes: Analytic results

Dynamics of magnetization domain walls (DWs) in thin ferromagnetic nanotubes subject to weak longitudinal external fields is addressed analytically in the regimes of strong and weak penalization. Exact solutions for the DW profiles and formulas for the DW propagation velocity are derived in both regimes. In particular, the DW speed is shown to depend nonlinearly on the nanotube radius

Huygens-Fresnel-Kirchhoff construction for quantum propagators with application to diffraction in space and time

We address the phenomenon of diffraction of non-relativistic matter waves on openings in absorbing screens. To this end, we expand the full quantum propagator, connecting two points on the opposite sides of the screen, in terms of the free particle propagator and spatio-temporal properties of the opening. Our construction, based on the Huygens-Fresnel principle, describes the quantum phenomena of diffraction in space and diffraction in time, as well as the interplay between the two. We illustrate the method by calculating diffraction patterns for localized wave packets passing through various time-dependent openings in one and two spatial dimensions

Fidelity decay for local perturbations: microwave evidence for oscillating decay exponents

We study fidelity decay in classically chaotic microwave billiards for a local, piston-like boundary perturbation. We experimentally verify a predicted non-monotonic cross-over from the Fermi Golden Rule to the escape-rate regime of the Loschmidt echo decay with increasing local boundary perturbation. In particular, we observe pronounced oscillations of the decay rate as a function of the piston position which quantitatively agree with corresponding theoretical results based on a refined semiclassical approach for local boundary perturbations

Scattering of quantum wave packets by shallow potential islands: a quantum lens

We consider the problem of quantum scattering of a localized wave packet by a weak Gaussian potential in two spatial dimensions. We show that, under certain conditions, this problem bears close analogy with that of focusing (or defocusing) of light rays by a thin optical lens: Quantum interference between straight paths yields the same lens equation as for refracted rays in classical optics

Influence of boundary conditions on quantum escape

It has recently been established that quantum statistics can play a crucial role in quantum escape. Here we demonstrate that boundary conditions can be equally important - moreover, in certain cases, may lead to a complete suppression of the escape. Our results are exact and hold for arbitrarily many particles.Comment: 6 pages, 3 figures, 1 tabl

Long-time saturation of the Loschmidt echo in quantum chaotic billiards

The Loschmidt echo (LE) (or fidelity) quantifies the sensitivity of the time evolution of a quantum system with respect to a perturbation of the Hamiltonian. In a typical chaotic system the LE has been previously argued to exhibit a long-time saturation at a value inversely proportional to the effective size of the Hilbert space of the system. However, until now no quantitative results have been known and, in particular, no explicit expression for the proportionality constant has been proposed. In this paper we perform a quantitative analysis of the phenomenon of the LE saturation and provide the analytical expression for its long-time saturation value for a semiclassical particle in a two-dimensional chaotic billiard. We further perform extensive (fully quantum mechanical) numerical calculations of the LE saturation value and find the numerical results to support the semiclassical theory.Comment: 5 pages, 2 figure